# Entrants' Sample Solutions

## E 1.4pre

Stephan Schulz
Technische Universität München, Germany

### Sample solution for SEU140+2

```# Preprocessing time       : 0.012 s
# Problem is unsatisfiable (or provable), constructing proof object
# SZS status Theorem
# SZS output start CNFRefutation.
fof(8, axiom,![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', d3_tarski)).
fof(27, axiom,![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)).
fof(43, axiom,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(51, conjecture,![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(57, negated_conjecture,~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))),inference(assume_negation,[status(cth)],[51])).
fof(66, plain,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),inference(fof_simplification,[status(thm)],[43,theory(equality)])).
fof(101, plain,![X1]:![X2]:((~(subset(X1,X2))|![X3]:(~(in(X3,X1))|in(X3,X2)))&(?[X3]:(in(X3,X1)&~(in(X3,X2)))|subset(X1,X2))),inference(fof_nnf,[status(thm)],[8])).
fof(102, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&(?[X7]:(in(X7,X4)&~(in(X7,X5)))|subset(X4,X5))),inference(variable_rename,[status(thm)],[101])).
fof(103, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(skolemize,[status(esa)],[102])).
fof(104, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(shift_quantors,[status(thm)],[103])).
fof(105, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)|subset(X4,X5))&(~(in(esk3_2(X4,X5),X5))|subset(X4,X5)))),inference(distribute,[status(thm)],[104])).
cnf(108,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)),inference(split_conjunct,[status(thm)],[105])).
fof(170, plain,![X1]:![X2]:(~(disjoint(X1,X2))|disjoint(X2,X1)),inference(fof_nnf,[status(thm)],[27])).
fof(171, plain,![X3]:![X4]:(~(disjoint(X3,X4))|disjoint(X4,X3)),inference(variable_rename,[status(thm)],[170])).
cnf(172,plain,(disjoint(X1,X2)|~disjoint(X2,X1)),inference(split_conjunct,[status(thm)],[171])).
fof(215, plain,![X1]:![X2]:((disjoint(X1,X2)|?[X3]:(in(X3,X1)&in(X3,X2)))&(![X3]:(~(in(X3,X1))|~(in(X3,X2)))|~(disjoint(X1,X2)))),inference(fof_nnf,[status(thm)],[66])).
fof(216, plain,![X4]:![X5]:((disjoint(X4,X5)|?[X6]:(in(X6,X4)&in(X6,X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(variable_rename,[status(thm)],[215])).
fof(217, plain,![X4]:![X5]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(skolemize,[status(esa)],[216])).
fof(218, plain,![X4]:![X5]:![X7]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(shift_quantors,[status(thm)],[217])).
fof(219, plain,![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(distribute,[status(thm)],[218])).
cnf(220,plain,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)),inference(split_conjunct,[status(thm)],[219])).
cnf(221,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)),inference(split_conjunct,[status(thm)],[219])).
cnf(222,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)),inference(split_conjunct,[status(thm)],[219])).
fof(244, negated_conjecture,?[X1]:?[X2]:?[X3]:((subset(X1,X2)&disjoint(X2,X3))&~(disjoint(X1,X3))),inference(fof_nnf,[status(thm)],[57])).
fof(245, negated_conjecture,?[X4]:?[X5]:?[X6]:((subset(X4,X5)&disjoint(X5,X6))&~(disjoint(X4,X6))),inference(variable_rename,[status(thm)],[244])).
fof(246, negated_conjecture,((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~(disjoint(esk11_0,esk13_0))),inference(skolemize,[status(esa)],[245])).
cnf(247,negated_conjecture,(~disjoint(esk11_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(248,negated_conjecture,(disjoint(esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(249,negated_conjecture,(subset(esk11_0,esk12_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(384,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)),inference(spm,[status(thm)],[172,221,theory(equality)])).
cnf(386,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)),inference(spm,[status(thm)],[172,222,theory(equality)])).
cnf(474,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)),inference(spm,[status(thm)],[108,249,theory(equality)])).
cnf(485,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)),inference(spm,[status(thm)],[220,248,theory(equality)])).
cnf(2151,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[247,384,theory(equality)])).
cnf(2160,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)),inference(spm,[status(thm)],[247,386,theory(equality)])).
cnf(2169,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)),inference(spm,[status(thm)],[485,2160,theory(equality)])).
cnf(2622,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[2169,474,theory(equality)])).
cnf(2640,negated_conjecture,(\$false),inference(rw,[status(thm)],[2622,2151,theory(equality)])).
cnf(2641,negated_conjecture,(\$false),inference(cn,[status(thm)],[2640,theory(equality)])).
cnf(2642,negated_conjecture,(\$false),2641,['proof']).
# SZS output end CNFRefutation
```

### Sample solution for NLP042+1

```# Preprocessing time       : 0.010 s
# Problem is satisfiable (or invalid), generating saturation derivation
# SZS status CounterSatisfiable
# SZS output start Saturation.
fof(1, axiom,![X1]:![X2]:(woman(X1,X2)=>female(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax1)).
fof(2, axiom,![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax2)).
fof(3, axiom,![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax3)).
fof(4, axiom,![X1]:![X2]:(organism(X1,X2)=>living(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax4)).
fof(5, axiom,![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax5)).
fof(6, axiom,![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax6)).
fof(7, axiom,![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax7)).
fof(8, axiom,![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax8)).
fof(9, axiom,![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax9)).
fof(10, axiom,![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax10)).
fof(11, axiom,![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax11)).
fof(12, axiom,![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax12)).
fof(13, axiom,![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax13)).
fof(14, axiom,![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax14)).
fof(15, axiom,![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax15)).
fof(16, axiom,![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax16)).
fof(17, axiom,![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax17)).
fof(18, axiom,![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax18)).
fof(19, axiom,![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax19)).
fof(20, axiom,![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax20)).
fof(21, axiom,![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax21)).
fof(22, axiom,![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax22)).
fof(23, axiom,![X1]:![X2]:(object(X1,X2)=>entity(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax23)).
fof(24, axiom,![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax24)).
fof(25, axiom,![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax25)).
fof(26, axiom,![X1]:![X2]:(beverage(X1,X2)=>food(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax26)).
fof(27, axiom,![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax27)).
fof(28, axiom,![X1]:![X2]:(order(X1,X2)=>event(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax28)).
fof(29, axiom,![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax29)).
fof(30, axiom,![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax30)).
fof(31, axiom,![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax31)).
fof(32, axiom,![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax32)).
fof(33, axiom,![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax33)).
fof(34, axiom,![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax34)).
fof(35, axiom,![X1]:![X2]:(act(X1,X2)=>event(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax35)).
fof(36, axiom,![X1]:![X2]:(order(X1,X2)=>act(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax36)).
fof(37, axiom,![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax37)).
fof(38, axiom,![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax38)).
fof(39, axiom,![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax39)).
fof(40, axiom,![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax40)).
fof(41, axiom,![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax41)).
fof(42, axiom,![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax42)).
fof(43, axiom,![X1]:![X2]:![X3]:(((entity(X1,X2)&forename(X1,X3))&of(X1,X3,X2))=>~(?[X4]:((forename(X1,X4)&~(X4=X3))&of(X1,X4,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax43)).
fof(44, axiom,![X1]:![X2]:![X3]:![X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>~(X3=X4)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax44)).
fof(45, conjecture,~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', co1)).
fof(46, negated_conjecture,~(~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))))),inference(assume_negation,[status(cth)],[45])).
fof(47, plain,![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2))),inference(fof_simplification,[status(thm)],[37,theory(equality)])).
fof(48, plain,![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))),inference(fof_simplification,[status(thm)],[38,theory(equality)])).
fof(49, plain,![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2))),inference(fof_simplification,[status(thm)],[39,theory(equality)])).
fof(50, plain,![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2))),inference(fof_simplification,[status(thm)],[40,theory(equality)])).
fof(51, plain,![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2))),inference(fof_simplification,[status(thm)],[41,theory(equality)])).
fof(52, plain,![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2))),inference(fof_simplification,[status(thm)],[42,theory(equality)])).
fof(53, plain,![X1]:![X2]:(~(woman(X1,X2))|female(X1,X2)),inference(fof_nnf,[status(thm)],[1])).
fof(54, plain,![X3]:![X4]:(~(woman(X3,X4))|female(X3,X4)),inference(variable_rename,[status(thm)],[53])).
cnf(55,plain,(female(X1,X2)|~woman(X1,X2)),inference(split_conjunct,[status(thm)],[54])).
fof(56, plain,![X1]:![X2]:(~(human_person(X1,X2))|animate(X1,X2)),inference(fof_nnf,[status(thm)],[2])).
fof(57, plain,![X3]:![X4]:(~(human_person(X3,X4))|animate(X3,X4)),inference(variable_rename,[status(thm)],[56])).
cnf(58,plain,(animate(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[57])).
fof(59, plain,![X1]:![X2]:(~(human_person(X1,X2))|human(X1,X2)),inference(fof_nnf,[status(thm)],[3])).
fof(60, plain,![X3]:![X4]:(~(human_person(X3,X4))|human(X3,X4)),inference(variable_rename,[status(thm)],[59])).
cnf(61,plain,(human(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[60])).
fof(62, plain,![X1]:![X2]:(~(organism(X1,X2))|living(X1,X2)),inference(fof_nnf,[status(thm)],[4])).
fof(63, plain,![X3]:![X4]:(~(organism(X3,X4))|living(X3,X4)),inference(variable_rename,[status(thm)],[62])).
cnf(64,plain,(living(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[63])).
fof(65, plain,![X1]:![X2]:(~(organism(X1,X2))|impartial(X1,X2)),inference(fof_nnf,[status(thm)],[5])).
fof(66, plain,![X3]:![X4]:(~(organism(X3,X4))|impartial(X3,X4)),inference(variable_rename,[status(thm)],[65])).
cnf(67,plain,(impartial(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[66])).
fof(68, plain,![X1]:![X2]:(~(organism(X1,X2))|entity(X1,X2)),inference(fof_nnf,[status(thm)],[6])).
fof(69, plain,![X3]:![X4]:(~(organism(X3,X4))|entity(X3,X4)),inference(variable_rename,[status(thm)],[68])).
cnf(70,plain,(entity(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[69])).
fof(71, plain,![X1]:![X2]:(~(human_person(X1,X2))|organism(X1,X2)),inference(fof_nnf,[status(thm)],[7])).
fof(72, plain,![X3]:![X4]:(~(human_person(X3,X4))|organism(X3,X4)),inference(variable_rename,[status(thm)],[71])).
cnf(73,plain,(organism(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[72])).
fof(74, plain,![X1]:![X2]:(~(woman(X1,X2))|human_person(X1,X2)),inference(fof_nnf,[status(thm)],[8])).
fof(75, plain,![X3]:![X4]:(~(woman(X3,X4))|human_person(X3,X4)),inference(variable_rename,[status(thm)],[74])).
cnf(76,plain,(human_person(X1,X2)|~woman(X1,X2)),inference(split_conjunct,[status(thm)],[75])).
fof(77, plain,![X1]:![X2]:(~(mia_forename(X1,X2))|forename(X1,X2)),inference(fof_nnf,[status(thm)],[9])).
fof(78, plain,![X3]:![X4]:(~(mia_forename(X3,X4))|forename(X3,X4)),inference(variable_rename,[status(thm)],[77])).
cnf(79,plain,(forename(X1,X2)|~mia_forename(X1,X2)),inference(split_conjunct,[status(thm)],[78])).
fof(80, plain,![X1]:![X2]:(~(abstraction(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[10])).
fof(81, plain,![X3]:![X4]:(~(abstraction(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[80])).
cnf(82,plain,(unisex(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[81])).
fof(83, plain,![X1]:![X2]:(~(abstraction(X1,X2))|general(X1,X2)),inference(fof_nnf,[status(thm)],[11])).
fof(84, plain,![X3]:![X4]:(~(abstraction(X3,X4))|general(X3,X4)),inference(variable_rename,[status(thm)],[83])).
cnf(85,plain,(general(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[84])).
fof(86, plain,![X1]:![X2]:(~(abstraction(X1,X2))|nonhuman(X1,X2)),inference(fof_nnf,[status(thm)],[12])).
fof(87, plain,![X3]:![X4]:(~(abstraction(X3,X4))|nonhuman(X3,X4)),inference(variable_rename,[status(thm)],[86])).
cnf(88,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[87])).
fof(89, plain,![X1]:![X2]:(~(abstraction(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[13])).
fof(90, plain,![X3]:![X4]:(~(abstraction(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[89])).
cnf(91,plain,(thing(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[90])).
fof(92, plain,![X1]:![X2]:(~(relation(X1,X2))|abstraction(X1,X2)),inference(fof_nnf,[status(thm)],[14])).
fof(93, plain,![X3]:![X4]:(~(relation(X3,X4))|abstraction(X3,X4)),inference(variable_rename,[status(thm)],[92])).
cnf(94,plain,(abstraction(X1,X2)|~relation(X1,X2)),inference(split_conjunct,[status(thm)],[93])).
fof(95, plain,![X1]:![X2]:(~(relname(X1,X2))|relation(X1,X2)),inference(fof_nnf,[status(thm)],[15])).
fof(96, plain,![X3]:![X4]:(~(relname(X3,X4))|relation(X3,X4)),inference(variable_rename,[status(thm)],[95])).
cnf(97,plain,(relation(X1,X2)|~relname(X1,X2)),inference(split_conjunct,[status(thm)],[96])).
fof(98, plain,![X1]:![X2]:(~(forename(X1,X2))|relname(X1,X2)),inference(fof_nnf,[status(thm)],[16])).
fof(99, plain,![X3]:![X4]:(~(forename(X3,X4))|relname(X3,X4)),inference(variable_rename,[status(thm)],[98])).
cnf(100,plain,(relname(X1,X2)|~forename(X1,X2)),inference(split_conjunct,[status(thm)],[99])).
fof(101, plain,![X1]:![X2]:(~(object(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[17])).
fof(102, plain,![X3]:![X4]:(~(object(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[101])).
cnf(103,plain,(unisex(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[102])).
fof(104, plain,![X1]:![X2]:(~(object(X1,X2))|impartial(X1,X2)),inference(fof_nnf,[status(thm)],[18])).
fof(105, plain,![X3]:![X4]:(~(object(X3,X4))|impartial(X3,X4)),inference(variable_rename,[status(thm)],[104])).
cnf(106,plain,(impartial(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[105])).
fof(107, plain,![X1]:![X2]:(~(object(X1,X2))|nonliving(X1,X2)),inference(fof_nnf,[status(thm)],[19])).
fof(108, plain,![X3]:![X4]:(~(object(X3,X4))|nonliving(X3,X4)),inference(variable_rename,[status(thm)],[107])).
cnf(109,plain,(nonliving(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[108])).
fof(110, plain,![X1]:![X2]:(~(entity(X1,X2))|existent(X1,X2)),inference(fof_nnf,[status(thm)],[20])).
fof(111, plain,![X3]:![X4]:(~(entity(X3,X4))|existent(X3,X4)),inference(variable_rename,[status(thm)],[110])).
cnf(112,plain,(existent(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[111])).
fof(113, plain,![X1]:![X2]:(~(entity(X1,X2))|specific(X1,X2)),inference(fof_nnf,[status(thm)],[21])).
fof(114, plain,![X3]:![X4]:(~(entity(X3,X4))|specific(X3,X4)),inference(variable_rename,[status(thm)],[113])).
cnf(115,plain,(specific(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[114])).
fof(116, plain,![X1]:![X2]:(~(entity(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[22])).
fof(117, plain,![X3]:![X4]:(~(entity(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[116])).
cnf(118,plain,(thing(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[117])).
fof(119, plain,![X1]:![X2]:(~(object(X1,X2))|entity(X1,X2)),inference(fof_nnf,[status(thm)],[23])).
fof(120, plain,![X3]:![X4]:(~(object(X3,X4))|entity(X3,X4)),inference(variable_rename,[status(thm)],[119])).
cnf(121,plain,(entity(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[120])).
fof(122, plain,![X1]:![X2]:(~(substance_matter(X1,X2))|object(X1,X2)),inference(fof_nnf,[status(thm)],[24])).
fof(123, plain,![X3]:![X4]:(~(substance_matter(X3,X4))|object(X3,X4)),inference(variable_rename,[status(thm)],[122])).
cnf(124,plain,(object(X1,X2)|~substance_matter(X1,X2)),inference(split_conjunct,[status(thm)],[123])).
fof(125, plain,![X1]:![X2]:(~(food(X1,X2))|substance_matter(X1,X2)),inference(fof_nnf,[status(thm)],[25])).
fof(126, plain,![X3]:![X4]:(~(food(X3,X4))|substance_matter(X3,X4)),inference(variable_rename,[status(thm)],[125])).
cnf(127,plain,(substance_matter(X1,X2)|~food(X1,X2)),inference(split_conjunct,[status(thm)],[126])).
fof(128, plain,![X1]:![X2]:(~(beverage(X1,X2))|food(X1,X2)),inference(fof_nnf,[status(thm)],[26])).
fof(129, plain,![X3]:![X4]:(~(beverage(X3,X4))|food(X3,X4)),inference(variable_rename,[status(thm)],[128])).
cnf(130,plain,(food(X1,X2)|~beverage(X1,X2)),inference(split_conjunct,[status(thm)],[129])).
fof(131, plain,![X1]:![X2]:(~(shake_beverage(X1,X2))|beverage(X1,X2)),inference(fof_nnf,[status(thm)],[27])).
fof(132, plain,![X3]:![X4]:(~(shake_beverage(X3,X4))|beverage(X3,X4)),inference(variable_rename,[status(thm)],[131])).
cnf(133,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)),inference(split_conjunct,[status(thm)],[132])).
fof(134, plain,![X1]:![X2]:(~(order(X1,X2))|event(X1,X2)),inference(fof_nnf,[status(thm)],[28])).
fof(135, plain,![X3]:![X4]:(~(order(X3,X4))|event(X3,X4)),inference(variable_rename,[status(thm)],[134])).
cnf(136,plain,(event(X1,X2)|~order(X1,X2)),inference(split_conjunct,[status(thm)],[135])).
fof(137, plain,![X1]:![X2]:(~(eventuality(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[29])).
fof(138, plain,![X3]:![X4]:(~(eventuality(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[137])).
cnf(139,plain,(unisex(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[138])).
fof(140, plain,![X1]:![X2]:(~(eventuality(X1,X2))|nonexistent(X1,X2)),inference(fof_nnf,[status(thm)],[30])).
fof(141, plain,![X3]:![X4]:(~(eventuality(X3,X4))|nonexistent(X3,X4)),inference(variable_rename,[status(thm)],[140])).
cnf(142,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[141])).
fof(143, plain,![X1]:![X2]:(~(eventuality(X1,X2))|specific(X1,X2)),inference(fof_nnf,[status(thm)],[31])).
fof(144, plain,![X3]:![X4]:(~(eventuality(X3,X4))|specific(X3,X4)),inference(variable_rename,[status(thm)],[143])).
cnf(145,plain,(specific(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[144])).
fof(146, plain,![X1]:![X2]:(~(thing(X1,X2))|singleton(X1,X2)),inference(fof_nnf,[status(thm)],[32])).
fof(147, plain,![X3]:![X4]:(~(thing(X3,X4))|singleton(X3,X4)),inference(variable_rename,[status(thm)],[146])).
cnf(148,plain,(singleton(X1,X2)|~thing(X1,X2)),inference(split_conjunct,[status(thm)],[147])).
fof(149, plain,![X1]:![X2]:(~(eventuality(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[33])).
fof(150, plain,![X3]:![X4]:(~(eventuality(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[149])).
cnf(151,plain,(thing(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[150])).
fof(152, plain,![X1]:![X2]:(~(event(X1,X2))|eventuality(X1,X2)),inference(fof_nnf,[status(thm)],[34])).
fof(153, plain,![X3]:![X4]:(~(event(X3,X4))|eventuality(X3,X4)),inference(variable_rename,[status(thm)],[152])).
cnf(154,plain,(eventuality(X1,X2)|~event(X1,X2)),inference(split_conjunct,[status(thm)],[153])).
fof(155, plain,![X1]:![X2]:(~(act(X1,X2))|event(X1,X2)),inference(fof_nnf,[status(thm)],[35])).
fof(156, plain,![X3]:![X4]:(~(act(X3,X4))|event(X3,X4)),inference(variable_rename,[status(thm)],[155])).
cnf(157,plain,(event(X1,X2)|~act(X1,X2)),inference(split_conjunct,[status(thm)],[156])).
fof(158, plain,![X1]:![X2]:(~(order(X1,X2))|act(X1,X2)),inference(fof_nnf,[status(thm)],[36])).
fof(159, plain,![X3]:![X4]:(~(order(X3,X4))|act(X3,X4)),inference(variable_rename,[status(thm)],[158])).
cnf(160,plain,(act(X1,X2)|~order(X1,X2)),inference(split_conjunct,[status(thm)],[159])).
fof(161, plain,![X1]:![X2]:(~(animate(X1,X2))|~(nonliving(X1,X2))),inference(fof_nnf,[status(thm)],[47])).
fof(162, plain,![X3]:![X4]:(~(animate(X3,X4))|~(nonliving(X3,X4))),inference(variable_rename,[status(thm)],[161])).
cnf(163,plain,(~nonliving(X1,X2)|~animate(X1,X2)),inference(split_conjunct,[status(thm)],[162])).
fof(164, plain,![X1]:![X2]:(~(existent(X1,X2))|~(nonexistent(X1,X2))),inference(fof_nnf,[status(thm)],[48])).
fof(165, plain,![X3]:![X4]:(~(existent(X3,X4))|~(nonexistent(X3,X4))),inference(variable_rename,[status(thm)],[164])).
cnf(166,plain,(~nonexistent(X1,X2)|~existent(X1,X2)),inference(split_conjunct,[status(thm)],[165])).
fof(167, plain,![X1]:![X2]:(~(nonhuman(X1,X2))|~(human(X1,X2))),inference(fof_nnf,[status(thm)],[49])).
fof(168, plain,![X3]:![X4]:(~(nonhuman(X3,X4))|~(human(X3,X4))),inference(variable_rename,[status(thm)],[167])).
cnf(169,plain,(~human(X1,X2)|~nonhuman(X1,X2)),inference(split_conjunct,[status(thm)],[168])).
fof(170, plain,![X1]:![X2]:(~(nonliving(X1,X2))|~(living(X1,X2))),inference(fof_nnf,[status(thm)],[50])).
fof(171, plain,![X3]:![X4]:(~(nonliving(X3,X4))|~(living(X3,X4))),inference(variable_rename,[status(thm)],[170])).
cnf(172,plain,(~living(X1,X2)|~nonliving(X1,X2)),inference(split_conjunct,[status(thm)],[171])).
fof(173, plain,![X1]:![X2]:(~(specific(X1,X2))|~(general(X1,X2))),inference(fof_nnf,[status(thm)],[51])).
fof(174, plain,![X3]:![X4]:(~(specific(X3,X4))|~(general(X3,X4))),inference(variable_rename,[status(thm)],[173])).
cnf(175,plain,(~general(X1,X2)|~specific(X1,X2)),inference(split_conjunct,[status(thm)],[174])).
fof(176, plain,![X1]:![X2]:(~(unisex(X1,X2))|~(female(X1,X2))),inference(fof_nnf,[status(thm)],[52])).
fof(177, plain,![X3]:![X4]:(~(unisex(X3,X4))|~(female(X3,X4))),inference(variable_rename,[status(thm)],[176])).
cnf(178,plain,(~female(X1,X2)|~unisex(X1,X2)),inference(split_conjunct,[status(thm)],[177])).
fof(179, plain,![X1]:![X2]:![X3]:(((~(entity(X1,X2))|~(forename(X1,X3)))|~(of(X1,X3,X2)))|![X4]:((~(forename(X1,X4))|X4=X3)|~(of(X1,X4,X2)))),inference(fof_nnf,[status(thm)],[43])).
fof(180, plain,![X5]:![X6]:![X7]:(((~(entity(X5,X6))|~(forename(X5,X7)))|~(of(X5,X7,X6)))|![X8]:((~(forename(X5,X8))|X8=X7)|~(of(X5,X8,X6)))),inference(variable_rename,[status(thm)],[179])).
fof(181, plain,![X5]:![X6]:![X7]:![X8]:(((~(entity(X5,X6))|~(forename(X5,X7)))|~(of(X5,X7,X6)))|((~(forename(X5,X8))|X8=X7)|~(of(X5,X8,X6)))),inference(shift_quantors,[status(thm)],[180])).
cnf(182,plain,(X2=X4|~of(X1,X2,X3)|~forename(X1,X2)|~of(X1,X4,X3)|~forename(X1,X4)|~entity(X1,X3)),inference(split_conjunct,[status(thm)],[181])).
fof(183, plain,![X1]:![X2]:![X3]:![X4]:(((~(nonreflexive(X1,X2))|~(agent(X1,X2,X3)))|~(patient(X1,X2,X4)))|~(X3=X4)),inference(fof_nnf,[status(thm)],[44])).
fof(184, plain,![X5]:![X6]:![X7]:![X8]:(((~(nonreflexive(X5,X6))|~(agent(X5,X6,X7)))|~(patient(X5,X6,X8)))|~(X7=X8)),inference(variable_rename,[status(thm)],[183])).
cnf(185,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)),inference(split_conjunct,[status(thm)],[184])).
fof(186, negated_conjecture,?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))),inference(fof_nnf,[status(thm)],[46])).
fof(187, negated_conjecture,?[X6]:(actual_world(X6)&?[X7]:?[X8]:?[X9]:?[X10]:((((((((((of(X6,X8,X7)&woman(X6,X7))&mia_forename(X6,X8))&forename(X6,X8))&shake_beverage(X6,X9))&event(X6,X10))&agent(X6,X10,X7))&patient(X6,X10,X9))&past(X6,X10))&nonreflexive(X6,X10))&order(X6,X10))),inference(variable_rename,[status(thm)],[186])).
fof(188, negated_conjecture,(actual_world(esk1_0)&((((((((((of(esk1_0,esk3_0,esk2_0)&woman(esk1_0,esk2_0))&mia_forename(esk1_0,esk3_0))&forename(esk1_0,esk3_0))&shake_beverage(esk1_0,esk4_0))&event(esk1_0,esk5_0))&agent(esk1_0,esk5_0,esk2_0))&patient(esk1_0,esk5_0,esk4_0))&past(esk1_0,esk5_0))&nonreflexive(esk1_0,esk5_0))&order(esk1_0,esk5_0))),inference(skolemize,[status(esa)],[187])).
cnf(189,negated_conjecture,(order(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(190,negated_conjecture,(nonreflexive(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(191,negated_conjecture,(past(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(192,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(193,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(194,negated_conjecture,(event(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(195,negated_conjecture,(shake_beverage(esk1_0,esk4_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(196,negated_conjecture,(forename(esk1_0,esk3_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(197,negated_conjecture,(mia_forename(esk1_0,esk3_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(198,negated_conjecture,(woman(esk1_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(199,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(200,negated_conjecture,(actual_world(esk1_0)),inference(split_conjunct,[status(thm)],[188])).
cnf(201,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)),inference(er,[status(thm)],[185,theory(equality)])).
cnf(206,negated_conjecture,(human_person(esk1_0,esk2_0)),inference(spm,[status(thm)],[76,198,theory(equality)])).
cnf(207,negated_conjecture,(eventuality(esk1_0,esk5_0)),inference(spm,[status(thm)],[154,194,theory(equality)])).
cnf(209,plain,(relation(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[97,100,theory(equality)])).
cnf(210,plain,(food(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[130,133,theory(equality)])).
cnf(211,plain,(~unisex(X1,X2)|~woman(X1,X2)),inference(spm,[status(thm)],[178,55,theory(equality)])).
cnf(212,plain,(entity(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[70,73,theory(equality)])).
cnf(213,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)|~nonreflexive(esk1_0,esk5_0)),inference(spm,[status(thm)],[201,192,theory(equality)])).
cnf(214,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)|\$false),inference(rw,[status(thm)],[213,190,theory(equality)])).
cnf(215,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)),inference(cn,[status(thm)],[214,theory(equality)])).
cnf(216,plain,(~existent(X1,X2)|~eventuality(X1,X2)),inference(spm,[status(thm)],[166,142,theory(equality)])).
cnf(217,plain,(~nonliving(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[163,58,theory(equality)])).
cnf(218,plain,(~human(X1,X2)|~abstraction(X1,X2)),inference(spm,[status(thm)],[169,88,theory(equality)])).
cnf(219,plain,(~specific(X1,X2)|~abstraction(X1,X2)),inference(spm,[status(thm)],[175,85,theory(equality)])).
cnf(220,plain,(~nonliving(X1,X2)|~organism(X1,X2)),inference(spm,[status(thm)],[172,64,theory(equality)])).
cnf(221,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,esk3_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(spm,[status(thm)],[182,199,theory(equality)])).
cnf(222,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|\$false|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(rw,[status(thm)],[221,196,theory(equality)])).
cnf(223,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(cn,[status(thm)],[222,theory(equality)])).
cnf(224,negated_conjecture,(~unisex(esk1_0,esk2_0)),inference(spm,[status(thm)],[211,198,theory(equality)])).
cnf(225,negated_conjecture,(~abstraction(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,82,theory(equality)])).
cnf(226,negated_conjecture,(~object(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,103,theory(equality)])).
cnf(227,negated_conjecture,(~eventuality(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,139,theory(equality)])).
cnf(228,plain,(abstraction(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[94,209,theory(equality)])).
cnf(229,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[127,210,theory(equality)])).
cnf(230,negated_conjecture,(~forename(esk1_0,esk2_0)),inference(spm,[status(thm)],[225,228,theory(equality)])).
cnf(231,negated_conjecture,(entity(esk1_0,esk2_0)),inference(spm,[status(thm)],[212,206,theory(equality)])).
cnf(232,plain,(~eventuality(X1,X2)|~entity(X1,X2)),inference(spm,[status(thm)],[216,112,theory(equality)])).
cnf(233,negated_conjecture,(~entity(esk1_0,esk5_0)),inference(spm,[status(thm)],[232,207,theory(equality)])).
cnf(234,plain,(object(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[124,229,theory(equality)])).
cnf(235,negated_conjecture,(object(esk1_0,esk4_0)),inference(spm,[status(thm)],[234,195,theory(equality)])).
cnf(236,negated_conjecture,(entity(esk1_0,esk4_0)),inference(spm,[status(thm)],[121,235,theory(equality)])).
cnf(237,plain,(~human_person(X1,X2)|~object(X1,X2)),inference(spm,[status(thm)],[217,109,theory(equality)])).
cnf(239,plain,(~abstraction(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[218,61,theory(equality)])).
cnf(241,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|\$false),inference(rw,[status(thm)],[223,231,theory(equality)])).
cnf(242,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)),inference(cn,[status(thm)],[241,theory(equality)])).
cnf(243,plain,(~abstraction(X1,X2)|~entity(X1,X2)),inference(spm,[status(thm)],[219,115,theory(equality)])).
cnf(244,plain,(~abstraction(X1,X2)|~eventuality(X1,X2)),inference(spm,[status(thm)],[219,145,theory(equality)])).
cnf(245,plain,(~organism(X1,X2)|~object(X1,X2)),inference(spm,[status(thm)],[220,109,theory(equality)])).
cnf(246,negated_conjecture,(~abstraction(esk1_0,esk5_0)),inference(spm,[status(thm)],[244,207,theory(equality)])).
cnf(247,negated_conjecture,(~forename(esk1_0,esk5_0)),inference(spm,[status(thm)],[246,228,theory(equality)])).
cnf(249,plain,(~entity(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[243,228,theory(equality)])).
cnf(250,negated_conjecture,(~entity(esk1_0,esk3_0)),inference(spm,[status(thm)],[249,196,theory(equality)])).
cnf(251,negated_conjecture,(actual_world(esk1_0)),200,['final']).
cnf(252,negated_conjecture,(woman(esk1_0,esk2_0)),198,['final']).
cnf(253,negated_conjecture,(mia_forename(esk1_0,esk3_0)),197,['final']).
cnf(254,negated_conjecture,(forename(esk1_0,esk3_0)),196,['final']).
cnf(255,negated_conjecture,(shake_beverage(esk1_0,esk4_0)),195,['final']).
cnf(256,negated_conjecture,(order(esk1_0,esk5_0)),189,['final']).
cnf(257,negated_conjecture,(event(esk1_0,esk5_0)),194,['final']).
cnf(258,negated_conjecture,(nonreflexive(esk1_0,esk5_0)),190,['final']).
cnf(259,negated_conjecture,(past(esk1_0,esk5_0)),191,['final']).
cnf(260,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)),199,['final']).
cnf(261,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)),193,['final']).
cnf(262,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)),192,['final']).
cnf(263,negated_conjecture,(human_person(esk1_0,esk2_0)),206,['final']).
cnf(264,negated_conjecture,(eventuality(esk1_0,esk5_0)),207,['final']).
cnf(265,negated_conjecture,(entity(esk1_0,esk2_0)),231,['final']).
cnf(266,negated_conjecture,(object(esk1_0,esk4_0)),235,['final']).
cnf(267,negated_conjecture,(entity(esk1_0,esk4_0)),236,['final']).
cnf(268,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)),215,['final']).
cnf(269,negated_conjecture,(~unisex(esk1_0,esk2_0)),224,['final']).
cnf(270,negated_conjecture,(~eventuality(esk1_0,esk2_0)),227,['final']).
cnf(271,negated_conjecture,(~object(esk1_0,esk2_0)),226,['final']).
cnf(272,negated_conjecture,(~abstraction(esk1_0,esk2_0)),225,['final']).
cnf(273,negated_conjecture,(~forename(esk1_0,esk2_0)),230,['final']).
cnf(274,negated_conjecture,(~entity(esk1_0,esk5_0)),233,['final']).
cnf(275,negated_conjecture,(~abstraction(esk1_0,esk5_0)),246,['final']).
cnf(276,negated_conjecture,(~forename(esk1_0,esk5_0)),247,['final']).
cnf(277,negated_conjecture,(~entity(esk1_0,esk3_0)),250,['final']).
cnf(278,plain,(forename(X1,X2)|~mia_forename(X1,X2)),79,['final']).
cnf(279,plain,(event(X1,X2)|~order(X1,X2)),136,['final']).
cnf(280,plain,(human_person(X1,X2)|~woman(X1,X2)),76,['final']).
cnf(281,plain,(eventuality(X1,X2)|~event(X1,X2)),154,['final']).
cnf(282,plain,(female(X1,X2)|~woman(X1,X2)),55,['final']).
cnf(283,plain,(relname(X1,X2)|~forename(X1,X2)),100,['final']).
cnf(284,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)),133,['final']).
cnf(285,plain,(event(X1,X2)|~act(X1,X2)),157,['final']).
cnf(286,plain,(act(X1,X2)|~order(X1,X2)),160,['final']).
cnf(287,plain,(animate(X1,X2)|~human_person(X1,X2)),58,['final']).
cnf(288,plain,(human(X1,X2)|~human_person(X1,X2)),61,['final']).
cnf(289,plain,(organism(X1,X2)|~human_person(X1,X2)),73,['final']).
cnf(290,plain,(relation(X1,X2)|~relname(X1,X2)),97,['final']).
cnf(291,plain,(food(X1,X2)|~beverage(X1,X2)),130,['final']).
cnf(292,plain,(~unisex(X1,X2)|~female(X1,X2)),178,['final']).
cnf(293,plain,(entity(X1,X2)|~organism(X1,X2)),70,['final']).
cnf(294,plain,(living(X1,X2)|~organism(X1,X2)),64,['final']).
cnf(295,plain,(impartial(X1,X2)|~organism(X1,X2)),67,['final']).
cnf(296,plain,(impartial(X1,X2)|~object(X1,X2)),106,['final']).
cnf(297,plain,(entity(X1,X2)|~object(X1,X2)),121,['final']).
cnf(298,plain,(abstraction(X1,X2)|~relation(X1,X2)),94,['final']).
cnf(299,plain,(unisex(X1,X2)|~eventuality(X1,X2)),139,['final']).
cnf(300,plain,(thing(X1,X2)|~entity(X1,X2)),118,['final']).
cnf(301,plain,(thing(X1,X2)|~eventuality(X1,X2)),151,['final']).
cnf(302,plain,(existent(X1,X2)|~entity(X1,X2)),112,['final']).
cnf(303,plain,(unisex(X1,X2)|~abstraction(X1,X2)),82,['final']).
cnf(304,plain,(unisex(X1,X2)|~object(X1,X2)),103,['final']).
cnf(305,plain,(specific(X1,X2)|~entity(X1,X2)),115,['final']).
cnf(306,plain,(general(X1,X2)|~abstraction(X1,X2)),85,['final']).
cnf(307,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)),88,['final']).
cnf(308,plain,(specific(X1,X2)|~eventuality(X1,X2)),145,['final']).
cnf(309,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)),142,['final']).
cnf(310,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)),201,['final']).
cnf(311,plain,(~nonexistent(X1,X2)|~existent(X1,X2)),166,['final']).
cnf(312,plain,(thing(X1,X2)|~abstraction(X1,X2)),91,['final']).
cnf(313,plain,(object(X1,X2)|~substance_matter(X1,X2)),124,['final']).
cnf(314,plain,(nonliving(X1,X2)|~object(X1,X2)),109,['final']).
cnf(315,plain,(substance_matter(X1,X2)|~food(X1,X2)),127,['final']).
cnf(316,plain,(singleton(X1,X2)|~thing(X1,X2)),148,['final']).
cnf(317,plain,(~nonliving(X1,X2)|~animate(X1,X2)),163,['final']).
cnf(318,plain,(~nonhuman(X1,X2)|~human(X1,X2)),169,['final']).
cnf(319,plain,(~specific(X1,X2)|~general(X1,X2)),175,['final']).
cnf(320,plain,(~nonliving(X1,X2)|~living(X1,X2)),172,['final']).
cnf(321,plain,(X1=X2|~of(X3,X2,X4)|~of(X3,X1,X4)|~forename(X3,X2)|~forename(X3,X1)|~entity(X3,X4)),182,['final']).
cnf(322,plain,(~unisex(X1,X2)|~woman(X1,X2)),211,['final']).
cnf(323,plain,(relation(X1,X2)|~forename(X1,X2)),209,['final']).
cnf(324,plain,(food(X1,X2)|~shake_beverage(X1,X2)),210,['final']).
cnf(325,plain,(abstraction(X1,X2)|~forename(X1,X2)),228,['final']).
cnf(326,plain,(entity(X1,X2)|~human_person(X1,X2)),212,['final']).
cnf(327,plain,(~eventuality(X1,X2)|~existent(X1,X2)),216,['final']).
cnf(328,plain,(~eventuality(X1,X2)|~entity(X1,X2)),232,['final']).
cnf(329,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)),229,['final']).
cnf(330,plain,(object(X1,X2)|~shake_beverage(X1,X2)),234,['final']).
cnf(331,plain,(~nonliving(X1,X2)|~human_person(X1,X2)),217,['final']).
cnf(332,plain,(~object(X1,X2)|~human_person(X1,X2)),237,['final']).
cnf(333,plain,(~abstraction(X1,X2)|~human(X1,X2)),218,['final']).
cnf(334,plain,(~abstraction(X1,X2)|~human_person(X1,X2)),239,['final']).
cnf(335,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)),242,['final']).
cnf(336,plain,(~specific(X1,X2)|~abstraction(X1,X2)),219,['final']).
cnf(337,plain,(~nonliving(X1,X2)|~organism(X1,X2)),220,['final']).
cnf(338,plain,(~eventuality(X1,X2)|~abstraction(X1,X2)),244,['final']).
cnf(339,plain,(~object(X1,X2)|~organism(X1,X2)),245,['final']).
cnf(340,plain,(~abstraction(X1,X2)|~entity(X1,X2)),243,['final']).
cnf(341,plain,(~forename(X1,X2)|~entity(X1,X2)),249,['final']).
# SZS output end Saturation.
```

### Sample solution for SWV017+1

```# Preprocessing time       : 0.010 s
# Problem is satisfiable (or invalid), generating saturation derivation
# SZS status Satisfiable
# SZS output start Saturation.
fof(1, axiom,a_holds(key(at,t)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)).
fof(2, axiom,party_of_protocol(a),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_is_party_of_protocol)).
fof(3, axiom,message(sent(a,b,pair(a,an_a_nonce))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)).
fof(4, axiom,a_stored(pair(b,an_a_nonce)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_stored_message_i)).
fof(6, axiom,b_holds(key(bt,t)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)).
fof(7, axiom,party_of_protocol(b),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_is_party_of_protocol)).
fof(8, axiom,fresh_to_b(an_a_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)).
fof(9, axiom,![X1]:![X2]:((message(sent(X1,b,pair(X1,X2)))&fresh_to_b(X2))=>(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)).
fof(10, axiom,![X2]:![X4]:![X5]:(((message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))&a_key(X2))&b_stored(pair(X4,X5)))=>b_holds(key(X2,X4))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)).
fof(11, axiom,t_holds(key(at,a)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)).
fof(12, axiom,t_holds(key(bt,b)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)).
fof(13, axiom,party_of_protocol(t),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_is_party_of_protocol)).
fof(15, axiom,![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_can_record)).
fof(16, axiom,![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)).
fof(17, axiom,![X1]:![X2]:![X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_triples)).
fof(19, axiom,![X1]:![X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_pairs)).
fof(20, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_triples)).
fof(22, axiom,![X1]:![X2]:![X3]:(((intruder_message(encrypt(X1,X2))&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_interception)).
fof(23, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&party_of_protocol(X2))&party_of_protocol(X3))=>message(sent(X2,X3,X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_message_sent)).
fof(24, axiom,![X2]:![X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_holds_key)).
fof(25, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(encrypt(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_key_encrypts)).
fof(26, axiom,a_nonce(an_a_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)).
fof(27, axiom,![X1]:~(a_nonce(generate_key(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)).
fof(28, axiom,![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)).
fof(29, axiom,![X1]:~((a_key(X1)&a_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)).
fof(30, axiom,![X1]:a_key(generate_key(X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_keys_are_keys)).
fof(31, axiom,fresh_intruder_nonce(an_intruder_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)).
fof(32, axiom,![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)).
fof(33, axiom,![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)).
fof(34, plain,![X1]:~(a_nonce(generate_key(X1))),inference(fof_simplification,[status(thm)],[27,theory(equality)])).
cnf(35,plain,(a_holds(key(at,t))),inference(split_conjunct,[status(thm)],[1])).
cnf(36,plain,(party_of_protocol(a)),inference(split_conjunct,[status(thm)],[2])).
cnf(37,plain,(message(sent(a,b,pair(a,an_a_nonce)))),inference(split_conjunct,[status(thm)],[3])).
cnf(38,plain,(a_stored(pair(b,an_a_nonce))),inference(split_conjunct,[status(thm)],[4])).
cnf(44,plain,(b_holds(key(bt,t))),inference(split_conjunct,[status(thm)],[6])).
cnf(45,plain,(party_of_protocol(b)),inference(split_conjunct,[status(thm)],[7])).
cnf(46,plain,(fresh_to_b(an_a_nonce)),inference(split_conjunct,[status(thm)],[8])).
fof(47, plain,![X1]:![X2]:((~(message(sent(X1,b,pair(X1,X2))))|~(fresh_to_b(X2)))|(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2)))),inference(fof_nnf,[status(thm)],[9])).
fof(48, plain,![X3]:![X4]:((~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4)))|(message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))&b_stored(pair(X3,X4)))),inference(variable_rename,[status(thm)],[47])).
fof(49, plain,![X3]:![X4]:((message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))|(~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4))))&(b_stored(pair(X3,X4))|(~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4))))),inference(distribute,[status(thm)],[48])).
cnf(50,plain,(b_stored(pair(X2,X1))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),inference(split_conjunct,[status(thm)],[49])).
cnf(51,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),inference(split_conjunct,[status(thm)],[49])).
fof(52, plain,![X2]:![X4]:![X5]:(((~(message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2)))))|~(a_key(X2)))|~(b_stored(pair(X4,X5))))|b_holds(key(X2,X4))),inference(fof_nnf,[status(thm)],[10])).
fof(53, plain,![X6]:![X7]:![X8]:(((~(message(sent(X7,b,pair(encrypt(triple(X7,X6,generate_expiration_time(X8)),bt),encrypt(generate_b_nonce(X8),X6)))))|~(a_key(X6)))|~(b_stored(pair(X7,X8))))|b_holds(key(X6,X7))),inference(variable_rename,[status(thm)],[52])).
cnf(54,plain,(b_holds(key(X1,X2))|~b_stored(pair(X2,X3))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))),inference(split_conjunct,[status(thm)],[53])).
cnf(55,plain,(t_holds(key(at,a))),inference(split_conjunct,[status(thm)],[11])).
cnf(56,plain,(t_holds(key(bt,b))),inference(split_conjunct,[status(thm)],[12])).
cnf(57,plain,(party_of_protocol(t)),inference(split_conjunct,[status(thm)],[13])).
fof(61, plain,![X1]:![X2]:![X3]:(~(message(sent(X1,X2,X3)))|intruder_message(X3)),inference(fof_nnf,[status(thm)],[15])).
fof(62, plain,![X4]:![X5]:![X6]:(~(message(sent(X4,X5,X6)))|intruder_message(X6)),inference(variable_rename,[status(thm)],[61])).
cnf(63,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))),inference(split_conjunct,[status(thm)],[62])).
fof(64, plain,![X1]:![X2]:(~(intruder_message(pair(X1,X2)))|(intruder_message(X1)&intruder_message(X2))),inference(fof_nnf,[status(thm)],[16])).
fof(65, plain,![X3]:![X4]:(~(intruder_message(pair(X3,X4)))|(intruder_message(X3)&intruder_message(X4))),inference(variable_rename,[status(thm)],[64])).
fof(66, plain,![X3]:![X4]:((intruder_message(X3)|~(intruder_message(pair(X3,X4))))&(intruder_message(X4)|~(intruder_message(pair(X3,X4))))),inference(distribute,[status(thm)],[65])).
cnf(67,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))),inference(split_conjunct,[status(thm)],[66])).
cnf(68,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))),inference(split_conjunct,[status(thm)],[66])).
fof(69, plain,![X1]:![X2]:![X3]:(~(intruder_message(triple(X1,X2,X3)))|((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))),inference(fof_nnf,[status(thm)],[17])).
fof(70, plain,![X4]:![X5]:![X6]:(~(intruder_message(triple(X4,X5,X6)))|((intruder_message(X4)&intruder_message(X5))&intruder_message(X6))),inference(variable_rename,[status(thm)],[69])).
fof(71, plain,![X4]:![X5]:![X6]:(((intruder_message(X4)|~(intruder_message(triple(X4,X5,X6))))&(intruder_message(X5)|~(intruder_message(triple(X4,X5,X6)))))&(intruder_message(X6)|~(intruder_message(triple(X4,X5,X6))))),inference(distribute,[status(thm)],[70])).
cnf(72,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])).
cnf(73,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])).
cnf(74,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])).
fof(82, plain,![X1]:![X2]:((~(intruder_message(X1))|~(intruder_message(X2)))|intruder_message(pair(X1,X2))),inference(fof_nnf,[status(thm)],[19])).
fof(83, plain,![X3]:![X4]:((~(intruder_message(X3))|~(intruder_message(X4)))|intruder_message(pair(X3,X4))),inference(variable_rename,[status(thm)],[82])).
cnf(84,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[83])).
fof(85, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(intruder_message(X2)))|~(intruder_message(X3)))|intruder_message(triple(X1,X2,X3))),inference(fof_nnf,[status(thm)],[20])).
fof(86, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(intruder_message(X5)))|~(intruder_message(X6)))|intruder_message(triple(X4,X5,X6))),inference(variable_rename,[status(thm)],[85])).
cnf(87,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[86])).
fof(91, plain,![X1]:![X2]:![X3]:(((~(intruder_message(encrypt(X1,X2)))|~(intruder_holds(key(X2,X3))))|~(party_of_protocol(X3)))|intruder_message(X2)),inference(fof_nnf,[status(thm)],[22])).
fof(92, plain,![X4]:![X5]:![X6]:(((~(intruder_message(encrypt(X4,X5)))|~(intruder_holds(key(X5,X6))))|~(party_of_protocol(X6)))|intruder_message(X5)),inference(variable_rename,[status(thm)],[91])).
cnf(93,plain,(intruder_message(X1)|~party_of_protocol(X2)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))),inference(split_conjunct,[status(thm)],[92])).
fof(94, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(party_of_protocol(X2)))|~(party_of_protocol(X3)))|message(sent(X2,X3,X1))),inference(fof_nnf,[status(thm)],[23])).
fof(95, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(party_of_protocol(X5)))|~(party_of_protocol(X6)))|message(sent(X5,X6,X4))),inference(variable_rename,[status(thm)],[94])).
cnf(96,plain,(message(sent(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)),inference(split_conjunct,[status(thm)],[95])).
fof(97, plain,![X2]:![X3]:((~(intruder_message(X2))|~(party_of_protocol(X3)))|intruder_holds(key(X2,X3))),inference(fof_nnf,[status(thm)],[24])).
fof(98, plain,![X4]:![X5]:((~(intruder_message(X4))|~(party_of_protocol(X5)))|intruder_holds(key(X4,X5))),inference(variable_rename,[status(thm)],[97])).
cnf(99,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[98])).
fof(100, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(intruder_holds(key(X2,X3))))|~(party_of_protocol(X3)))|intruder_message(encrypt(X1,X2))),inference(fof_nnf,[status(thm)],[25])).
fof(101, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(intruder_holds(key(X5,X6))))|~(party_of_protocol(X6)))|intruder_message(encrypt(X4,X5))),inference(variable_rename,[status(thm)],[100])).
cnf(102,plain,(intruder_message(encrypt(X1,X2))|~party_of_protocol(X3)|~intruder_holds(key(X2,X3))|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[101])).
cnf(103,plain,(a_nonce(an_a_nonce)),inference(split_conjunct,[status(thm)],[26])).
fof(104, plain,![X2]:~(a_nonce(generate_key(X2))),inference(variable_rename,[status(thm)],[34])).
cnf(105,plain,(~a_nonce(generate_key(X1))),inference(split_conjunct,[status(thm)],[104])).
fof(106, plain,![X2]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X2))),inference(variable_rename,[status(thm)],[28])).
cnf(107,plain,(a_nonce(generate_b_nonce(X1))),inference(split_conjunct,[status(thm)],[106])).
cnf(108,plain,(a_nonce(generate_expiration_time(X1))),inference(split_conjunct,[status(thm)],[106])).
fof(109, plain,![X1]:(~(a_key(X1))|~(a_nonce(X1))),inference(fof_nnf,[status(thm)],[29])).
fof(110, plain,![X2]:(~(a_key(X2))|~(a_nonce(X2))),inference(variable_rename,[status(thm)],[109])).
cnf(111,plain,(~a_nonce(X1)|~a_key(X1)),inference(split_conjunct,[status(thm)],[110])).
fof(112, plain,![X2]:a_key(generate_key(X2)),inference(variable_rename,[status(thm)],[30])).
cnf(113,plain,(a_key(generate_key(X1))),inference(split_conjunct,[status(thm)],[112])).
cnf(114,plain,(fresh_intruder_nonce(an_intruder_nonce)),inference(split_conjunct,[status(thm)],[31])).
fof(115, plain,![X1]:(~(fresh_intruder_nonce(X1))|fresh_intruder_nonce(generate_intruder_nonce(X1))),inference(fof_nnf,[status(thm)],[32])).
fof(116, plain,![X2]:(~(fresh_intruder_nonce(X2))|fresh_intruder_nonce(generate_intruder_nonce(X2))),inference(variable_rename,[status(thm)],[115])).
cnf(117,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[116])).
fof(118, plain,![X1]:(~(fresh_intruder_nonce(X1))|(fresh_to_b(X1)&intruder_message(X1))),inference(fof_nnf,[status(thm)],[33])).
fof(119, plain,![X2]:(~(fresh_intruder_nonce(X2))|(fresh_to_b(X2)&intruder_message(X2))),inference(variable_rename,[status(thm)],[118])).
fof(120, plain,![X2]:((fresh_to_b(X2)|~(fresh_intruder_nonce(X2)))&(intruder_message(X2)|~(fresh_intruder_nonce(X2)))),inference(distribute,[status(thm)],[119])).
cnf(121,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[120])).
cnf(122,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[120])).
cnf(123,plain,(intruder_message(an_intruder_nonce)),inference(spm,[status(thm)],[121,114,theory(equality)])).
cnf(125,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),inference(spm,[status(thm)],[121,117,theory(equality)])).
cnf(126,plain,(intruder_message(pair(a,an_a_nonce))),inference(spm,[status(thm)],[63,37,theory(equality)])).
cnf(133,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~party_of_protocol(X3)|~intruder_message(X2)),inference(spm,[status(thm)],[102,99,theory(equality)])).
cnf(135,plain,(b_stored(pair(a,an_a_nonce))|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[50,37,theory(equality)])).
cnf(136,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|~party_of_protocol(b)|~party_of_protocol(X1)),inference(spm,[status(thm)],[50,96,theory(equality)])).
cnf(137,plain,(b_stored(pair(a,an_a_nonce))|\$false),inference(rw,[status(thm)],[135,46,theory(equality)])).
cnf(138,plain,(b_stored(pair(a,an_a_nonce))),inference(cn,[status(thm)],[137,theory(equality)])).
cnf(139,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|\$false|~party_of_protocol(X1)),inference(rw,[status(thm)],[136,45,theory(equality)])).
cnf(140,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|~party_of_protocol(X1)),inference(cn,[status(thm)],[139,theory(equality)])).
cnf(147,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[51,37,theory(equality)])).
cnf(148,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|~party_of_protocol(b)|~party_of_protocol(X2)),inference(spm,[status(thm)],[51,96,theory(equality)])).
cnf(149,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))|\$false),inference(rw,[status(thm)],[147,46,theory(equality)])).
cnf(150,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))),inference(cn,[status(thm)],[149,theory(equality)])).
cnf(151,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|\$false|~party_of_protocol(X2)),inference(rw,[status(thm)],[148,45,theory(equality)])).
cnf(152,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|~party_of_protocol(X2)),inference(cn,[status(thm)],[151,theory(equality)])).
cnf(155,plain,(intruder_message(a)),inference(spm,[status(thm)],[68,126,theory(equality)])).
cnf(156,plain,(intruder_message(an_a_nonce)),inference(spm,[status(thm)],[67,126,theory(equality)])).
cnf(157,plain,(b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))),inference(spm,[status(thm)],[54,138,theory(equality)])).
cnf(158,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[133,45,theory(equality)])).
cnf(162,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[140,84,theory(equality)])).
cnf(167,plain,(b_holds(key(X1,X2))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~intruder_message(X3)|~intruder_message(X2)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(spm,[status(thm)],[54,162,theory(equality)])).
cnf(168,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),inference(spm,[status(thm)],[63,150,theory(equality)])).
cnf(175,plain,(intruder_message(b)),inference(spm,[status(thm)],[74,168,theory(equality)])).
cnf(176,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[72,168,theory(equality)])).
cnf(177,plain,(intruder_message(generate_b_nonce(an_a_nonce))),inference(spm,[status(thm)],[73,168,theory(equality)])).
cnf(178,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~party_of_protocol(b)|~party_of_protocol(a)),inference(spm,[status(thm)],[157,96,theory(equality)])).
cnf(179,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|\$false|~party_of_protocol(a)),inference(rw,[status(thm)],[178,45,theory(equality)])).
cnf(180,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|\$false|\$false),inference(rw,[status(thm)],[179,36,theory(equality)])).
cnf(181,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))),inference(cn,[status(thm)],[180,theory(equality)])).
cnf(187,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~party_of_protocol(X2)|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[152,84,theory(equality)])).
cnf(194,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[181,84,theory(equality)])).
cnf(195,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|~intruder_message(generate_b_nonce(an_a_nonce))|~intruder_message(X1)),inference(spm,[status(thm)],[194,158,theory(equality)])).
cnf(196,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|\$false|~intruder_message(X1)),inference(rw,[status(thm)],[195,177,theory(equality)])).
cnf(197,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|~intruder_message(X1)),inference(cn,[status(thm)],[196,theory(equality)])).
cnf(198,plain,(b_holds(key(X1,a))|~intruder_message(X1)|~a_key(X1)|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)),inference(spm,[status(thm)],[197,158,theory(equality)])).
cnf(199,plain,(b_holds(key(an_a_nonce,a))|~intruder_message(an_a_nonce)|~a_key(an_a_nonce)),inference(spm,[status(thm)],[197,176,theory(equality)])).
cnf(200,plain,(b_holds(key(an_a_nonce,a))|\$false|~a_key(an_a_nonce)),inference(rw,[status(thm)],[199,156,theory(equality)])).
cnf(201,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)),inference(cn,[status(thm)],[200,theory(equality)])).
cnf(204,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)),inference(csr,[status(thm)],[198,73])).
cnf(205,plain,(intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[63,187,theory(equality)])).
cnf(207,plain,(intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),inference(spm,[status(thm)],[72,205,theory(equality)])).
cnf(208,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[73,205,theory(equality)])).
cnf(224,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~party_of_protocol(b)),inference(spm,[status(thm)],[167,96,theory(equality)])).
cnf(225,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|\$false),inference(rw,[status(thm)],[224,45,theory(equality)])).
cnf(226,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))),inference(cn,[status(thm)],[225,theory(equality)])).
cnf(229,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))),inference(spm,[status(thm)],[226,84,theory(equality)])).
cnf(230,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(generate_b_nonce(X3))|~intruder_message(X1)),inference(spm,[status(thm)],[229,158,theory(equality)])).
cnf(231,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X1)|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[230,208])).
cnf(232,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)),inference(spm,[status(thm)],[231,158,theory(equality)])).
cnf(234,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[231,207,theory(equality)])).
cnf(240,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[232,73])).
cnf(241,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[240,74])).
cnf(267,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[72,249,theory(equality)])).
cnf(268,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[73,249,theory(equality)])).
cnf(269,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|~intruder_message(b)|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(spm,[status(thm)],[231,268,theory(equality)])).
cnf(271,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(rw,[status(thm)],[269,175,theory(equality)])).
cnf(272,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(rw,[status(thm)],[271,113,theory(equality)])).
cnf(273,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|\$false|~a_nonce(X1)),inference(rw,[status(thm)],[272,45,theory(equality)])).
cnf(274,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|~intruder_message(generate_key(X1))|~fresh_to_b(X1)|~a_nonce(X1)),inference(cn,[status(thm)],[273,theory(equality)])).
cnf(276,plain,(a_holds(key(generate_key(an_a_nonce),b))),inference(spm,[status(thm)],[145,260,theory(equality)])).
cnf(277,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))),inference(spm,[status(thm)],[146,260,theory(equality)])).
cnf(282,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))),inference(spm,[status(thm)],[63,277,theory(equality)])).
cnf(283,plain,(b_holds(key(generate_key(an_a_nonce),a))|~intruder_message(an_a_nonce)|~intruder_message(a)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(spm,[status(thm)],[167,277,theory(equality)])).
cnf(285,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|~intruder_message(a)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[283,156,theory(equality)])).
cnf(286,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[285,155,theory(equality)])).
cnf(287,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|\$false|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[286,113,theory(equality)])).
cnf(288,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|\$false|\$false|~party_of_protocol(a)),inference(rw,[status(thm)],[287,46,theory(equality)])).
cnf(289,plain,(b_holds(key(generate_key(an_a_nonce),a))|\$false|\$false|\$false|\$false|\$false),inference(rw,[status(thm)],[288,36,theory(equality)])).
cnf(290,plain,(b_holds(key(generate_key(an_a_nonce),a))),inference(cn,[status(thm)],[289,theory(equality)])).
cnf(294,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[68,282,theory(equality)])).
cnf(295,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[140,282,theory(equality)])).
cnf(296,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[67,282,theory(equality)])).
cnf(297,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[152,282,theory(equality)])).
cnf(311,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(an_a_nonce)|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(spm,[status(thm)],[229,296,theory(equality)])).
cnf(315,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|\$false|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(rw,[status(thm)],[311,156,theory(equality)])).
cnf(316,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|\$false|~intruder_message(X1)|\$false|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(rw,[status(thm)],[315,113,theory(equality)])).
cnf(317,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|\$false|~intruder_message(X1)|\$false|\$false|~party_of_protocol(X1)),inference(rw,[status(thm)],[316,46,theory(equality)])).
cnf(318,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)),inference(cn,[status(thm)],[317,theory(equality)])).
cnf(331,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X1)|~party_of_protocol(X1)|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)),inference(spm,[status(thm)],[318,158,theory(equality)])).
cnf(332,plain,(b_holds(key(generate_key(an_a_nonce),b))|~intruder_message(b)|~party_of_protocol(b)|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[318,268,theory(equality)])).
cnf(334,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|~party_of_protocol(b)|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[332,175,theory(equality)])).
cnf(335,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[334,45,theory(equality)])).
cnf(336,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|\$false|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[335,156,theory(equality)])).
cnf(337,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|\$false|\$false|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[336,103,theory(equality)])).
cnf(338,plain,(b_holds(key(generate_key(an_a_nonce),b))|\$false|\$false|\$false|\$false|\$false),inference(rw,[status(thm)],[337,46,theory(equality)])).
cnf(339,plain,(b_holds(key(generate_key(an_a_nonce),b))),inference(cn,[status(thm)],[338,theory(equality)])).
cnf(348,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)),inference(csr,[status(thm)],[331,74])).
cnf(379,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[192,369,theory(equality)])).
cnf(381,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[63,379,theory(equality)])).
cnf(382,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(a)),inference(spm,[status(thm)],[51,379,theory(equality)])).
cnf(384,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(a)),inference(spm,[status(thm)],[50,379,theory(equality)])).
cnf(386,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|\$false),inference(rw,[status(thm)],[382,155,theory(equality)])).
cnf(387,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(cn,[status(thm)],[386,theory(equality)])).
cnf(393,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|\$false),inference(rw,[status(thm)],[384,155,theory(equality)])).
cnf(394,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(cn,[status(thm)],[393,theory(equality)])).
cnf(401,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(spm,[status(thm)],[226,381,theory(equality)])).
cnf(403,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[140,381,theory(equality)])).
cnf(404,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[67,381,theory(equality)])).
cnf(405,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[152,381,theory(equality)])).
cnf(411,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|\$false|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(rw,[status(thm)],[401,113,theory(equality)])).
cnf(412,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(cn,[status(thm)],[411,theory(equality)])).
cnf(420,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(spm,[status(thm)],[404,275,theory(equality)])).
cnf(452,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[394,122,theory(equality)])).
cnf(453,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[403,122,theory(equality)])).
cnf(454,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),inference(csr,[status(thm)],[412,208])).
cnf(455,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)),inference(spm,[status(thm)],[454,158,theory(equality)])).
cnf(456,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)),inference(spm,[status(thm)],[454,207,theory(equality)])).
cnf(485,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)),inference(csr,[status(thm)],[455,74])).
cnf(489,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[73,472,theory(equality)])).
cnf(503,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|~intruder_message(a)|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(spm,[status(thm)],[231,489,theory(equality)])).
cnf(513,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(rw,[status(thm)],[503,155,theory(equality)])).
cnf(514,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(rw,[status(thm)],[513,113,theory(equality)])).
cnf(515,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|\$false|~intruder_message(generate_key(X1))|\$false|~fresh_to_b(X1)|\$false|~a_nonce(X1)),inference(rw,[status(thm)],[514,36,theory(equality)])).
cnf(516,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|~intruder_message(generate_key(X1))|~fresh_to_b(X1)|~a_nonce(X1)),inference(cn,[status(thm)],[515,theory(equality)])).
cnf(548,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[387,122,theory(equality)])).
cnf(551,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)),inference(spm,[status(thm)],[146,365,theory(equality)])).
cnf(553,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)),inference(spm,[status(thm)],[63,551,theory(equality)])).
cnf(569,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)),inference(spm,[status(thm)],[140,553,theory(equality)])).
cnf(571,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)),inference(spm,[status(thm)],[152,553,theory(equality)])).
cnf(599,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[295,122,theory(equality)])).
cnf(600,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[297,122,theory(equality)])).
cnf(605,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[405,122,theory(equality)])).
cnf(634,plain,(party_of_protocol(t)),57,['final']).
cnf(635,plain,(party_of_protocol(a)),36,['final']).
cnf(636,plain,(party_of_protocol(b)),45,['final']).
cnf(637,plain,(fresh_to_b(an_a_nonce)),46,['final']).
cnf(638,plain,(a_nonce(an_a_nonce)),103,['final']).
cnf(639,plain,(fresh_intruder_nonce(an_intruder_nonce)),114,['final']).
cnf(640,plain,(a_key(generate_key(X1))),113,['final']).
cnf(641,plain,(a_nonce(generate_b_nonce(X1))),107,['final']).
cnf(642,plain,(a_nonce(generate_expiration_time(X1))),108,['final']).
cnf(643,plain,(a_holds(key(at,t))),35,['final']).
cnf(644,plain,(a_stored(pair(b,an_a_nonce))),38,['final']).
cnf(645,plain,(b_holds(key(bt,t))),44,['final']).
cnf(646,plain,(t_holds(key(at,a))),55,['final']).
cnf(647,plain,(t_holds(key(bt,b))),56,['final']).
cnf(648,plain,(message(sent(a,b,pair(a,an_a_nonce)))),37,['final']).
cnf(649,plain,(intruder_message(an_intruder_nonce)),123,['final']).
cnf(650,plain,(intruder_message(pair(a,an_a_nonce))),126,['final']).
cnf(651,plain,(intruder_message(a)),155,['final']).
cnf(652,plain,(intruder_message(an_a_nonce)),156,['final']).
cnf(653,plain,(b_stored(pair(a,an_a_nonce))),138,['final']).
cnf(654,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))),150,['final']).
cnf(655,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),168,['final']).
cnf(656,plain,(intruder_message(b)),175,['final']).
cnf(657,plain,(intruder_message(generate_b_nonce(an_a_nonce))),177,['final']).
cnf(658,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),176,['final']).
cnf(660,plain,(a_holds(key(generate_key(an_a_nonce),b))),276,['final']).
cnf(661,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))),277,['final']).
cnf(662,plain,(b_holds(key(generate_key(an_a_nonce),a))),290,['final']).
cnf(663,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))),282,['final']).
cnf(664,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),296,['final']).
cnf(665,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),294,['final']).
cnf(666,plain,(b_holds(key(generate_key(an_a_nonce),b))),339,['final']).
cnf(669,plain,(~a_nonce(generate_key(X1))),105,['final']).
cnf(670,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)),122,['final']).
cnf(671,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)),121,['final']).
cnf(672,plain,(~a_nonce(X1)|~a_key(X1)),111,['final']).
cnf(673,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),117,['final']).
cnf(674,plain,(intruder_message(X1)|~intruder_message(pair(X2,X1))),67,['final']).
cnf(675,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))),68,['final']).
cnf(676,plain,(intruder_message(X1)|~intruder_message(triple(X2,X3,X1))),72,['final']).
cnf(677,plain,(intruder_message(X1)|~intruder_message(triple(X2,X1,X3))),73,['final']).
cnf(678,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))),63,['final']).
cnf(679,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))),74,['final']).
cnf(681,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)),84,['final']).
cnf(685,plain,(intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)),99,['final']).
cnf(686,plain,(message(sent(X1,X2,X3))|~intruder_message(X3)|~party_of_protocol(X2)|~party_of_protocol(X1)),96,['final']).
cnf(687,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),87,['final']).
cnf(688,plain,(intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~intruder_message(X1)|~party_of_protocol(X3)),102,['final']).
cnf(689,plain,(intruder_message(X1)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))|~party_of_protocol(X2)),93,['final']).
cnf(690,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~message(sent(X1,b,pair(X1,X2)))),50,['final']).
cnf(694,plain,(b_holds(key(X1,X2))|~a_key(X1)|~b_stored(pair(X2,X3))|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))),54,['final']).
cnf(695,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),51,['final']).
cnf(697,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),125,['final']).
cnf(698,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)),158,['final']).
cnf(699,plain,(b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)),140,['final']).
cnf(700,plain,(b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),162,['final']).
cnf(705,plain,(b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))),157,['final']).
cnf(707,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(pair(X2,X1))|~fresh_to_b(X1)|~party_of_protocol(X2)),152,['final']).
cnf(711,plain,(b_holds(key(X1,a))|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~a_key(X1)),181,['final']).
cnf(712,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~a_key(X1)),194,['final']).
cnf(713,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~a_key(X1)),197,['final']).
cnf(714,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)),201,['final']).
cnf(716,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)),204,['final']).
cnf(717,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),187,['final']).
cnf(718,plain,(intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),205,['final']).
cnf(719,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),208,['final']).
cnf(720,plain,(intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),207,['final']).
cnf(722,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~party_of_protocol(X2)),167,['final']).
cnf(724,plain,(b_holds(key(X1,X2))|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),226,['final']).
cnf(725,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),229,['final']).
cnf(726,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),231,['final']).
cnf(727,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)),234,['final']).
cnf(728,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),241,['final']).
cnf(735,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),267,['final']).
cnf(736,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),268,['final']).
cnf(737,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),274,['final']).
cnf(740,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)),318,['final']).
cnf(742,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)),348,['final']).
cnf(745,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)),379,['final']).
cnf(746,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)),381,['final']).
cnf(747,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),420,['final']).
cnf(748,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))),394,['final']).
cnf(749,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),452,['final']).
cnf(750,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)),403,['final']).
cnf(751,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)),453,['final']).
cnf(752,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),454,['final']).
cnf(753,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)),456,['final']).
cnf(755,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)),485,['final']).
cnf(758,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),489,['final']).
cnf(759,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),516,['final']).
cnf(763,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))),387,['final']).
cnf(764,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),548,['final']).
cnf(766,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)),551,['final']).
cnf(767,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)),553,['final']).
cnf(771,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),295,['final']).
cnf(772,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),297,['final']).
cnf(777,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),599,['final']).
cnf(778,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),569,['final']).
cnf(779,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)),405,['final']).
cnf(782,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)),605,['final']).
cnf(783,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),571,['final']).
cnf(784,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),600,['final']).
# SZS output end Saturation.
```

```# SZS status Theorem
# SZS answers Tuple [[s__agent__m, s__experiencer__m]|_]

# Proof found!
```

## E-Darwin 1.4

Björn Pelzer
University Koblenz-Landau, Germany

### Sample solution for NLP042+1

```START OF MODEL (DIG):
abstraction(esk1_0, esk3_0)
act(esk1_0, esk5_0)
actual_world(esk1_0)
agent(esk1_0, esk5_0, esk2_0)
animate(esk1_0, esk2_0)
beverage(esk1_0, esk4_0)
entity(esk1_0, esk4_0)
entity(esk1_0, esk2_0)
event(esk1_0, esk5_0)
eventuality(esk1_0, esk5_0)
existent(esk1_0, esk4_0)
existent(esk1_0, esk2_0)
female(esk1_0, esk2_0)
food(esk1_0, esk4_0)
forename(esk1_0, esk3_0)
general(esk1_0, esk3_0)
human(esk1_0, esk2_0)
human_person(esk1_0, esk2_0)
impartial(esk1_0, esk4_0)
impartial(esk1_0, esk2_0)
living(esk1_0, esk2_0)
mia_forename(esk1_0, esk3_0)
nonexistent(esk1_0, esk5_0)
nonhuman(esk1_0, esk3_0)
nonliving(esk1_0, esk4_0)
nonreflexive(esk1_0, esk5_0)
object(esk1_0, esk4_0)
of(esk1_0, esk3_0, esk2_0)
order(esk1_0, esk5_0)
organism(esk1_0, esk2_0)
past(esk1_0, esk5_0)
patient(esk1_0, esk5_0, esk4_0)
relation(esk1_0, esk3_0)
relname(esk1_0, esk3_0)
shake_beverage(esk1_0, esk4_0)
singleton(esk1_0, esk4_0)
singleton(esk1_0, esk5_0)
singleton(esk1_0, esk2_0)
singleton(esk1_0, esk3_0)
specific(esk1_0, esk4_0)
specific(esk1_0, esk5_0)
specific(esk1_0, esk2_0)
substance_matter(esk1_0, esk4_0)
thing(esk1_0, esk4_0)
thing(esk1_0, esk5_0)
thing(esk1_0, esk2_0)
thing(esk1_0, esk3_0)
unisex(esk1_0, esk4_0)
unisex(esk1_0, esk5_0)
unisex(esk1_0, esk3_0)
woman(esk1_0, esk2_0)
END OF MODEL
```

### Sample solution for SWV017+1

System does not solve the problem.

## E-KRHyper 1.2

Björn Pelzer
University Koblenz-Landau, Germany

```% SZS status Theorem
```

## E-MaLeS 1.0

Daniel Kuehlwein, Josef Urban, Stephan Schulz2
Radboud Universiteit Nijmegen, The Netherlands, 2Technische Universität München, Germany

### Sample solution for SEU140+2

```# Preprocessing time       : 0.012 s
# Problem is unsatisfiable (or provable), constructing proof object
# SZS status Theorem
# SZS output start CNFRefutation.
fof(8, axiom,![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', d3_tarski)).
fof(27, axiom,![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)).
fof(43, axiom,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t3_xboole_0)).
fof(51, conjecture,![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t63_xboole_1)).
fof(57, negated_conjecture,~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))),inference(assume_negation,[status(cth)],[51])).
fof(66, plain,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),inference(fof_simplification,[status(thm)],[43,theory(equality)])).
fof(101, plain,![X1]:![X2]:((~(subset(X1,X2))|![X3]:(~(in(X3,X1))|in(X3,X2)))&(?[X3]:(in(X3,X1)&~(in(X3,X2)))|subset(X1,X2))),inference(fof_nnf,[status(thm)],[8])).
fof(102, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&(?[X7]:(in(X7,X4)&~(in(X7,X5)))|subset(X4,X5))),inference(variable_rename,[status(thm)],[101])).
fof(103, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(skolemize,[status(esa)],[102])).
fof(104, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(shift_quantors,[status(thm)],[103])).
fof(105, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)|subset(X4,X5))&(~(in(esk3_2(X4,X5),X5))|subset(X4,X5)))),inference(distribute,[status(thm)],[104])).
cnf(108,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)),inference(split_conjunct,[status(thm)],[105])).
fof(170, plain,![X1]:![X2]:(~(disjoint(X1,X2))|disjoint(X2,X1)),inference(fof_nnf,[status(thm)],[27])).
fof(171, plain,![X3]:![X4]:(~(disjoint(X3,X4))|disjoint(X4,X3)),inference(variable_rename,[status(thm)],[170])).
cnf(172,plain,(disjoint(X1,X2)|~disjoint(X2,X1)),inference(split_conjunct,[status(thm)],[171])).
fof(215, plain,![X1]:![X2]:((disjoint(X1,X2)|?[X3]:(in(X3,X1)&in(X3,X2)))&(![X3]:(~(in(X3,X1))|~(in(X3,X2)))|~(disjoint(X1,X2)))),inference(fof_nnf,[status(thm)],[66])).
fof(216, plain,![X4]:![X5]:((disjoint(X4,X5)|?[X6]:(in(X6,X4)&in(X6,X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(variable_rename,[status(thm)],[215])).
fof(217, plain,![X4]:![X5]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(skolemize,[status(esa)],[216])).
fof(218, plain,![X4]:![X5]:![X7]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(shift_quantors,[status(thm)],[217])).
fof(219, plain,![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(distribute,[status(thm)],[218])).
cnf(220,plain,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)),inference(split_conjunct,[status(thm)],[219])).
cnf(221,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)),inference(split_conjunct,[status(thm)],[219])).
cnf(222,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)),inference(split_conjunct,[status(thm)],[219])).
fof(244, negated_conjecture,?[X1]:?[X2]:?[X3]:((subset(X1,X2)&disjoint(X2,X3))&~(disjoint(X1,X3))),inference(fof_nnf,[status(thm)],[57])).
fof(245, negated_conjecture,?[X4]:?[X5]:?[X6]:((subset(X4,X5)&disjoint(X5,X6))&~(disjoint(X4,X6))),inference(variable_rename,[status(thm)],[244])).
fof(246, negated_conjecture,((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~(disjoint(esk11_0,esk13_0))),inference(skolemize,[status(esa)],[245])).
cnf(247,negated_conjecture,(~disjoint(esk11_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(248,negated_conjecture,(disjoint(esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(249,negated_conjecture,(subset(esk11_0,esk12_0)),inference(split_conjunct,[status(thm)],[246])).
cnf(384,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)),inference(spm,[status(thm)],[172,221,theory(equality)])).
cnf(386,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)),inference(spm,[status(thm)],[172,222,theory(equality)])).
cnf(474,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)),inference(spm,[status(thm)],[108,249,theory(equality)])).
cnf(485,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)),inference(spm,[status(thm)],[220,248,theory(equality)])).
cnf(2151,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[247,384,theory(equality)])).
cnf(2160,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)),inference(spm,[status(thm)],[247,386,theory(equality)])).
cnf(2169,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)),inference(spm,[status(thm)],[485,2160,theory(equality)])).
cnf(2622,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[2169,474,theory(equality)])).
cnf(2640,negated_conjecture,(\$false),inference(rw,[status(thm)],[2622,2151,theory(equality)])).
cnf(2641,negated_conjecture,(\$false),inference(cn,[status(thm)],[2640,theory(equality)])).
cnf(2642,negated_conjecture,(\$false),2641,['proof']).
# SZS output end CNFRefutation
```

## FIMO 0.2

Orkunt Sabuncu
University of Potsdam, Germany

### Sample solution for NLP042+1

```finite domain: {1,2,3,4}
esk2_0 = 1
esk3_0 = 2
esk4_0 = 3
esk5_0 = 4
esk1_0 = 1
abstraction/2:
(1,2) <=> True
(X1,X2) <=> abstraction(1,X2) : X1>1
impartial/2:
(X0,X1) <=> True *p*
woman/2:
(1,1) <=> True
(X1,X2) <=> woman(1,X2) : X1>1
act/2:
(1,4) <=> True
(X1,X2) <=> act(1,X2) : X1>1
animate/2:
(1,1) <=> True
(X1,X2) <=> animate(1,X2) : X1>1
thing/2:
(X0,X1) <=> True *p*
organism/2:
(1,1) <=> True
(X1,X2) <=> organism(1,X2) : X1>1
relname/2:
(1,2) <=> True
(X1,X2) <=> relname(1,X2) : X1>1
nonexistent/2:
(1,4) <=> True
(X1,X2) <=> nonexistent(1,X2) : X1>1
general/2:
(1,2) <=> True
(X1,X2) <=> general(1,X2) : X1>1
food/2:
(1,3) <=> True
(X1,X2) <=> food(1,X2) : X1>1
female/2:
(1,1) <=> True
(X1,X2) <=> female(1,X2) : X1>1
shake_beverage/2:
(1,3) <=> True
(X1,X2) <=> shake_beverage(1,X2) : X1>1
of/3:
(1,2,1) <=> True
(X1,X2,X3) <=> of(1,X2,X3) : X1>1
forename/2:
(1,2) <=> True
(X1,X2) <=> forename(1,X2) : X1>1
beverage/2:
(1,3) <=> True
(X1,X2) <=> beverage(1,X2) : X1>1
order/2:
(1,4) <=> True
(X1,X2) <=> order(1,X2) : X1>1
existent/2:
(1,1) <=> True
(1,2) <=> True
(1,3) <=> True
(X1,X2) <=> existent(1,X2) : X1>1
nonreflexive/2:
(1,4) <=> True
(X1,X2) <=> nonreflexive(1,X2) : X1>1
singleton/2:
(X0,X1) <=> True *p*
living/2:
(1,1) <=> True
(X1,X2) <=> living(1,X2) : X1>1
specific/2:
(1,1) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> specific(1,X2) : X1>1
patient/3:
(1,4,3) <=> True
(X1,X2,X3) <=> patient(1,X2,X3) : X1>1
actual_world/1:
(X0) <=> True *p*
object/2:
(1,3) <=> True
(X1,X2) <=> object(1,X2) : X1>1
past/2:
(X0,X1) <=> True *p*
agent/3:
(1,4,1) <=> True
(X1,X2,X3) <=> agent(1,X2,X3) : X1>1
human/2:
(1,1) <=> True
(X1,X2) <=> human(1,X2) : X1>1
event/2:
(1,4) <=> True
(X1,X2) <=> event(1,X2) : X1>1
nonliving/2:
(1,2) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> nonliving(1,X2) : X1>1
human_person/2:
(1,1) <=> True
(X1,X2) <=> human_person(1,X2) : X1>1
eventuality/2:
(1,4) <=> True
(X1,X2) <=> eventuality(1,X2) : X1>1
unisex/2:
(1,2) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> unisex(1,X2) : X1>1
entity/2:
(1,1) <=> True
(1,3) <=> True
(X1,X2) <=> entity(1,X2) : X1>1
relation/2:
(1,2) <=> True
(X1,X2) <=> relation(1,X2) : X1>1
nonhuman/2:
(1,2) <=> True
(1,3) <=> True
(1,4) <=> True
(X1,X2) <=> nonhuman(1,X2) : X1>1
mia_forename/2:
(1,2) <=> True
(X1,X2) <=> mia_forename(1,X2) : X1>1
substance_matter/2:
(1,3) <=> True
(X1,X2) <=> substance_matter(1,X2) : X1>1
```

### Sample solution for SWV017+1

```finite domain: {1,2}
a = 1
b = 1
bt = 1
an_intruder_nonce = 2
t = 1
an_a_nonce = 2
at = 2
triple/3:
(1,1,1) = 1
(1,1,2) = 2
(1,2,2) = 2
(2,1,1) = 2
(2,1,2) = 2
(2,2,1) = 2
(1,2,1) = 1
(2,2,2) = 1
generate_expiration_time/1:
(2) = 2
(1) = 2
key/2:
(2,1) = 2
(1,1) = 2
(1,2) = 1
(2,2) = 1
generate_intruder_nonce/1:
(1) = 1
(2) = 2
sent/3:
(1,1,2) = 2
(1,2,1) = 2
(1,2,2) = 2
(2,1,1) = 2
(2,1,2) = 2
(2,2,1) = 2
(1,1,1) = 2
(2,2,2) = 1
(1,1,1,2) = 2
(1,2,1,1) = 2
(1,2,1,2) = 2
(2,1,1,1) = 2
(2,1,1,2) = 2
(2,2,1,1) = 2
(2,2,1,2) = 2
(1,1,2,1) = 2
(1,1,2,2) = 2
(1,2,2,1) = 2
(1,2,2,2) = 2
(2,2,2,1) = 2
(2,2,2,2) = 2
(1,1,1,1) = 2
(2,1,2,1) = 1
(2,1,2,2) = 1
generate_b_nonce/1:
(2) = 2
(1) = 2
generate_key/1:
(1) = 1
(2) = 1
encrypt/2:
(1,1) = 1
(2,2) = 2
(2,1) = 1
(1,2) = 1
pair/2:
(2,1) = 2
(1,2) = 2
(2,2) = 2
(1,1) = 2
t_holds/1:
(2) <=> True
a_holds/1:
(X0) <=> True *p*
message/1:
(2) <=> True
b_stored/1:
(X0) <=> True *p*
intruder_message/1:
(1) <=> True
(2) <=> True
fresh_intruder_nonce/1:
(2) <=> True
a_key/1:
(1) <=> True
b_holds/1:
(X0) <=> True *p*
a_nonce/1:
(2) <=> True
a_stored/1:
(2) <=> True
intruder_holds/1:
(2) <=> True
fresh_to_b/1:
(2) <=> True
party_of_protocol/1:
(1) <=> True
```

## iProver 0.9

Konstantin Korovin
University of Manchester, United Kingdom

### Sample solution for NLP042+1

```% SZS output start Model

%------ Negative definition of \$equality_sorted
fof(lit_def,axiom,
(! [X0,X1,X2] :
( ~(\$equality_sorted(X0,X1,X2)) <=>
(
(
( X0=\$i & X1=sK2 )
&
( X2!=sK2 )
)

|
(
( X0=\$i & X1=sK1 )
&
( X2!=sK1 )
)

|
(
( X0=\$i & X1=sK3 )
&
( X2!=sK3 )
)

|
(
( X0=\$i & X1=sK4 )
&
( X2!=sK4 )
)

|
(
( X0=\$i & X2=sK2 )
&
( X1!=sK2 )
)

|
(
( X0=\$i & X2=sK1 )
&
( X1!=sK1 )
)

|
(
( X0=\$i & X2=sK3 )
&
( X1!=sK3 )
)

|
(
( X0=\$i & X2=sK4 )
&
( X1!=sK4 )
)

)
)
)
).

%------ Positive definition of female
fof(lit_def,axiom,
(! [X0,X1] :
( female(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of woman
fof(lit_def,axiom,
(! [X0,X1] :
( woman(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of animate
fof(lit_def,axiom,
(! [X0,X1] :
( animate(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of human_person
fof(lit_def,axiom,
(! [X0,X1] :
( human_person(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of human
fof(lit_def,axiom,
(! [X0,X1] :
( human(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of living
fof(lit_def,axiom,
(! [X0,X1] :
( living(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of organism
fof(lit_def,axiom,
(! [X0,X1] :
( organism(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X1=sK1 )
)

)
)
)
).

%------ Positive definition of entity
fof(lit_def,axiom,
(! [X0,X1] :
( entity(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK1 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of forename
fof(lit_def,axiom,
(! [X0,X1] :
( forename(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
&
( X0!=sK0 )
)

)
)
)
).

%------ Positive definition of mia_forename
fof(lit_def,axiom,
(! [X0,X1] :
( mia_forename(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
)

)
)
)
).

%------ Positive definition of unisex
fof(lit_def,axiom,
(! [X0,X1] :
( unisex(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X0=sK0 & X1=sK3 )
)

|
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK2 )
)

|
(
( X1=sK3 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of abstraction
fof(lit_def,axiom,
(! [X0,X1] :
( abstraction(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
)

)
)
)
).

%------ Positive definition of general
fof(lit_def,axiom,
(! [X0,X1] :
( general(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
)

)
)
)
).

%------ Positive definition of nonhuman
fof(lit_def,axiom,
(! [X0,X1] :
( nonhuman(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
)

)
)
)
).

%------ Positive definition of relation
fof(lit_def,axiom,
(! [X0,X1] :
( relation(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
)

)
)
)
).

%------ Positive definition of relname
fof(lit_def,axiom,
(! [X0,X1] :
( relname(X0,X1) <=>
(
(
( X0=sK0 & X1=sK2 )
)

|
(
( X1=sK2 )
)

)
)
)
).

%------ Positive definition of object
fof(lit_def,axiom,
(! [X0,X1] :
( object(X0,X1) <=>
(
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of nonliving
fof(lit_def,axiom,
(! [X0,X1] :
( nonliving(X0,X1) <=>
(
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of existent
fof(lit_def,axiom,
(! [X0,X1] :
( existent(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK1 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of specific
fof(lit_def,axiom,
(! [X0,X1] :
( specific(X0,X1) <=>
(
(
( X0=sK0 & X1=sK1 )
)

|
(
( X0=sK0 & X1=sK3 )
)

|
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK1 )
)

|
(
( X1=sK3 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of substance_matter
fof(lit_def,axiom,
(! [X0,X1] :
( substance_matter(X0,X1) <=>
(
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of food
fof(lit_def,axiom,
(! [X0,X1] :
( food(X0,X1) <=>
(
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of beverage
fof(lit_def,axiom,
(! [X0,X1] :
( beverage(X0,X1) <=>
(
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of shake_beverage
fof(lit_def,axiom,
(! [X0,X1] :
( shake_beverage(X0,X1) <=>
(
(
( X0=sK0 & X1=sK3 )
)

|
(
( X1=sK3 )
)

)
)
)
).

%------ Positive definition of event
fof(lit_def,axiom,
(! [X0,X1] :
( event(X0,X1) <=>
(
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of order
fof(lit_def,axiom,
(! [X0,X1] :
( order(X0,X1) <=>
(
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of eventuality
fof(lit_def,axiom,
(! [X0,X1] :
( eventuality(X0,X1) <=>
(
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of nonexistent
fof(lit_def,axiom,
(! [X0,X1] :
( nonexistent(X0,X1) <=>
(
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of act
fof(lit_def,axiom,
(! [X0,X1] :
( act(X0,X1) <=>
(
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of of
fof(lit_def,axiom,
(! [X0,X1,X2] :
( of(X0,X1,X2) <=>
(
(
( X0=sK0 & X1=sK2 & X2=sK1 )
)

|
(
( X1=sK2 & X2=sK1 )
)

)
)
)
).

%------ Positive definition of nonreflexive
fof(lit_def,axiom,
(! [X0,X1] :
( nonreflexive(X0,X1) <=>
(
(
( X0=sK0 & X1=sK4 )
)

|
(
( X1=sK4 )
)

)
)
)
).

%------ Positive definition of agent
fof(lit_def,axiom,
(! [X0,X1,X2] :
( agent(X0,X1,X2) <=>
(
(
( X0=sK0 & X1=sK4 & X2=sK1 )
)

|
(
( X1=sK4 & X2=sK1 )
)

)
)
)
).

%------ Positive definition of patient
fof(lit_def,axiom,
(! [X0,X1,X2] :
( patient(X0,X1,X2) <=>
(
(
( X0=sK0 & X1=sK4 & X2=sK3 )
)

|
(
( X1=sK4 & X2=sK3 )
)

)
)
)
).

% SZS output end Model
```

### Sample solution for SWV017+1

```% SZS output start Model

%------ Positive definition of \$equality_sorted
fof(lit_def,axiom,
(! [X0,X1,X2] :
( \$equality_sorted(X0,X1,X2) <=>
\$false
)
)
).

%------ Negative definition of party_of_protocol
fof(lit_def,axiom,
(! [X0] :
( ~(party_of_protocol(X0)) <=>
\$false
)
)
).

%------ Positive definition of message
fof(lit_def,axiom,
(! [X0] :
( message(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of a_stored
fof(lit_def,axiom,
(! [X0] :
( a_stored(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of fresh_to_b
fof(lit_def,axiom,
(! [X0] :
( fresh_to_b(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 )
)

)
)
)
).

%------ Positive definition of t_holds
fof(lit_def,axiom,
(! [X0] :
( t_holds(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of a_nonce
fof(lit_def,axiom,
(! [X0] :
( a_nonce(X0) <=>
(
(
( X0=iProver_Domain_2 )
)

)
)
)
).

%------ Negative definition of intruder_message
fof(lit_def,axiom,
(! [X0] :
( ~(intruder_message(X0)) <=>
\$false
)
)
).

%------ Positive definition of intruder_holds
fof(lit_def,axiom,
(! [X0] :
( intruder_holds(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of a_key
fof(lit_def,axiom,
(! [X0] :
( a_key(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of fresh_intruder_nonce
fof(lit_def,axiom,
(! [X0] :
( fresh_intruder_nonce(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_a
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_a(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_an_a_nonce
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_an_a_nonce(X0) <=>
(
(
( X0=iProver_Domain_2 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_an_intruder_nonce
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_an_intruder_nonce(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_at
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_at(X0) <=>
(
(
( X0=iProver_Domain_2 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_b
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_b(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_bt
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_bt(X0) <=>
(
(
( X0=iProver_Domain_2 )
)

)
)
)
).

%------ Negative definition of iProver_Flat_encrypt
fof(lit_def,axiom,
(! [X0,X1,X2] :
( ~(iProver_Flat_encrypt(X0,X1,X2)) <=>
(
(
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X2=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_2 )
&
( X2!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 )
)

|
(
( X2=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
)

|
(
( X2=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_generate_b_nonce
fof(lit_def,axiom,
(! [X0,X1] :
( iProver_Flat_generate_b_nonce(X0,X1) <=>
(
(
( X0=iProver_Domain_2 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_2 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_generate_expiration_time
fof(lit_def,axiom,
(! [X0,X1] :
( iProver_Flat_generate_expiration_time(X0,X1) <=>
(
(
( X0=iProver_Domain_2 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_2 )
)

)
)
)
).

%------ Negative definition of iProver_Flat_generate_intruder_nonce
fof(lit_def,axiom,
(! [X0,X1] :
( ~(iProver_Flat_generate_intruder_nonce(X0,X1)) <=>
(
(
( X1=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_generate_key
fof(lit_def,axiom,
(! [X0,X1] :
( iProver_Flat_generate_key(X0,X1) <=>
(
(
( X0=iProver_Domain_1 )
&
( X1!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_2 )
)

)
)
)
).

%------ Negative definition of iProver_Flat_key
fof(lit_def,axiom,
(! [X0,X1,X2] :
( ~(iProver_Flat_key(X0,X1,X2)) <=>
(
(
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 & X2=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_2 & X2=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_pair
fof(lit_def,axiom,
(! [X0,X1,X2] :
( iProver_Flat_pair(X0,X1,X2) <=>
(
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 )
&
( X2!=iProver_Domain_1 )
&
( X2!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X2=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X2=iProver_Domain_2 )
&
( X1!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 )
&
( X2!=iProver_Domain_1 )
&
( X2!=iProver_Domain_2 )
)

)
)
)
).

fof(lit_def,axiom,
(! [X0,X1,X2,X3,X4] :
(
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 )
&
( X2!=iProver_Domain_2 | X3!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_1 & X4=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_2 & X2=iProver_Domain_2 & X3=iProver_Domain_1 & X4=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X2=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X3=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 )
&
( X1!=iProver_Domain_2 | X2!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X4=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 | X3!=iProver_Domain_1 )
&
( X1!=iProver_Domain_2 | X2!=iProver_Domain_2 | X3!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 | X3!=iProver_Domain_1 )
&
( X2!=iProver_Domain_1 )
&
( X3!=iProver_Domain_1 )
&
( X4!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_2 & X2=iProver_Domain_2 & X3=iProver_Domain_1 )
&
( X4!=iProver_Domain_1 )
)

)
)
)
).

%------ Negative definition of iProver_Flat_sent
fof(lit_def,axiom,
(! [X0,X1,X2,X3] :
( ~(iProver_Flat_sent(X0,X1,X2,X3)) <=>
(
(
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 )
&
( X3!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X2=iProver_Domain_1 & X3=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_1 & X3=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 & X3=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 )
)

|
(
( X3=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_1 )
)

)
)
)
).

%------ Positive definition of iProver_Flat_t
fof(lit_def,axiom,
(! [X0] :
( iProver_Flat_t(X0) <=>
(
(
( X0=iProver_Domain_1 )
)

)
)
)
).

%------ Negative definition of iProver_Flat_triple
fof(lit_def,axiom,
(! [X0,X1,X2,X3] :
( ~(iProver_Flat_triple(X0,X1,X2,X3)) <=>
(
(
( X0=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_2 )
&
( X2!=iProver_Domain_1 )
&
( X3!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_1 )
&
( X3!=iProver_Domain_1 )
&
( X3!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 )
&
( X3!=iProver_Domain_1 )
&
( X3!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_1 & X3=iProver_Domain_2 )
&
( X1!=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_1 )
&
( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 )
&
( X1!=iProver_Domain_2 )
&
( X2!=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X3=iProver_Domain_1 )
)

|
(
( X0=iProver_Domain_2 & X1=iProver_Domain_2 & X2=iProver_Domain_2 )
)

|
(
( X0=iProver_Domain_2 & X2=iProver_Domain_2 & X3=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_1 & X2=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_2 )
&
( X0!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_1 & X2=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_2 )
&
( X0!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 & X3=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
&
( X0!=iProver_Domain_2 | X2!=iProver_Domain_1 )
)

|
(
( X1=iProver_Domain_1 & X3=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X2!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_2 & X2=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_2 )
)

|
(
( X1=iProver_Domain_2 & X2=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
)

|
(
( X2=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
)

|
(
( X2=iProver_Domain_2 & X3=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
&
( X0!=iProver_Domain_2 | X1!=iProver_Domain_1 )
)

|
(
( X2=iProver_Domain_2 & X3=iProver_Domain_2 )
&
( X0!=iProver_Domain_1 | X1!=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 | X1!=iProver_Domain_2 )
&
( X0!=iProver_Domain_2 )
)

|
(
( X3=iProver_Domain_1 )
&
( X0!=iProver_Domain_1 )
&
( X0!=iProver_Domain_2 )
)

)
)
)
).

% SZS output end Model
```

## leanCoP 2.2

Jens Otten
University of Potsdam, Germany

### Sample solution for SEU140+2

```Start of proof for SEU140+2.p
%-----------------------------------------------------
fof(t63_xboole_1,conjecture,![_G24899, _G24902, _G24905]: (subset(_G24899, _G24902)&disjoint(_G24902, _G24905)=>disjoint(_G24899, _G24905)),file('SEU140+2.p',t63_xboole_1)).
fof(d3_tarski,axiom,![_G24976, _G24979]: (subset(_G24976, _G24979)<=>![_G24985]: (in(_G24985, _G24976)=>in(_G24985, _G24979))),file('SEU140+2.p',d3_tarski)).
fof(t3_xboole_0,lemma,![_G25040, _G25043]: (~ (~disjoint(_G25040, _G25043)&![_G25051]: ~ (in(_G25051, _G25040)&in(_G25051, _G25043)))& ~ (?[_G25051]: (in(_G25051, _G25040)&in(_G25051, _G25043))&disjoint(_G25040, _G25043))),file('SEU140+2.p',t3_xboole_0)).

cnf(1, plain, [-subset(11^[], 12^[])], clausify(t63_xboole_1)).
cnf(2, plain, [-disjoint(12^[], 13^[])], clausify(t63_xboole_1)).
cnf(3, plain, [disjoint(11^[], 13^[])], clausify(t63_xboole_1)).
cnf(4, plain, [subset(_G2576, _G2577), in(_G2581, _G2576), -in(_G2581, _G2577)], clausify(d3_tarski)).
cnf(5, plain, [-disjoint(_G2968, _G2969), -in(9^[_G2969, _G2968], _G2968)], clausify(t3_xboole_0)).
cnf(6, plain, [-disjoint(_G2968, _G2969), -in(9^[_G2969, _G2968], _G2969)], clausify(t3_xboole_0)).
cnf(7, plain, [disjoint(_G2968, _G2969), in(_G2975, _G2968), in(_G2975, _G2969)], clausify(t3_xboole_0)).

cnf('1',plain,[disjoint(12^[], 13^[]), in(9^[13^[], 11^[]], 12^[]), in(9^[13^[], 11^[]], 13^[])],start(7,bind([[_G2968, _G2975, _G2969], [12^[], 9^[13^[], 11^[]], 13^[]]]))).
cnf('1.1',plain,[-disjoint(12^[], 13^[])],extension(2)).
cnf('1.2',plain,[-in(9^[13^[], 11^[]], 12^[]), subset(11^[], 12^[]), in(9^[13^[], 11^[]], 11^[])],extension(4,bind([[_G2577, _G2581, _G2576], [12^[], 9^[13^[], 11^[]], 11^[]]]))).
cnf('1.2.1',plain,[-subset(11^[], 12^[])],extension(1)).
cnf('1.2.2',plain,[-in(9^[13^[], 11^[]], 11^[]), -disjoint(11^[], 13^[])],extension(5,bind([[_G2968, _G2969], [11^[], 13^[]]]))).
cnf('1.2.2.1',plain,[disjoint(11^[], 13^[])],extension(3)).
cnf('1.3',plain,[-in(9^[13^[], 11^[]], 13^[]), -disjoint(11^[], 13^[])],extension(6,bind([[_G2968, _G2969], [11^[], 13^[]]]))).
cnf('1.3.1',plain,[disjoint(11^[], 13^[])],extension(3)).
%-----------------------------------------------------
End of proof for SEU140+2.p
```

## Metis 2.3

Joe Hurd
Galois Inc., USA

Metis uses the following proof steps ...

```(* ========================================================================= *)
(* A LOGICAL KERNEL FOR FIRST ORDER CLAUSAL THEOREMS                         *)
(* ========================================================================= *)

signature Thm =
sig

(* ------------------------------------------------------------------------- *)
(* An abstract type of first order logic theorems.                           *)
(* ------------------------------------------------------------------------- *)

type thm

(* ------------------------------------------------------------------------- *)
(* Primitive rules of inference.                                             *)
(* ------------------------------------------------------------------------- *)

(* ------------------------------------------------------------------------- *)
(*                                                                           *)
(* ----- axiom C                                                             *)
(*   C                                                                       *)
(* ------------------------------------------------------------------------- *)

val axiom : clause -> thm

(* ------------------------------------------------------------------------- *)
(*                                                                           *)
(* ----------- assume L                                                      *)
(*   L \/ ~L                                                                 *)
(* ------------------------------------------------------------------------- *)

val assume : literal -> thm

(* ------------------------------------------------------------------------- *)
(*    C                                                                      *)
(* -------- subst s                                                          *)
(*   C[s]                                                                    *)
(* ------------------------------------------------------------------------- *)

val subst : subst -> thm -> thm

(* ------------------------------------------------------------------------- *)
(*   L \/ C    ~L \/ D                                                       *)
(* --------------------- resolve L                                           *)
(*        C \/ D                                                             *)
(*                                                                           *)
(* The literal L must occur in the first theorem, and the literal ~L must    *)
(* occur in the second theorem.                                              *)
(* ------------------------------------------------------------------------- *)

val resolve : literal -> thm -> thm -> thm

(* ------------------------------------------------------------------------- *)
(*                                                                           *)
(* --------- refl t                                                          *)
(*   t = t                                                                   *)
(* ------------------------------------------------------------------------- *)

val refl : term -> thm

(* ------------------------------------------------------------------------- *)
(*                                                                           *)
(* ------------------------ equality L p t                                   *)
(*   ~(s = t) \/ ~L \/ L'                                                    *)
(*                                                                           *)
(* where s is the subterm of L at path p, and L' is L with the subterm at    *)
(* path p being replaced by t.                                               *)
(* ------------------------------------------------------------------------- *)

val equality : literal -> path -> term -> thm

end
```

### Sample solution for SEU140+2

```SZS status Theorem for data/problems/all/SEU140+2.tptp

SZS output start CNFRefutation for data/problems/all/SEU140+2.tptp
fof(commutativity_k2_xboole_0, axiom,
(! [A, B] : set_union2(A, B) = set_union2(B, A))).

fof(d3_xboole_0, axiom,
(! [A, B, C] :
(C = set_intersection2(A, B) <=>
! [D] : (in(D, C) <=> (in(D, A) & in(D, B)))))).

fof(d4_xboole_0, axiom,
(! [A, B, C] :
(C = set_difference(A, B) <=>
! [D] : (in(D, C) <=> (in(D, A) & ~ in(D, B)))))).

fof(d7_xboole_0, axiom,
(! [A, B] : (disjoint(A, B) <=> set_intersection2(A, B) = empty_set))).

fof(symmetry_r1_xboole_0, axiom,
(! [A, B] : (disjoint(A, B) => disjoint(B, A)))).

fof(t12_xboole_1, lemma,
(! [A, B] : (subset(A, B) => set_union2(A, B) = B))).

fof(t1_boole, axiom, (! [A] : set_union2(A, empty_set) = A)).

fof(t2_boole, axiom,
(! [A] : set_intersection2(A, empty_set) = empty_set)).

fof(t36_xboole_1, lemma, (! [A, B] : subset(set_difference(A, B), A))).

fof(t39_xboole_1, lemma,
(! [A, B] : set_union2(A, set_difference(B, A)) = set_union2(A, B))).

fof(t3_boole, axiom, (! [A] : set_difference(A, empty_set) = A)).

fof(t3_xboole_0, lemma,
(! [A, B] :
(~ (~ disjoint(A, B) & ! [C] : ~ (in(C, A) & in(C, B))) &
~ (? [C] : (in(C, A) & in(C, B)) & disjoint(A, B))))).

fof(t40_xboole_1, lemma,
(! [A, B] :
set_difference(set_union2(A, B), B) = set_difference(A, B))).

fof(t48_xboole_1, lemma,
(! [A, B] :
set_difference(A, set_difference(A, B)) = set_intersection2(A, B))).

fof(t63_xboole_1, conjecture,
(! [A, B, C] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C)))).

fof(subgoal_0, plain,
(! [A, B, C] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))),
inference(strip, [], [t63_xboole_1])).

fof(negate_0_0, plain,
(~ ! [A, B, C] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))),
inference(negate, [], [subgoal_0])).

fof(normalize_0_0, plain, (! [A, B] : (~ disjoint(A, B) | disjoint(B, A))),
inference(canonicalize, [], [symmetry_r1_xboole_0])).

fof(normalize_0_1, plain, (! [A, B] : (~ disjoint(A, B) | disjoint(B, A))),
inference(specialize, [], [normalize_0_0])).

fof(normalize_0_2, plain,
(! [A, B] : (~ disjoint(A, B) | ! [C] : (~ in(C, A) | ~ in(C, B))) &
! [A, B] : (disjoint(A, B) | ? [C] : (in(C, A) & in(C, B)))),
inference(canonicalize, [], [t3_xboole_0])).

fof(normalize_0_3, plain,
(! [A, B] : (disjoint(A, B) | ? [C] : (in(C, A) & in(C, B)))),
inference(conjunct, [], [normalize_0_2])).

fof(normalize_0_4, plain,
(! [A, B] : (disjoint(A, B) | ? [C] : (in(C, A) & in(C, B)))),
inference(specialize, [], [normalize_0_3])).

fof(normalize_0_5, plain,
(! [A, B] :
((disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), A)) &
(disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), B)))),
inference(clausify, [], [normalize_0_4])).

fof(normalize_0_6, plain,
(! [A, B] : (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), B))),
inference(conjunct, [], [normalize_0_5])).

fof(normalize_0_7, plain,
(! [A, B, C] :
(C != set_intersection2(A, B) <=>
? [D] : (~ in(D, C) <=> (in(D, A) & in(D, B))))),
inference(canonicalize, [], [d3_xboole_0])).

fof(normalize_0_8, plain,
(! [A, B, C] :
(C != set_intersection2(A, B) <=>
? [D] : (~ in(D, C) <=> (in(D, A) & in(D, B))))),
inference(specialize, [], [normalize_0_7])).

fof(normalize_0_9, plain,
(! [A, B, C, D] :
((C != set_intersection2(A, B) | ~ in(D, C) | in(D, A)) &
(C != set_intersection2(A, B) | ~ in(D, C) | in(D, B)) &
(C = set_intersection2(A, B) | in(skolemFOFtoCNF_D_1(A, B, C), A) |
in(skolemFOFtoCNF_D_1(A, B, C), C)) &
(C = set_intersection2(A, B) | in(skolemFOFtoCNF_D_1(A, B, C), B) |
in(skolemFOFtoCNF_D_1(A, B, C), C)) &
(C != set_intersection2(A, B) | ~ in(D, A) | ~ in(D, B) |
in(D, C)) &
(~ in(skolemFOFtoCNF_D_1(A, B, C), A) |
~ in(skolemFOFtoCNF_D_1(A, B, C), B) |
~ in(skolemFOFtoCNF_D_1(A, B, C), C) |
C = set_intersection2(A, B)))),
inference(clausify, [], [normalize_0_8])).

fof(normalize_0_10, plain,
(! [A, B, C, D] :
(C != set_intersection2(A, B) | ~ in(D, C) | in(D, B))),
inference(conjunct, [], [normalize_0_9])).

fof(normalize_0_11, plain,
(! [A, B] :
set_difference(A, set_difference(A, B)) = set_intersection2(A, B)),
inference(canonicalize, [], [t48_xboole_1])).

fof(normalize_0_12, plain,
(! [A, B] :
set_difference(A, set_difference(A, B)) = set_intersection2(A, B)),
inference(specialize, [], [normalize_0_11])).

fof(normalize_0_13, plain,
(! [A, B] :
set_difference(set_union2(A, B), B) = set_difference(A, B)),
inference(canonicalize, [], [t40_xboole_1])).

fof(normalize_0_14, plain,
(! [A, B] :
set_difference(set_union2(A, B), B) = set_difference(A, B)),
inference(specialize, [], [normalize_0_13])).

fof(normalize_0_15, plain,
(! [A, B] : set_union2(A, set_difference(B, A)) = set_union2(A, B)),
inference(canonicalize, [], [t39_xboole_1])).

fof(normalize_0_16, plain,
(! [A, B] : set_union2(A, set_difference(B, A)) = set_union2(A, B)),
inference(specialize, [], [normalize_0_15])).

fof(normalize_0_17, plain,
(! [A, B] : set_union2(A, B) = set_union2(B, A)),
inference(canonicalize, [], [commutativity_k2_xboole_0])).

fof(normalize_0_18, plain,
(! [A, B] : set_union2(A, B) = set_union2(B, A)),
inference(specialize, [], [normalize_0_17])).

fof(normalize_0_19, plain, (! [A] : set_difference(A, empty_set) = A),
inference(canonicalize, [], [t3_boole])).

fof(normalize_0_20, plain, (! [A] : set_difference(A, empty_set) = A),
inference(specialize, [], [normalize_0_19])).

fof(normalize_0_21, plain,
(! [A] : set_intersection2(A, empty_set) = empty_set),
inference(canonicalize, [], [t2_boole])).

fof(normalize_0_22, plain,
(! [A] : set_intersection2(A, empty_set) = empty_set),
inference(specialize, [], [normalize_0_21])).

fof(normalize_0_23, plain,
(? [A, B, C] : (~ disjoint(A, C) & disjoint(B, C) & subset(A, B))),
inference(canonicalize, [], [negate_0_0])).

fof(normalize_0_24, plain,
(~ disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4) &
disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) &
subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(skolemize, [], [normalize_0_23])).

fof(normalize_0_25, plain,
(subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(conjunct, [], [normalize_0_24])).

fof(normalize_0_26, plain,
(! [A, B] : (~ subset(A, B) | set_union2(A, B) = B)),
inference(canonicalize, [], [t12_xboole_1])).

fof(normalize_0_27, plain,
(! [A, B] : (~ subset(A, B) | set_union2(A, B) = B)),
inference(specialize, [], [normalize_0_26])).

fof(normalize_0_28, plain,
(! [A, B] : (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), A))),
inference(conjunct, [], [normalize_0_5])).

fof(normalize_0_29, plain,
(! [A, B, C] :
(C != set_difference(A, B) <=>
? [D] : (~ in(D, C) <=> (~ in(D, B) & in(D, A))))),
inference(canonicalize, [], [d4_xboole_0])).

fof(normalize_0_30, plain,
(! [A, B, C] :
(C != set_difference(A, B) <=>
? [D] : (~ in(D, C) <=> (~ in(D, B) & in(D, A))))),
inference(specialize, [], [normalize_0_29])).

fof(normalize_0_31, plain,
(! [A, B, C, D] :
((C != set_difference(A, B) | ~ in(D, B) | ~ in(D, C)) &
(C != set_difference(A, B) | ~ in(D, C) | in(D, A)) &
(~ in(skolemFOFtoCNF_D_2(A, B, C), B) | C = set_difference(A, B) |
in(skolemFOFtoCNF_D_2(A, B, C), C)) &
(C = set_difference(A, B) | in(skolemFOFtoCNF_D_2(A, B, C), A) |
in(skolemFOFtoCNF_D_2(A, B, C), C)) &
(C != set_difference(A, B) | ~ in(D, A) | in(D, B) | in(D, C)) &
(~ in(skolemFOFtoCNF_D_2(A, B, C), A) |
~ in(skolemFOFtoCNF_D_2(A, B, C), C) | C = set_difference(A, B) |
in(skolemFOFtoCNF_D_2(A, B, C), B)))),
inference(clausify, [], [normalize_0_30])).

fof(normalize_0_32, plain,
(! [A, B, C, D] :
(C != set_difference(A, B) | ~ in(D, B) | ~ in(D, C))),
inference(conjunct, [], [normalize_0_31])).

fof(normalize_0_33, plain, (! [A, B] : subset(set_difference(A, B), A)),
inference(canonicalize, [], [t36_xboole_1])).

fof(normalize_0_34, plain, (! [A, B] : subset(set_difference(A, B), A)),
inference(specialize, [], [normalize_0_33])).

fof(normalize_0_35, plain,
(disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)),
inference(conjunct, [], [normalize_0_24])).

fof(normalize_0_36, plain,
(! [A, B] :
(set_intersection2(A, B) != empty_set <=> ~ disjoint(A, B))),
inference(canonicalize, [], [d7_xboole_0])).

fof(normalize_0_37, plain,
(! [A, B] :
(set_intersection2(A, B) != empty_set <=> ~ disjoint(A, B))),
inference(specialize, [], [normalize_0_36])).

fof(normalize_0_38, plain,
(! [A, B] :
((set_intersection2(A, B) != empty_set | disjoint(A, B)) &
(~ disjoint(A, B) | set_intersection2(A, B) = empty_set))),
inference(clausify, [], [normalize_0_37])).

fof(normalize_0_39, plain,
(! [A, B] : (~ disjoint(A, B) | set_intersection2(A, B) = empty_set)),
inference(conjunct, [], [normalize_0_38])).

fof(normalize_0_40, plain, (! [A] : set_union2(A, empty_set) = A),
inference(canonicalize, [], [t1_boole])).

fof(normalize_0_41, plain, (! [A] : set_union2(A, empty_set) = A),
inference(specialize, [], [normalize_0_40])).

fof(normalize_0_42, plain,
(~ disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)),
inference(conjunct, [], [normalize_0_24])).

cnf(refute_0_0, plain, (~ disjoint(A, B) | disjoint(B, A)),
inference(canonicalize, [], [normalize_0_1])).

cnf(refute_0_1, plain,
(~ disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2) |
disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)),
inference(subst, [],
[refute_0_0 :
[bind(A, \$fot(skolemFOFtoCNF_C_4)),
bind(B, \$fot(skolemFOFtoCNF_A_2))]])).

cnf(refute_0_2, plain, (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), B)),
inference(canonicalize, [], [normalize_0_6])).

cnf(refute_0_3, plain,
(disjoint(A, skolemFOFtoCNF_A_2) |
in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_A_2)),
inference(subst, [],
[refute_0_2 : [bind(B, \$fot(skolemFOFtoCNF_A_2))]])).

cnf(refute_0_4, plain,
(C != set_intersection2(A, B) | ~ in(D, C) | in(D, B)),
inference(canonicalize, [], [normalize_0_10])).

cnf(refute_0_5, plain,
(set_intersection2(A, B) != set_intersection2(A, B) |
~ in(D, set_intersection2(A, B)) | in(D, B)),
inference(subst, [],
[refute_0_4 : [bind(C, \$fot(set_intersection2(A, B)))]])).

cnf(refute_0_6, plain, (set_intersection2(A, B) = set_intersection2(A, B)),
introduced(tautology, [refl, [\$fot(set_intersection2(A, B))]])).

cnf(refute_0_7, plain, (~ in(D, set_intersection2(A, B)) | in(D, B)),
inference(resolve,
[\$cnf(\$equal(set_intersection2(A, B),
set_intersection2(A, B)))],
[refute_0_6, refute_0_5])).

cnf(refute_0_8, plain,
(~
in(X_311,
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) |
in(X_311, skolemFOFtoCNF_B_1)),
inference(subst, [],
[refute_0_7 :
[bind(A, \$fot(skolemFOFtoCNF_A_2)),
bind(B, \$fot(skolemFOFtoCNF_B_1)),
bind(D, \$fot(X_311))]])).

cnf(refute_0_9, plain,
(set_difference(A, set_difference(A, B)) = set_intersection2(A, B)),
inference(canonicalize, [], [normalize_0_12])).

cnf(refute_0_10, plain,
(set_difference(skolemFOFtoCNF_A_2,
set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(subst, [],
[refute_0_9 :
[bind(A, \$fot(skolemFOFtoCNF_A_2)),
bind(B, \$fot(skolemFOFtoCNF_B_1))]])).

cnf(refute_0_11, plain,
(set_difference(set_union2(A, B), B) = set_difference(A, B)),
inference(canonicalize, [], [normalize_0_14])).

cnf(refute_0_12, plain,
(set_difference(set_union2(set_union2(X_80, X_79),
set_union2(X_79, X_80)), set_union2(X_79, X_80)) =
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))),
inference(subst, [],
[refute_0_11 :
[bind(A, \$fot(set_union2(X_80, X_79))),
bind(B, \$fot(set_union2(X_79, X_80)))]])).

cnf(refute_0_13, plain,
(set_union2(A, set_difference(B, A)) = set_union2(A, B)),
inference(canonicalize, [], [normalize_0_16])).

cnf(refute_0_14, plain,
(set_union2(A, set_difference(set_union2(X_65, A), A)) =
set_union2(A, set_union2(X_65, A))),
inference(subst, [],
[refute_0_13 : [bind(B, \$fot(set_union2(X_65, A)))]])).

cnf(refute_0_15, plain,
(set_difference(set_union2(X_65, A), A) = set_difference(X_65, A)),
inference(subst, [],
[refute_0_11 : [bind(A, \$fot(X_65)), bind(B, \$fot(A))]])).

cnf(refute_0_16, plain,
(set_difference(set_union2(X_65, A), A) != set_difference(X_65, A) |
set_union2(A, set_difference(set_union2(X_65, A), A)) !=
set_union2(A, set_union2(X_65, A)) |
set_union2(A, set_difference(X_65, A)) =
set_union2(A, set_union2(X_65, A))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(A,
set_difference(set_union2(X_65, A), A)),
set_union2(A, set_union2(X_65, A)))), [0, 1],
\$fot(set_difference(X_65, A))]])).

cnf(refute_0_17, plain,
(set_union2(A, set_difference(set_union2(X_65, A), A)) !=
set_union2(A, set_union2(X_65, A)) |
set_union2(A, set_difference(X_65, A)) =
set_union2(A, set_union2(X_65, A))),
inference(resolve,
[\$cnf(\$equal(set_difference(set_union2(X_65, A), A),
set_difference(X_65, A)))],
[refute_0_15, refute_0_16])).

cnf(refute_0_18, plain,
(set_union2(A, set_difference(X_65, A)) =
set_union2(A, set_union2(X_65, A))),
inference(resolve,
[\$cnf(\$equal(set_union2(A,
set_difference(set_union2(X_65, A), A)),
set_union2(A, set_union2(X_65, A))))],
[refute_0_14, refute_0_17])).

cnf(refute_0_19, plain,
(set_union2(A, set_difference(X_65, A)) = set_union2(A, X_65)),
inference(subst, [], [refute_0_13 : [bind(B, \$fot(X_65))]])).

cnf(refute_0_20, plain,
(set_union2(A, set_difference(X_65, A)) != set_union2(A, X_65) |
set_union2(A, set_difference(X_65, A)) !=
set_union2(A, set_union2(X_65, A)) |
set_union2(A, X_65) = set_union2(A, set_union2(X_65, A))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(A, set_difference(X_65, A)),
set_union2(A, set_union2(X_65, A)))), [0],
\$fot(set_union2(A, X_65))]])).

cnf(refute_0_21, plain,
(set_union2(A, set_difference(X_65, A)) !=
set_union2(A, set_union2(X_65, A)) |
set_union2(A, X_65) = set_union2(A, set_union2(X_65, A))),
inference(resolve,
[\$cnf(\$equal(set_union2(A, set_difference(X_65, A)),
set_union2(A, X_65)))], [refute_0_19, refute_0_20])).

cnf(refute_0_22, plain,
(set_union2(A, X_65) = set_union2(A, set_union2(X_65, A))),
inference(resolve,
[\$cnf(\$equal(set_union2(A, set_difference(X_65, A)),
set_union2(A, set_union2(X_65, A))))],
[refute_0_18, refute_0_21])).

cnf(refute_0_23, plain,
(set_union2(set_union2(X_76, X_65), X_65) =
set_union2(set_union2(X_76, X_65),
set_union2(X_65, set_union2(X_76, X_65)))),
inference(subst, [],
[refute_0_22 : [bind(A, \$fot(set_union2(X_76, X_65)))]])).

cnf(refute_0_24, plain,
(set_union2(X_65, X_76) = set_union2(X_65, set_union2(X_76, X_65))),
inference(subst, [],
[refute_0_22 :
[bind(A, \$fot(X_65)), bind(X_65, \$fot(X_76))]])).

cnf(refute_0_25, plain, (X = X), introduced(tautology, [refl, [\$fot(X)]])).

cnf(refute_0_26, plain, (X != X | X != Y | Y = X),
introduced(tautology, [equality, [\$cnf(\$equal(X, X)), [0], \$fot(Y)]])).

cnf(refute_0_27, plain, (X != Y | Y = X),
inference(resolve, [\$cnf(\$equal(X, X))], [refute_0_25, refute_0_26])).

cnf(refute_0_28, plain,
(set_union2(X_65, X_76) != set_union2(X_65, set_union2(X_76, X_65)) |
set_union2(X_65, set_union2(X_76, X_65)) = set_union2(X_65, X_76)),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(set_union2(X_65, X_76))),
bind(Y,
\$fot(set_union2(X_65, set_union2(X_76, X_65))))]])).

cnf(refute_0_29, plain,
(set_union2(X_65, set_union2(X_76, X_65)) = set_union2(X_65, X_76)),
inference(resolve,
[\$cnf(\$equal(set_union2(X_65, X_76),
set_union2(X_65, set_union2(X_76, X_65))))],
[refute_0_24, refute_0_28])).

cnf(refute_0_30, plain,
(set_union2(X_65, set_union2(X_76, X_65)) != set_union2(X_65, X_76) |
set_union2(set_union2(X_76, X_65), X_65) !=
set_union2(set_union2(X_76, X_65),
set_union2(X_65, set_union2(X_76, X_65))) |
set_union2(set_union2(X_76, X_65), X_65) =
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_union2(X_76, X_65), X_65),
set_union2(set_union2(X_76, X_65),
set_union2(X_65, set_union2(X_76, X_65))))),
[1, 1], \$fot(set_union2(X_65, X_76))]])).

cnf(refute_0_31, plain,
(set_union2(set_union2(X_76, X_65), X_65) !=
set_union2(set_union2(X_76, X_65),
set_union2(X_65, set_union2(X_76, X_65))) |
set_union2(set_union2(X_76, X_65), X_65) =
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))),
inference(resolve,
[\$cnf(\$equal(set_union2(X_65, set_union2(X_76, X_65)),
set_union2(X_65, X_76)))],
[refute_0_29, refute_0_30])).

cnf(refute_0_32, plain,
(set_union2(set_union2(X_76, X_65), X_65) =
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))),
inference(resolve,
[\$cnf(\$equal(set_union2(set_union2(X_76, X_65), X_65),
set_union2(set_union2(X_76, X_65),
set_union2(X_65, set_union2(X_76, X_65)))))],
[refute_0_23, refute_0_31])).

cnf(refute_0_33, plain, (set_union2(A, B) = set_union2(B, A)),
inference(canonicalize, [], [normalize_0_18])).

cnf(refute_0_34, plain,
(set_union2(A, B) != set_union2(B, A) |
set_union2(B, A) = set_union2(A, B)),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(set_union2(A, B))),
bind(Y, \$fot(set_union2(B, A)))]])).

cnf(refute_0_35, plain, (set_union2(B, A) = set_union2(A, B)),
inference(resolve, [\$cnf(\$equal(set_union2(A, B), set_union2(B, A)))],
[refute_0_33, refute_0_34])).

cnf(refute_0_36, plain,
(set_union2(set_union2(X_76, X_65), X_65) =
set_union2(X_65, set_union2(X_76, X_65))),
inference(subst, [],
[refute_0_35 :
[bind(A, \$fot(X_65)),
bind(B, \$fot(set_union2(X_76, X_65)))]])).

cnf(refute_0_37, plain, (Y != X | Y != Z | X = Z),
introduced(tautology, [equality, [\$cnf(\$equal(Y, Z)), [0], \$fot(X)]])).

cnf(refute_0_38, plain, (X != Y | Y != Z | X = Z),
inference(resolve, [\$cnf(\$equal(Y, X))], [refute_0_27, refute_0_37])).

cnf(refute_0_39, plain,
(set_union2(X_65, set_union2(X_76, X_65)) != set_union2(X_65, X_76) |
set_union2(set_union2(X_76, X_65), X_65) !=
set_union2(X_65, set_union2(X_76, X_65)) |
set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, X_76)),
inference(subst, [],
[refute_0_38 :
[bind(X, \$fot(set_union2(set_union2(X_76, X_65), X_65))),
bind(Y, \$fot(set_union2(X_65, set_union2(X_76, X_65)))),
bind(Z, \$fot(set_union2(X_65, X_76)))]])).

cnf(refute_0_40, plain,
(set_union2(X_65, set_union2(X_76, X_65)) != set_union2(X_65, X_76) |
set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, X_76)),
inference(resolve,
[\$cnf(\$equal(set_union2(set_union2(X_76, X_65), X_65),
set_union2(X_65, set_union2(X_76, X_65))))],
[refute_0_36, refute_0_39])).

cnf(refute_0_41, plain,
(set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, X_76)),
inference(resolve,
[\$cnf(\$equal(set_union2(X_65, set_union2(X_76, X_65)),
set_union2(X_65, X_76)))],
[refute_0_29, refute_0_40])).

cnf(refute_0_42, plain,
(set_union2(set_union2(X_76, X_65), X_65) != set_union2(X_65, X_76) |
set_union2(set_union2(X_76, X_65), X_65) !=
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76)) |
set_union2(X_65, X_76) =
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_union2(X_76, X_65), X_65),
set_union2(set_union2(X_76, X_65),
set_union2(X_65, X_76)))), [0],
\$fot(set_union2(X_65, X_76))]])).

cnf(refute_0_43, plain,
(set_union2(set_union2(X_76, X_65), X_65) !=
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76)) |
set_union2(X_65, X_76) =
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))),
inference(resolve,
[\$cnf(\$equal(set_union2(set_union2(X_76, X_65), X_65),
set_union2(X_65, X_76)))],
[refute_0_41, refute_0_42])).

cnf(refute_0_44, plain,
(set_union2(X_65, X_76) =
set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))),
inference(resolve,
[\$cnf(\$equal(set_union2(set_union2(X_76, X_65), X_65),
set_union2(set_union2(X_76, X_65),
set_union2(X_65, X_76))))],
[refute_0_32, refute_0_43])).

cnf(refute_0_45, plain,
(set_union2(X_79, X_80) =
set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80))),
inference(subst, [],
[refute_0_44 :
[bind(X_65, \$fot(X_79)), bind(X_76, \$fot(X_80))]])).

cnf(refute_0_46, plain,
(set_union2(X_79, X_80) !=
set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) =
set_union2(X_79, X_80)),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(set_union2(X_79, X_80))),
bind(Y,
\$fot(set_union2(set_union2(X_80, X_79),
set_union2(X_79, X_80))))]])).

cnf(refute_0_47, plain,
(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) =
set_union2(X_79, X_80)),
inference(resolve,
[\$cnf(\$equal(set_union2(X_79, X_80),
set_union2(set_union2(X_80, X_79),
set_union2(X_79, X_80))))],
[refute_0_45, refute_0_46])).

cnf(refute_0_48, plain,
(set_difference(set_union2(set_union2(X_80, X_79),
set_union2(X_79, X_80)), set_union2(X_79, X_80)) !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) !=
set_union2(X_79, X_80) |
set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) =
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_difference(set_union2(set_union2(X_80,
X_79), set_union2(X_79, X_80)),
set_union2(X_79, X_80)),
set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80)))), [0, 0],
\$fot(set_union2(X_79, X_80))]])).

cnf(refute_0_49, plain,
(set_difference(set_union2(set_union2(X_80, X_79),
set_union2(X_79, X_80)), set_union2(X_79, X_80)) !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) =
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))),
inference(resolve,
[\$cnf(\$equal(set_union2(set_union2(X_80, X_79),
set_union2(X_79, X_80)), set_union2(X_79, X_80)))],
[refute_0_47, refute_0_48])).

cnf(refute_0_50, plain,
(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) =
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))),
inference(resolve,
[\$cnf(\$equal(set_difference(set_union2(set_union2(X_80,
X_79), set_union2(X_79, X_80)),
set_union2(X_79, X_80)),
set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80))))],
[refute_0_12, refute_0_49])).

cnf(refute_0_51, plain,
(set_difference(X_50, set_difference(X_50, empty_set)) =
set_intersection2(X_50, empty_set)),
inference(subst, [],
[refute_0_9 :
[bind(A, \$fot(X_50)), bind(B, \$fot(empty_set))]])).

cnf(refute_0_52, plain, (set_difference(A, empty_set) = A),
inference(canonicalize, [], [normalize_0_20])).

cnf(refute_0_53, plain, (set_difference(X_50, empty_set) = X_50),
inference(subst, [], [refute_0_52 : [bind(A, \$fot(X_50))]])).

cnf(refute_0_54, plain,
(set_difference(X_50, empty_set) != X_50 |
set_difference(X_50, set_difference(X_50, empty_set)) !=
set_intersection2(X_50, empty_set) |
set_difference(X_50, X_50) = set_intersection2(X_50, empty_set)),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_difference(X_50,
set_difference(X_50, empty_set)),
set_intersection2(X_50, empty_set))), [0, 1],
\$fot(X_50)]])).

cnf(refute_0_55, plain,
(set_difference(X_50, set_difference(X_50, empty_set)) !=
set_intersection2(X_50, empty_set) |
set_difference(X_50, X_50) = set_intersection2(X_50, empty_set)),
inference(resolve,
[\$cnf(\$equal(set_difference(X_50, empty_set), X_50))],
[refute_0_53, refute_0_54])).

cnf(refute_0_56, plain,
(set_difference(X_50, X_50) = set_intersection2(X_50, empty_set)),
inference(resolve,
[\$cnf(\$equal(set_difference(X_50,
set_difference(X_50, empty_set)),
set_intersection2(X_50, empty_set)))],
[refute_0_51, refute_0_55])).

cnf(refute_0_57, plain, (set_intersection2(A, empty_set) = empty_set),
inference(canonicalize, [], [normalize_0_22])).

cnf(refute_0_58, plain, (set_intersection2(X_50, empty_set) = empty_set),
inference(subst, [], [refute_0_57 : [bind(A, \$fot(X_50))]])).

cnf(refute_0_59, plain,
(set_difference(X_50, X_50) != set_intersection2(X_50, empty_set) |
set_intersection2(X_50, empty_set) != empty_set |
set_difference(X_50, X_50) = empty_set),
introduced(tautology,
[equality,
[\$cnf(~ \$equal(set_difference(X_50, X_50), empty_set)),
[0], \$fot(set_intersection2(X_50, empty_set))]])).

cnf(refute_0_60, plain,
(set_difference(X_50, X_50) != set_intersection2(X_50, empty_set) |
set_difference(X_50, X_50) = empty_set),
inference(resolve,
[\$cnf(\$equal(set_intersection2(X_50, empty_set),
empty_set))], [refute_0_58, refute_0_59])).

cnf(refute_0_61, plain, (set_difference(X_50, X_50) = empty_set),
inference(resolve,
[\$cnf(\$equal(set_difference(X_50, X_50),
set_intersection2(X_50, empty_set)))],
[refute_0_56, refute_0_60])).

cnf(refute_0_62, plain,
(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) =
empty_set),
inference(subst, [],
[refute_0_61 : [bind(X_50, \$fot(set_union2(X_79, X_80)))]])).

cnf(refute_0_63, plain,
(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) !=
empty_set |
set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
empty_set =
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_difference(set_union2(X_79, X_80),
set_union2(X_79, X_80)),
set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80)))), [0],
\$fot(empty_set)]])).

cnf(refute_0_64, plain,
(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
empty_set =
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))),
inference(resolve,
[\$cnf(\$equal(set_difference(set_union2(X_79, X_80),
set_union2(X_79, X_80)), empty_set))],
[refute_0_62, refute_0_63])).

cnf(refute_0_65, plain,
(set_difference(set_union2(A, set_union2(X_76, A)),
set_union2(X_76, A)) = set_difference(A, set_union2(X_76, A))),
inference(subst, [],
[refute_0_11 : [bind(B, \$fot(set_union2(X_76, A)))]])).

cnf(refute_0_66, plain,
(set_union2(A, X_76) = set_union2(A, set_union2(X_76, A))),
inference(subst, [], [refute_0_22 : [bind(X_65, \$fot(X_76))]])).

cnf(refute_0_67, plain,
(set_union2(A, X_76) != set_union2(A, set_union2(X_76, A)) |
set_union2(A, set_union2(X_76, A)) = set_union2(A, X_76)),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(set_union2(A, X_76))),
bind(Y, \$fot(set_union2(A, set_union2(X_76, A))))]])).

cnf(refute_0_68, plain,
(set_union2(A, set_union2(X_76, A)) = set_union2(A, X_76)),
inference(resolve,
[\$cnf(\$equal(set_union2(A, X_76),
set_union2(A, set_union2(X_76, A))))],
[refute_0_66, refute_0_67])).

cnf(refute_0_69, plain,
(set_difference(set_union2(A, set_union2(X_76, A)),
set_union2(X_76, A)) != set_difference(A, set_union2(X_76, A)) |
set_union2(A, set_union2(X_76, A)) != set_union2(A, X_76) |
set_difference(set_union2(A, X_76), set_union2(X_76, A)) =
set_difference(A, set_union2(X_76, A))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_difference(set_union2(A,
set_union2(X_76, A)), set_union2(X_76, A)),
set_difference(A, set_union2(X_76, A)))), [0, 0],
\$fot(set_union2(A, X_76))]])).

cnf(refute_0_70, plain,
(set_difference(set_union2(A, set_union2(X_76, A)),
set_union2(X_76, A)) != set_difference(A, set_union2(X_76, A)) |
set_difference(set_union2(A, X_76), set_union2(X_76, A)) =
set_difference(A, set_union2(X_76, A))),
inference(resolve,
[\$cnf(\$equal(set_union2(A, set_union2(X_76, A)),
set_union2(A, X_76)))], [refute_0_68, refute_0_69])).

cnf(refute_0_71, plain,
(set_difference(set_union2(A, X_76), set_union2(X_76, A)) =
set_difference(A, set_union2(X_76, A))),
inference(resolve,
[\$cnf(\$equal(set_difference(set_union2(A,
set_union2(X_76, A)), set_union2(X_76, A)),
set_difference(A, set_union2(X_76, A))))],
[refute_0_65, refute_0_70])).

cnf(refute_0_72, plain,
(set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) =
set_difference(X_80, set_union2(X_79, X_80))),
inference(subst, [],
[refute_0_71 :
[bind(A, \$fot(X_80)), bind(X_76, \$fot(X_79))]])).

cnf(refute_0_73, plain,
(empty_set !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) !=
set_difference(X_80, set_union2(X_79, X_80)) |
empty_set = set_difference(X_80, set_union2(X_79, X_80))),
introduced(tautology,
[equality,
[\$cnf(~ \$equal(empty_set,
set_difference(X_80, set_union2(X_79, X_80)))),
[0],
\$fot(set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80)))]])).

cnf(refute_0_74, plain,
(empty_set !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
empty_set = set_difference(X_80, set_union2(X_79, X_80))),
inference(resolve,
[\$cnf(\$equal(set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80)),
set_difference(X_80, set_union2(X_79, X_80))))],
[refute_0_72, refute_0_73])).

cnf(refute_0_75, plain,
(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) !=
set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) |
empty_set = set_difference(X_80, set_union2(X_79, X_80))),
inference(resolve,
[\$cnf(\$equal(empty_set,
set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80))))],
[refute_0_64, refute_0_74])).

cnf(refute_0_76, plain,
(empty_set = set_difference(X_80, set_union2(X_79, X_80))),
inference(resolve,
[\$cnf(\$equal(set_difference(set_union2(X_79, X_80),
set_union2(X_79, X_80)),
set_difference(set_union2(X_80, X_79),
set_union2(X_79, X_80))))],
[refute_0_50, refute_0_75])).

cnf(refute_0_77, plain,
(empty_set = set_difference(X_82, set_union2(X_81, X_82))),
inference(subst, [],
[refute_0_76 :
[bind(X_79, \$fot(X_81)), bind(X_80, \$fot(X_82))]])).

cnf(refute_0_78, plain, (set_union2(X_82, X_81) = set_union2(X_81, X_82)),
inference(subst, [],
[refute_0_33 : [bind(A, \$fot(X_82)), bind(B, \$fot(X_81))]])).

cnf(refute_0_79, plain,
(set_union2(X_82, X_81) != set_union2(X_81, X_82) |
set_union2(X_81, X_82) = set_union2(X_82, X_81)),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(set_union2(X_82, X_81))),
bind(Y, \$fot(set_union2(X_81, X_82)))]])).

cnf(refute_0_80, plain, (set_union2(X_81, X_82) = set_union2(X_82, X_81)),
inference(resolve,
[\$cnf(\$equal(set_union2(X_82, X_81),
set_union2(X_81, X_82)))],
[refute_0_78, refute_0_79])).

cnf(refute_0_81, plain,
(empty_set != set_difference(X_82, set_union2(X_81, X_82)) |
set_union2(X_81, X_82) != set_union2(X_82, X_81) |
empty_set = set_difference(X_82, set_union2(X_82, X_81))),
introduced(tautology,
[equality,
[\$cnf(\$equal(empty_set,
set_difference(X_82, set_union2(X_81, X_82)))),
[1, 1], \$fot(set_union2(X_82, X_81))]])).

cnf(refute_0_82, plain,
(empty_set != set_difference(X_82, set_union2(X_81, X_82)) |
empty_set = set_difference(X_82, set_union2(X_82, X_81))),
inference(resolve,
[\$cnf(\$equal(set_union2(X_81, X_82),
set_union2(X_82, X_81)))],
[refute_0_80, refute_0_81])).

cnf(refute_0_83, plain,
(empty_set = set_difference(X_82, set_union2(X_82, X_81))),
inference(resolve,
[\$cnf(\$equal(empty_set,
set_difference(X_82, set_union2(X_81, X_82))))],
[refute_0_77, refute_0_82])).

cnf(refute_0_84, plain,
(empty_set =
set_difference(skolemFOFtoCNF_A_2,
set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))),
inference(subst, [],
[refute_0_83 :
[bind(X_81, \$fot(skolemFOFtoCNF_B_1)),
bind(X_82, \$fot(skolemFOFtoCNF_A_2))]])).

cnf(refute_0_85, plain, (subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(canonicalize, [], [normalize_0_25])).

cnf(refute_0_86, plain, (~ subset(A, B) | set_union2(A, B) = B),
inference(canonicalize, [], [normalize_0_27])).

cnf(refute_0_87, plain,
(~ subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) =
skolemFOFtoCNF_B_1),
inference(subst, [],
[refute_0_86 :
[bind(A, \$fot(skolemFOFtoCNF_A_2)),
bind(B, \$fot(skolemFOFtoCNF_B_1))]])).

cnf(refute_0_88, plain,
(set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) =
skolemFOFtoCNF_B_1),
inference(resolve,
[\$cnf(subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))],
[refute_0_85, refute_0_87])).

cnf(refute_0_89, plain,
(empty_set !=
set_difference(skolemFOFtoCNF_A_2,
set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) |
set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) !=
skolemFOFtoCNF_B_1 |
empty_set = set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
introduced(tautology,
[equality,
[\$cnf(\$equal(empty_set,
set_difference(skolemFOFtoCNF_A_2,
set_union2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))), [1, 1],
\$fot(skolemFOFtoCNF_B_1)]])).

cnf(refute_0_90, plain,
(empty_set !=
set_difference(skolemFOFtoCNF_A_2,
set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) |
empty_set = set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(\$equal(set_union2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1), skolemFOFtoCNF_B_1))],
[refute_0_88, refute_0_89])).

cnf(refute_0_91, plain,
(empty_set = set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(\$equal(empty_set,
set_difference(skolemFOFtoCNF_A_2,
set_union2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1))))],
[refute_0_84, refute_0_90])).

cnf(refute_0_92, plain,
(empty_set != set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = empty_set),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(empty_set)),
bind(Y,
\$fot(set_difference(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))]])).

cnf(refute_0_93, plain,
(set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = empty_set),
inference(resolve,
[\$cnf(\$equal(empty_set,
set_difference(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))],
[refute_0_91, refute_0_92])).

cnf(refute_0_94, plain,
(set_difference(skolemFOFtoCNF_A_2,
set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) !=
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) != empty_set |
set_difference(skolemFOFtoCNF_A_2, empty_set) =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_A_2,
set_difference(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)),
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1))), [0, 1],
\$fot(empty_set)]])).

cnf(refute_0_95, plain,
(set_difference(skolemFOFtoCNF_A_2,
set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) !=
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
set_difference(skolemFOFtoCNF_A_2, empty_set) =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1), empty_set))],
[refute_0_93, refute_0_94])).

cnf(refute_0_96, plain,
(set_difference(skolemFOFtoCNF_A_2, empty_set) =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_A_2,
set_difference(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)),
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))],
[refute_0_10, refute_0_95])).

cnf(refute_0_97, plain,
(set_difference(skolemFOFtoCNF_A_2, empty_set) = skolemFOFtoCNF_A_2),
inference(subst, [],
[refute_0_52 : [bind(A, \$fot(skolemFOFtoCNF_A_2))]])).

cnf(refute_0_98, plain,
(set_difference(skolemFOFtoCNF_A_2, empty_set) !=
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
set_difference(skolemFOFtoCNF_A_2, empty_set) != skolemFOFtoCNF_A_2 |
skolemFOFtoCNF_A_2 =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_A_2, empty_set),
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1))), [0],
\$fot(skolemFOFtoCNF_A_2)]])).

cnf(refute_0_99, plain,
(set_difference(skolemFOFtoCNF_A_2, empty_set) !=
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
skolemFOFtoCNF_A_2 =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_A_2, empty_set),
skolemFOFtoCNF_A_2))], [refute_0_97, refute_0_98])).

cnf(refute_0_100, plain,
(skolemFOFtoCNF_A_2 =
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_A_2, empty_set),
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))],
[refute_0_96, refute_0_99])).

cnf(refute_0_101, plain,
(skolemFOFtoCNF_A_2 !=
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) |
set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) =
skolemFOFtoCNF_A_2),
inference(subst, [],
[refute_0_27 :
[bind(X, \$fot(skolemFOFtoCNF_A_2)),
bind(Y,
\$fot(set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))]])).

cnf(refute_0_102, plain,
(set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) =
skolemFOFtoCNF_A_2),
inference(resolve,
[\$cnf(\$equal(skolemFOFtoCNF_A_2,
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))],
[refute_0_100, refute_0_101])).

cnf(refute_0_103, plain,
(set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) !=
skolemFOFtoCNF_A_2 | ~ in(X_311, skolemFOFtoCNF_A_2) |
in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))),
introduced(tautology,
[equality,
[\$cnf(~ in(X_311,
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1))), [1],
\$fot(skolemFOFtoCNF_A_2)]])).

cnf(refute_0_104, plain,
(~ in(X_311, skolemFOFtoCNF_A_2) |
in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))),
inference(resolve,
[\$cnf(\$equal(set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1), skolemFOFtoCNF_A_2))],
[refute_0_102, refute_0_103])).

cnf(refute_0_105, plain,
(~ in(X_311, skolemFOFtoCNF_A_2) | in(X_311, skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(in(X_311,
set_intersection2(skolemFOFtoCNF_A_2,
skolemFOFtoCNF_B_1)))],
[refute_0_104, refute_0_8])).

cnf(refute_0_106, plain,
(~ in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_A_2) |
in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1)),
inference(subst, [],
[refute_0_105 :
[bind(X_311,
\$fot(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2)))]])).

cnf(refute_0_107, plain,
(disjoint(A, skolemFOFtoCNF_A_2) |
in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1)),
inference(resolve,
[\$cnf(in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2),
skolemFOFtoCNF_A_2))], [refute_0_3, refute_0_106])).

cnf(refute_0_108, plain,
(disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2) |
in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2),
skolemFOFtoCNF_B_1)),
inference(subst, [],
[refute_0_107 : [bind(A, \$fot(skolemFOFtoCNF_C_4))]])).

cnf(refute_0_109, plain,
(disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), A)),
inference(canonicalize, [], [normalize_0_28])).

cnf(refute_0_110, plain,
(disjoint(skolemFOFtoCNF_C_4, B) |
in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_C_4)),
inference(subst, [],
[refute_0_109 : [bind(A, \$fot(skolemFOFtoCNF_C_4))]])).

cnf(refute_0_111, plain,
(C != set_difference(A, B) | ~ in(D, B) | ~ in(D, C)),
inference(canonicalize, [], [normalize_0_32])).

cnf(refute_0_112, plain,
(set_difference(A, B) != set_difference(A, B) | ~ in(D, B) |
~ in(D, set_difference(A, B))),
inference(subst, [],
[refute_0_111 : [bind(C, \$fot(set_difference(A, B)))]])).

cnf(refute_0_113, plain, (set_difference(A, B) = set_difference(A, B)),
introduced(tautology, [refl, [\$fot(set_difference(A, B))]])).

cnf(refute_0_114, plain, (~ in(D, B) | ~ in(D, set_difference(A, B))),
inference(resolve,
[\$cnf(\$equal(set_difference(A, B), set_difference(A, B)))],
[refute_0_113, refute_0_112])).

cnf(refute_0_115, plain,
(~ in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) |
~ in(X_332, skolemFOFtoCNF_C_4)),
inference(subst, [],
[refute_0_114 :
[bind(A, \$fot(skolemFOFtoCNF_B_1)),
bind(B, \$fot(skolemFOFtoCNF_C_4)),
bind(D, \$fot(X_332))]])).

cnf(refute_0_116, plain,
(set_union2(set_difference(X_62, B),
set_difference(X_62, set_difference(X_62, B))) =
set_union2(set_difference(X_62, B), X_62)),
inference(subst, [],
[refute_0_13 :
[bind(A, \$fot(set_difference(X_62, B))),
bind(B, \$fot(X_62))]])).

cnf(refute_0_117, plain,
(set_difference(X_62, set_difference(X_62, B)) =
set_intersection2(X_62, B)),
inference(subst, [], [refute_0_9 : [bind(A, \$fot(X_62))]])).

cnf(refute_0_118, plain,
(set_difference(X_62, set_difference(X_62, B)) !=
set_intersection2(X_62, B) |
set_union2(set_difference(X_62, B),
set_difference(X_62, set_difference(X_62, B))) !=
set_union2(set_difference(X_62, B), X_62) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
set_union2(set_difference(X_62, B), X_62)),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_difference(X_62, B),
set_difference(X_62, set_difference(X_62, B))),
set_union2(set_difference(X_62, B), X_62))),
[0, 1], \$fot(set_intersection2(X_62, B))]])).

cnf(refute_0_119, plain,
(set_union2(set_difference(X_62, B),
set_difference(X_62, set_difference(X_62, B))) !=
set_union2(set_difference(X_62, B), X_62) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
set_union2(set_difference(X_62, B), X_62)),
inference(resolve,
[\$cnf(\$equal(set_difference(X_62, set_difference(X_62, B)),
set_intersection2(X_62, B)))],
[refute_0_117, refute_0_118])).

cnf(refute_0_120, plain,
(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
set_union2(set_difference(X_62, B), X_62)),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(X_62, B),
set_difference(X_62, set_difference(X_62, B))),
set_union2(set_difference(X_62, B), X_62)))],
[refute_0_116, refute_0_119])).

cnf(refute_0_121, plain,
(set_union2(set_difference(X_62, B), X_62) =
set_union2(X_62, set_difference(X_62, B))),
inference(subst, [],
[refute_0_35 :
[bind(A, \$fot(X_62)),
bind(B, \$fot(set_difference(X_62, B)))]])).

cnf(refute_0_122, plain,
(set_union2(set_difference(X_62, B), X_62) !=
set_union2(X_62, set_difference(X_62, B)) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) !=
set_union2(set_difference(X_62, B), X_62) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
set_union2(X_62, set_difference(X_62, B))),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_difference(X_62, B),
set_intersection2(X_62, B)),
set_union2(set_difference(X_62, B), X_62))), [1],
\$fot(set_union2(X_62, set_difference(X_62, B)))]])).

cnf(refute_0_123, plain,
(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) !=
set_union2(set_difference(X_62, B), X_62) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
set_union2(X_62, set_difference(X_62, B))),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(X_62, B), X_62),
set_union2(X_62, set_difference(X_62, B))))],
[refute_0_121, refute_0_122])).

cnf(refute_0_124, plain,
(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
set_union2(X_62, set_difference(X_62, B))),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(X_62, B),
set_intersection2(X_62, B)),
set_union2(set_difference(X_62, B), X_62)))],
[refute_0_120, refute_0_123])).

cnf(refute_0_125, plain, (subset(set_difference(A, B), A)),
inference(canonicalize, [], [normalize_0_34])).

cnf(refute_0_126, plain, (subset(set_difference(X_113, B), X_113)),
inference(subst, [], [refute_0_125 : [bind(A, \$fot(X_113))]])).

cnf(refute_0_127, plain,
(~ subset(set_difference(X_113, B), X_113) |
set_union2(set_difference(X_113, B), X_113) = X_113),
inference(subst, [],
[refute_0_86 :
[bind(A, \$fot(set_difference(X_113, B))),
bind(B, \$fot(X_113))]])).

cnf(refute_0_128, plain,
(set_union2(set_difference(X_113, B), X_113) = X_113),
inference(resolve, [\$cnf(subset(set_difference(X_113, B), X_113))],
[refute_0_126, refute_0_127])).

cnf(refute_0_129, plain,
(set_union2(set_difference(X_113, B), X_113) =
set_union2(X_113, set_difference(X_113, B))),
inference(subst, [],
[refute_0_35 :
[bind(A, \$fot(X_113)),
bind(B, \$fot(set_difference(X_113, B)))]])).

cnf(refute_0_130, plain,
(set_union2(set_difference(X_113, B), X_113) != X_113 |
set_union2(set_difference(X_113, B), X_113) !=
set_union2(X_113, set_difference(X_113, B)) |
set_union2(X_113, set_difference(X_113, B)) = X_113),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_difference(X_113, B), X_113),
X_113)), [0],
\$fot(set_union2(X_113, set_difference(X_113, B)))]])).

cnf(refute_0_131, plain,
(set_union2(set_difference(X_113, B), X_113) != X_113 |
set_union2(X_113, set_difference(X_113, B)) = X_113),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(X_113, B), X_113),
set_union2(X_113, set_difference(X_113, B))))],
[refute_0_129, refute_0_130])).

cnf(refute_0_132, plain,
(set_union2(X_113, set_difference(X_113, B)) = X_113),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(X_113, B), X_113),
X_113))], [refute_0_128, refute_0_131])).

cnf(refute_0_133, plain,
(set_union2(X_62, set_difference(X_62, B)) = X_62),
inference(subst, [], [refute_0_132 : [bind(X_113, \$fot(X_62))]])).

cnf(refute_0_134, plain,
(set_union2(X_62, set_difference(X_62, B)) != X_62 |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) !=
set_union2(X_62, set_difference(X_62, B)) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
X_62),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_difference(X_62, B),
set_intersection2(X_62, B)),
set_union2(X_62, set_difference(X_62, B)))), [1],
\$fot(X_62)]])).

cnf(refute_0_135, plain,
(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) !=
set_union2(X_62, set_difference(X_62, B)) |
set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
X_62),
inference(resolve,
[\$cnf(\$equal(set_union2(X_62, set_difference(X_62, B)),
X_62))], [refute_0_133, refute_0_134])).

cnf(refute_0_136, plain,
(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) =
X_62),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(X_62, B),
set_intersection2(X_62, B)),
set_union2(X_62, set_difference(X_62, B))))],
[refute_0_124, refute_0_135])).

cnf(refute_0_137, plain,
(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) =
skolemFOFtoCNF_B_1),
inference(subst, [],
[refute_0_136 :
[bind(B, \$fot(skolemFOFtoCNF_C_4)),
bind(X_62, \$fot(skolemFOFtoCNF_B_1))]])).

cnf(refute_0_138, plain,
(disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)),
inference(canonicalize, [], [normalize_0_35])).

cnf(refute_0_139, plain,
(~ disjoint(A, B) | set_intersection2(A, B) = empty_set),
inference(canonicalize, [], [normalize_0_39])).

cnf(refute_0_140, plain,
(~ disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) |
set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) =
empty_set),
inference(subst, [],
[refute_0_139 :
[bind(A, \$fot(skolemFOFtoCNF_B_1)),
bind(B, \$fot(skolemFOFtoCNF_C_4))]])).

cnf(refute_0_141, plain,
(set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) =
empty_set),
inference(resolve,
[\$cnf(disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))],
[refute_0_138, refute_0_140])).

cnf(refute_0_142, plain,
(set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) !=
empty_set |
set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) !=
skolemFOFtoCNF_B_1 |
set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) = skolemFOFtoCNF_B_1),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4),
set_intersection2(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4)), skolemFOFtoCNF_B_1)),
[0, 1], \$fot(empty_set)]])).

cnf(refute_0_143, plain,
(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) !=
skolemFOFtoCNF_B_1 |
set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) = skolemFOFtoCNF_B_1),
inference(resolve,
[\$cnf(\$equal(set_intersection2(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4), empty_set))],
[refute_0_141, refute_0_142])).

cnf(refute_0_144, plain,
(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) = skolemFOFtoCNF_B_1),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4),
set_intersection2(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4)), skolemFOFtoCNF_B_1))],
[refute_0_137, refute_0_143])).

cnf(refute_0_145, plain, (set_union2(A, empty_set) = A),
inference(canonicalize, [], [normalize_0_41])).

cnf(refute_0_146, plain,
(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) =
set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)),
inference(subst, [],
[refute_0_145 :
[bind(A,
\$fot(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4)))]])).

cnf(refute_0_147, plain,
(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) !=
set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) |
set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) != skolemFOFtoCNF_B_1 |
set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) =
skolemFOFtoCNF_B_1),
introduced(tautology,
[equality,
[\$cnf(\$equal(set_union2(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4), empty_set),
skolemFOFtoCNF_B_1)), [0],
\$fot(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4))]])).

cnf(refute_0_148, plain,
(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4),
empty_set) != skolemFOFtoCNF_B_1 |
set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) =
skolemFOFtoCNF_B_1),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4), empty_set),
set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4)))],
[refute_0_146, refute_0_147])).

cnf(refute_0_149, plain,
(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) =
skolemFOFtoCNF_B_1),
inference(resolve,
[\$cnf(\$equal(set_union2(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4), empty_set),
skolemFOFtoCNF_B_1))],
[refute_0_144, refute_0_148])).

cnf(refute_0_150, plain,
(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) !=
skolemFOFtoCNF_B_1 | ~ in(X_332, skolemFOFtoCNF_B_1) |
in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))),
introduced(tautology,
[equality,
[\$cnf(~ in(X_332,
set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4))), [1],
\$fot(skolemFOFtoCNF_B_1)]])).

cnf(refute_0_151, plain,
(~ in(X_332, skolemFOFtoCNF_B_1) |
in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))),
inference(resolve,
[\$cnf(\$equal(set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4), skolemFOFtoCNF_B_1))],
[refute_0_149, refute_0_150])).

cnf(refute_0_152, plain,
(~ in(X_332, skolemFOFtoCNF_B_1) | ~ in(X_332, skolemFOFtoCNF_C_4)),
inference(resolve,
[\$cnf(in(X_332,
set_difference(skolemFOFtoCNF_B_1,
skolemFOFtoCNF_C_4)))],
[refute_0_151, refute_0_115])).

cnf(refute_0_153, plain,
(~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_B_1) |
~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_C_4)),
inference(subst, [],
[refute_0_152 :
[bind(X_332,
\$fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B)))]])).

cnf(refute_0_154, plain,
(~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_B_1) |
disjoint(skolemFOFtoCNF_C_4, B)),
inference(resolve,
[\$cnf(in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B),
skolemFOFtoCNF_C_4))],
[refute_0_110, refute_0_153])).

cnf(refute_0_155, plain,
(~
in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2),
skolemFOFtoCNF_B_1) |
disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2)),
inference(subst, [],
[refute_0_154 : [bind(B, \$fot(skolemFOFtoCNF_A_2))]])).

cnf(refute_0_156, plain,
(disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2)),
inference(resolve,
[\$cnf(in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4,
skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1))],
[refute_0_108, refute_0_155])).

cnf(refute_0_157, plain,
(disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)),
inference(resolve,
[\$cnf(disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2))],
[refute_0_156, refute_0_1])).

cnf(refute_0_158, plain,
(~ disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)),
inference(canonicalize, [], [normalize_0_42])).

cnf(refute_0_159, plain, (\$false),
inference(resolve,
[\$cnf(disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4))],
[refute_0_157, refute_0_158])).
SZS output end CNFRefutation for data/problems/all/SEU140+2.tptp
```

Dominique Pastre
University Paris Descartes, France

### Sample solution for SEU140+2

```SZS status Theorem for SEU140+2.p

SZS output start proof for SEU140+2.p

* * * * * * * * * * * * * * * * * * * * * * * *
in the following, N is the number of a (sub)theorem
E is the current step
or the step when a hypothesis or conclusion has been added or modified
hyp(N,H,E) means that H is an hypothesis of (sub)theorem N
concl(N,C,E) means that C is the conclusion of (sub)theorem N
obj_ct(N,C) means that C is a created object or a given constant
newconcl(N,C,E) means that the new conclusion of N is C
(C replaces the precedent conclusion)
a subtheorem N-i or N+i is a subtheorem of the (sub)theorem N
N is proved if all N-i have been proved (&-node)
or if one N+i have been proved (|-node)
the initial theorem is numbered 0

* * * theorem to be proved
![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C))

* * * proof :

* * * * * * theoreme 0 * * * * * *
*** newconcl(0, ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C)), 1)
*** explanation : initial theorem
------------------------------------------------------- action ini
create object(s) z3 z2 z1
*** newconcl(0, subset(z1, z2)&disjoint(z2, z3)=>disjoint(z1, z3), 2)
*** because concl((0, ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C))), 1)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** newconcl(0, disjoint(z1, z3), 3)
*** because concl(0, subset(z1, z2)&disjoint(z2, z3)=>disjoint(z1, z3), 2)
*** explanation : to prove H=>C, assume H and prove C
------------------------------------------------------- rule =>
*** because hyp(0, disjoint(z2, z3), 3)
*** explanation : rule if hyp(A, disjoint(B, C), _)then addhyp(A, set_intersection2(B, C)::empty_set, _)
built from the definition of disjoint (fof d7_xboole_0 )
------------------------------------------------------- rule disjoint
*** because hyp(0, subset(z1, z2), 3), obj_ct(0, z1), obj_ct(0, z2)
*** explanation : rule if (hyp(A, subset(B, C), _), obj_ct(A, B), obj_ct(A, C))then addhyp(A, set_difference(B, C)::empty_set, _)
built from the axiom l32_xboole_1
------------------------------------------------------- rule l32_xboole_1_1
*** newconcl(0, set_intersection2(z1, z3)::empty_set, 109)
*** because concl(0, disjoint(z1, z3), 3)
*** explanation : the conclusion  disjoint(z1, z3) is replaced by its definition(fof d7_xboole_0 )
------------------------------------------------------- rule def_concl_pred
*** newconcl(0, seul(set_intersection2(z1, z3)::A, A=empty_set), 110)
*** because concl(0, set_intersection2(z1, z3)::empty_set, 109)
*** explanation :  FX::Y is rewriten only(FX::Z, Z=Y)
------------------------------------------------------- rule concl2pts
*** addhyp(0, set_intersection2(z1, z3)::z4, 111), newconcl(0, z4=empty_set, 111)
*** because concl(0, seul(set_intersection2(z1, z3)::A, A=empty_set), 110)
*** explanation : creation of object z4 and of its definition
------------------------------------------------------- rule concl_only
*** because hyp(0, set_intersection2(z1, z3)::z4, 111), obj_ct(0, z1), obj_ct(0, z3)
*** explanation : rule if (hyp(A, set_intersection2(B, C)::D, _), obj_ct(A, B), obj_ct(A, C))then addhyp(A, set_intersection2(C, B)::D, _)
built from the axiom commutativity_k3_xboole_0
------------------------------------------------------- rule commutativity_k3_xboole_0_1
*** newconcl(0, ![A]: ~in(A, z4), 114)
*** because concl(0, z4=empty_set, 111)
*** explanation : sufficient condition (rule :  d1_xboole_0_1 (fof d1_xboole_0 )
------------------------------------------------------- rule d1_xboole_0_1_cs
create object(s) z5
*** newconcl(0, ~in(z5, z4), 115)
*** because concl((0, ![A]: ~in(A, z4)), 114)
*** explanation : the universal variable(s) of the conclusion is(are) instantiated
------------------------------------------------------- rule !
*** addhyp(0, in(z5, z4), 116), newconcl(0, false, 116)
*** because concl(0, ~in(z5, z4), 115)
*** explanation : assume in(z5, z4) and search for a contradiction
------------------------------------------------------- rule concl_not
*** because hyp(0, set_intersection2(z1, z3)::z4, 111), hyp(0, in(z5, z4), 116), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_intersection2(D, _)::B, _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _)
built from the definition of set_intersection2 (fof d3_xboole_0 )
------------------------------------------------------- rule set_intersection2
*** because hyp(0, subset(z1, z2), 3), hyp(0, in(z5, z1), 118), obj_ct(0, z5)
*** explanation : rule if (hyp(A, subset(B, D), _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _)
built from the definition of subset (fof d3_tarski )
------------------------------------------------------- rule subset
*** because hyp(0, set_intersection2(z3, z1)::z4, 113), hyp(0, in(z5, z4), 116), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_intersection2(D, _)::B, _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _)
built from the definition of set_intersection2 (fof d3_xboole_0 )
------------------------------------------------------- rule set_intersection2
*** because hyp(0, set_intersection2(z2, z3)::empty_set, 4), hyp(0, in(z5, z2), 119), hyp(0, in(z5, z3), 120), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_intersection2(B, D)::E, _), hyp(A, in(C, B), _), hyp(A, in(C, D), _), obj_ct(A, C))then addhyp(A, in(C, E), _)
built from the definition of set_intersection2 (fof d3_xboole_0 )
------------------------------------------------------- rule set_intersection4
*** because hyp(0, set_difference(z1, z2)::empty_set, 21), hyp(0, in(z5, empty_set), 121), hyp(0, in(z5, z2), 119), obj_ct(0, z5)
*** explanation : rule if (hyp(A, set_difference(_, D)::B, _), hyp(A, in(C, B), _), hyp(A, in(C, D), _), obj_ct(A, C))then addhyp(A, false, _)
built from the definition of set_difference (fof d4_xboole_0 )
------------------------------------------------------- rule set_difference1
*** newconcl(0, true, 123)
*** because hyp(0, false, 122), concl(0, false, 116)
*** explanation : the conclusion false to be proved is a hypothesis
------------------------------------------------------- rule stop_hyp_concl
then the initial theorem is proved
* * * * * * * * * * * * * * * * * * * * * * * *

SZS output end proof for SEU140+2.p
```

## Nitrox 0.2

Jasmin C. Blanchette1, Emina Torlak2
1Technische Universität München, Germany
2IBM Research, USA

The domain elements of a model are of the form iN. Function mappings are provided for all tuples of domain elements. Predicate mappings are listed for the true cases.

### Sample solution for NLP042+1

```  Constants:
abstraction = {(i4, i2)}
act = {(i4, i1)}
actual_world = {i3, i4}
agent = {(i4, i1, i3)}
animate = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
beverage = {(i4, i4)}
entity =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3), (i4, i4)}
event = {(i4, i1)}
eventuality = {(i4, i1)}
existent =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3), (i4, i4)}
female =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i3, i3), (i4, i3)}
food = {(i4, i4)}
forename = {(i4, i2)}
general = {(i4, i2)}
human = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
human_person =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
impartial =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3), (i4, i4)}
living = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
mia_forename = {(i4, i2)}
nonexistent = {(i4, i1)}
nonhuman = {(i4, i2)}
nonliving = {(i4, i4)}
nonreflexive = {(i4, i1)}
object = {(i4, i4)}
of = {(i4, i2, i3)}
order = {(i4, i1)}
organism = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
past = {(i4, i1)}
patient = {(i4, i1, i4)}
relation = {(i4, i2)}
relname = {(i4, i2)}
shake_beverage = {(i4, i4)}
singleton =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i1), (i4, i2),
(i4, i3), (i4, i4)}
specific =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i1), (i4, i3),
(i4, i4)}
substance_matter = {(i4, i4)}
thing =
{(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i1), (i4, i2),
(i4, i3), (i4, i4)}
unisex = {(i4, i1), (i4, i2), (i4, i4)}
woman = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
```

### Sample solution for SWV017+1

```    a = i1
a_holds = {i2}
a_key = {i2}
a_nonce = {i1}
a_stored = {i1}
an_a_nonce = i1
an_intruder_nonce = i1
at = i2
b = i2
b_holds = {i2}
b_stored = {i1, i2}
bt = i1
encrypt =
(%x. _)
((i1, i1) := i1, (i1, i2) := i1, (i2, i1) := i1, (i2, i2) := i1)
fresh_intruder_nonce = {i1}
fresh_to_b = {i1}
generate_b_nonce = (%x. _)(i1 := i1, i2 := i1)
generate_expiration_time = (%x. _)(i1 := i1, i2 := i1)
generate_intruder_nonce = (%x. _)(i1 := i1, i2 := i1)
generate_key = (%x. _)(i1 := i2, i2 := i2)
intruder_holds = {i2}
intruder_message = {i1, i2}
key =
(%x. _)
((i1, i1) := i2, (i1, i2) := i2, (i2, i1) := i2, (i2, i2) := i2)
message = {i1}
pair =
(%x. _)
((i1, i1) := i2, (i1, i2) := i1, (i2, i1) := i1, (i2, i2) := i2)
party_of_protocol = {i1, i2}
(%x. _)
((i1, i1, i1, i1) := i1, (i1, i1, i1, i2) := i1,
(i1, i1, i2, i1) := i1, (i1, i1, i2, i2) := i1,
(i1, i2, i1, i1) := i1, (i1, i2, i1, i2) := i1,
(i1, i2, i2, i1) := i1, (i1, i2, i2, i2) := i1,
(i2, i1, i1, i1) := i1, (i2, i1, i1, i2) := i1,
(i2, i1, i2, i1) := i1, (i2, i1, i2, i2) := i1,
(i2, i2, i1, i1) := i1, (i2, i2, i1, i2) := i1,
(i2, i2, i2, i1) := i1, (i2, i2, i2, i2) := i1)
sent =
(%x. _)
((i1, i1, i1) := i1, (i1, i1, i2) := i1, (i1, i2, i1) := i1,
(i1, i2, i2) := i1, (i2, i1, i1) := i1, (i2, i1, i2) := i1,
(i2, i2, i1) := i1, (i2, i2, i2) := i1)
t = i2
t_holds = {i2}
triple =
(%x. _)
((i1, i1, i1) := i2, (i1, i1, i2) := i1, (i1, i2, i1) := i1,
(i1, i2, i2) := i1, (i2, i1, i1) := i2, (i2, i1, i2) := i1,
(i2, i2, i1) := i1, (i2, i2, i2) := i1)
```

Koen Claessen
Chalmers University of Technology, Sweden

### Sample solution for MGT019+2

```% domain size is 1
disbanding_rate(!1,!1) = !1
efficient_producers = !1
environment(!1) <=> \$true
first_movers = !1
founding_rate(!1,!1) = !1
greater(!1,!1) <=> \$false
greater_or_equal(!1,!1) <=> \$true
growth_rate(!1,!1) = !1
in_environment(!1,!1) <=> \$true
stable(!1) <=> \$true
subpopulations(!1,!1,!1,!1) <=> \$true
```

### Sample solution for SWV010+1

```% domain size is 1
a_holds(X1)
a_stored(X1)
b_holds(X1)
b_stored(X1)
fresh_to_b(X1)
message(X1)
party_of_protocol(X1)
t_holds(X1)
```

## Vampire 0.6

Andrei Voronkov, Kryštof Hoder
University of Manchester, United Kingdom

### Sample solution for SYN075+1

```% SZS status Theorem for SYN075+1
% SZS output start Proof for SYN075+1
fof(f509,plain,(
\$false),
inference(subsumption_resolution,[],[f508,f145])).
fof(f145,plain,(
big_f(\$sk3,\$sk4)),
inference(backtracking_split_refutation,[],[f69,f70_D,f124])).
fof(f124,plain,(
\$false | \$spl1),
inference(subsumption_resolution,[],[f123,f110])).
fof(f110,plain,(
( ! [X0] : (~big_f(\$sk3,X0)) ) | \$spl1),
inference(forward_demodulation,[],[f106,f92])).
fof(f92,plain,(
( ! [X0] : (\$sk2(\$sk3,X0) = \$sk3) ) | \$spl1),
inference(factoring,[],[f85])).
fof(f85,plain,(
( ! [X2,X3] : (\$sk2(X2,X3) = X2 | \$sk2(X2,X3) = \$sk3) ) | \$spl1),
inference(resolution,[],[f82,f15])).
fof(f15,plain,(
( ! [X2,X3] : (~big_f(X2,X3) | \$sk3 = X2) )),
inference(cnf_transformation,[],[f10])).
fof(f10,plain,(
! [X2,X3] : ((~big_f(X2,X3) | (\$sk3 = X2 & \$sk4 = X3)) & (\$sk3 != X2 | \$sk4 != X3 | big_f(X2,X3)))),
inference(skolemisation,[status(esa)],[f9])).
fof(f9,plain,(
? [X0,X1] : ! [X2,X3] : ((~big_f(X2,X3) | (X0 = X2 & X1 = X3)) & (X0 != X2 | X1 != X3 | big_f(X2,X3)))),
inference(flattening,[],[f8])).
fof(f8,plain,(
? [X0,X1] : ! [X2,X3] : ((~big_f(X2,X3) | (X0 = X2 & X1 = X3)) & ((X0 != X2 | X1 != X3) | big_f(X2,X3)))),
inference(nnf_transformation,[],[f1])).
fof(f1,axiom,(
? [X0,X1] : ! [X2,X3] : (big_f(X2,X3) <=> (X0 = X2 & X1 = X3))),
file('/tmp/SystemOnTPTP10164/SYN075+1.tptp',pel52_1)).
fof(f82,plain,(
( ! [X4,X0] : (big_f(\$sk2(X4,X0),X0) | \$sk2(X4,X0) = X4) ) | \$spl1),
inference(subsumption_resolution,[],[f73,f70])).
fof(f73,plain,(
( ! [X4,X0] : (big_f(\$sk2(X4,X0),X0) | \$sk0(X0) != X0 | \$sk2(X4,X0) = X4) ) | \$spl1),
inference(backward_demodulation,[],[f70,f13])).
fof(f13,plain,(
( ! [X4,X0] : (\$sk0(X0) != X0 | \$sk2(X4,X0) = X4 | big_f(\$sk2(X4,X0),\$sk0(X0))) )),
inference(cnf_transformation,[],[f7])).
fof(f7,plain,(
! [X0] : ((! [X3] : ((~big_f(X3,\$sk0(X0)) | \$sk1(X0) = X3) & (\$sk1(X0) != X3 | big_f(X3,\$sk0(X0)))) | \$sk0(X0) = X0) & (! [X4] : ((big_f(\$sk2(X4,X0),\$sk0(X0)) | \$sk2(X4,X0) = X4) & (~big_f(\$sk2(X4,X0),\$sk0(X0)) | \$sk2(X4,X0) != X4)) | \$sk0(X0) != X0))),
inference(skolemisation,[status(esa)],[f6])).
fof(f6,plain,(
! [X0] : ? [X1] : ((? [X2] : ! [X3] : ((~big_f(X3,X1) | X2 = X3) & (X2 != X3 | big_f(X3,X1))) | X0 = X1) & (! [X4] : ? [X5] : ((big_f(X5,X1) | X4 = X5) & (~big_f(X5,X1) | X4 != X5)) | X0 != X1))),
inference(rectify,[],[f5])).
fof(f5,plain,(
! [X0] : ? [X1] : ((? [X2] : ! [X3] : ((~big_f(X3,X1) | X2 = X3) & (X2 != X3 | big_f(X3,X1))) | X0 = X1) & (! [X2] : ? [X3] : ((big_f(X3,X1) | X2 = X3) & (~big_f(X3,X1) | X2 != X3)) | X0 != X1))),
inference(nnf_transformation,[],[f4])).
fof(f4,plain,(
! [X0] : ? [X1] : (? [X2] : ! [X3] : (big_f(X3,X1) <=> X2 = X3) <~> X0 = X1)),
inference(ennf_transformation,[],[f3])).
fof(f3,plain,(
~? [X0] : ! [X1] : (? [X2] : ! [X3] : (big_f(X3,X1) <=> X2 = X3) <=> X0 = X1)),
inference(rectify,[],[f2])).
fof(f2,negated_conjecture,(
~? [X1] : ! [X3] : (? [X0] : ! [X2] : (big_f(X2,X3) <=> X0 = X2) <=> X1 = X3)),
file('/tmp/SystemOnTPTP10164/SYN075+1.tptp',pel52)).
fof(f106,plain,(
( ! [X0] : (~big_f(\$sk2(\$sk3,X0),X0)) ) | \$spl1),
inference(resolution,[],[f92,f83])).
fof(f83,plain,(
( ! [X4,X0] : (\$sk2(X4,X0) != X4 | ~big_f(\$sk2(X4,X0),X0)) ) | \$spl1),
inference(subsumption_resolution,[],[f74,f70])).
fof(f74,plain,(
( ! [X4,X0] : (~big_f(\$sk2(X4,X0),X0) | \$sk0(X0) != X0 | \$sk2(X4,X0) != X4) ) | \$spl1),
inference(backward_demodulation,[],[f70,f14])).
fof(f14,plain,(
( ! [X4,X0] : (\$sk2(X4,X0) != X4 | \$sk0(X0) != X0 | ~big_f(\$sk2(X4,X0),\$sk0(X0))) )),
inference(cnf_transformation,[],[f7])).
fof(f123,plain,(
big_f(\$sk3,\$sk4) | \$spl1),
inference(forward_demodulation,[],[f118,f92])).
fof(f118,plain,(
( ! [X2] : (big_f(\$sk2(\$sk3,X2),\$sk4)) ) | \$spl1),
inference(resolution,[],[f116,f92])).
fof(f116,plain,(
( ! [X0] : (\$sk3 != X0 | big_f(X0,\$sk4)) ) | \$spl1),
inference(forward_demodulation,[],[f112,f70])).
fof(f112,plain,(
( ! [X0] : (big_f(X0,\$sk0(\$sk4)) | \$sk3 != X0) ) | \$spl1),
inference(resolution,[],[f17,f70])).
fof(f17,plain,(
( ! [X2,X3] : (\$sk4 != X3 | big_f(X2,X3) | \$sk3 != X2) )),
inference(cnf_transformation,[],[f10])).
fof(f70,plain,(
( ! [X0] : (\$sk0(X0) = X0) ) | \$spl1),
inference(cnf_transformation,[],[f70_D])).
fof(f70_D,plain,(
( ! [X0] : (\$sk0(X0) = X0) ) <=> ~\$spl1),
introduced(backtracking_splitting_component,[])).
fof(f69,plain,(
( ! [X0] : (big_f(\$sk3,\$sk4) | \$sk0(X0) = X0) )),
inference(duplicate_literal_removal,[],[f68])).
fof(f68,plain,(
( ! [X0] : (big_f(\$sk3,\$sk4) | \$sk0(X0) = X0 | \$sk0(X0) = X0) )),
inference(superposition,[],[f34,f21])).
fof(f21,plain,(
( ! [X2] : (\$sk1(X2) = \$sk3 | \$sk0(X2) = X2) )),
inference(resolution,[],[f18,f15])).
fof(f18,plain,(
( ! [X0] : (big_f(\$sk1(X0),\$sk0(X0)) | \$sk0(X0) = X0) )),
inference(equality_resolution,[],[f12])).
fof(f12,plain,(
( ! [X0,X3] : (\$sk1(X0) != X3 | big_f(X3,\$sk0(X0)) | \$sk0(X0) = X0) )),
inference(cnf_transformation,[],[f7])).
fof(f34,plain,(
( ! [X0] : (big_f(\$sk1(X0),\$sk4) | \$sk0(X0) = X0) )),
inference(duplicate_literal_removal,[],[f29])).
fof(f29,plain,(
( ! [X0] : (big_f(\$sk1(X0),\$sk4) | \$sk0(X0) = X0 | \$sk0(X0) = X0) )),
inference(superposition,[],[f18,f20])).
fof(f20,plain,(
( ! [X1] : (\$sk0(X1) = X1 | \$sk0(X1) = \$sk4) )),
inference(resolution,[],[f18,f16])).
fof(f16,plain,(
( ! [X2,X3] : (~big_f(X2,X3) | \$sk4 = X3) )),
inference(cnf_transformation,[],[f10])).
fof(f508,plain,(
~big_f(\$sk3,\$sk4)),
inference(forward_demodulation,[],[f507,f24])).
fof(f24,plain,(
\$sk0(\$sk4) = \$sk4),
inference(factoring,[],[f20])).
fof(f507,plain,(
~big_f(\$sk3,\$sk0(\$sk4))),
inference(forward_demodulation,[],[f506,f293])).
fof(f293,plain,(
\$sk2(\$sk3,\$sk4) = \$sk3),
inference(factoring,[],[f234])).
fof(f234,plain,(
( ! [X1] : (\$sk2(X1,\$sk4) = X1 | \$sk2(X1,\$sk4) = \$sk3) )),
inference(resolution,[],[f64,f15])).
fof(f64,plain,(
( ! [X3] : (big_f(\$sk2(X3,\$sk4),\$sk4) | \$sk2(X3,\$sk4) = X3) )),
inference(forward_demodulation,[],[f57,f24])).
fof(f57,plain,(
( ! [X3] : (\$sk2(X3,\$sk4) = X3 | big_f(\$sk2(X3,\$sk4),\$sk0(\$sk4))) )),
inference(resolution,[],[f13,f24])).
fof(f506,plain,(
~big_f(\$sk2(\$sk3,\$sk4),\$sk0(\$sk4))),
inference(subsumption_resolution,[],[f496,f16])).
fof(f496,plain,(
\$sk0(\$sk4) != \$sk4 | ~big_f(\$sk2(\$sk3,\$sk4),\$sk0(\$sk4))),
inference(resolution,[],[f14,f293])).
% SZS output end Proof for SYN075+1
```

## Vampire 1.8

Krystof Hoder, Andrei Voronkov
The University of Manchester, United Kingdom

### Sample solution for SEU140+2

```% SZS status Theorem for SEU140+2
% SZS output start Proof for SEU140+2
fof(f7254,plain,(
\$false),
inference(subsumption_resolution,[],[f7250,f129])).
fof(f129,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f99])).
fof(f99,plain,(
subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
inference(skolemisation,[status(esa)],[f71])).
fof(f71,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f70])).
fof(f70,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f51])).
fof(f51,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f7250,plain,(
~subset(sK0,sK1)),
inference(resolution,[],[f7008,f131])).
fof(f131,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f99])).
fof(f7008,plain,(
( ! [X0] : (disjoint(X0,sK2) | ~subset(X0,sK1)) )),
inference(superposition,[],[f6994,f145])).
fof(f145,plain,(
( ! [X0,X1] : (set_intersection2(X0,X1) = X0 | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f75])).
fof(f75,plain,(
! [X0,X1] : (~subset(X0,X1) | set_intersection2(X0,X1) = X0)),
inference(ennf_transformation,[],[f34])).
fof(f34,axiom,(
! [X0,X1] : (subset(X0,X1) => set_intersection2(X0,X1) = X0)),
file('Problems/SEU/SEU140+2.p',t28_xboole_1)).
fof(f6994,plain,(
( ! [X0] : (disjoint(set_intersection2(X0,sK1),sK2)) )),
inference(duplicate_literal_removal,[],[f6963])).
fof(f6963,plain,(
( ! [X0] : (disjoint(set_intersection2(X0,sK1),sK2) | disjoint(set_intersection2(X0,sK1),sK2)) )),
inference(resolution,[],[f988,f530])).
fof(f530,plain,(
( ! [X1] : (~in(sK4(sK2,X1),sK1) | disjoint(X1,sK2)) )),
inference(resolution,[],[f522,f143])).
fof(f143,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f101])).
fof(f101,plain,(
! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))),
inference(skolemisation,[status(esa)],[f74])).
fof(f74,plain,(
! [X0,X1] : ((disjoint(X0,X1) | ? [X2] : (in(X2,X0) & in(X2,X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))),
inference(ennf_transformation,[],[f60])).
fof(f60,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))),
inference(flattening,[],[f58])).
fof(f58,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f522,plain,(
( ! [X20] : (~in(X20,sK2) | ~in(X20,sK1)) )),
inference(resolution,[],[f144,f130])).
fof(f130,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f99])).
fof(f144,plain,(
( ! [X0,X3,X1] : (~disjoint(X0,X1) | ~in(X3,X1) | ~in(X3,X0)) )),
inference(cnf_transformation,[],[f101])).
fof(f988,plain,(
( ! [X4,X2,X3] : (in(sK4(X2,set_intersection2(X3,X4)),X4) | disjoint(set_intersection2(X3,X4),X2)) )),
inference(resolution,[],[f214,f142])).
fof(f142,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f101])).
fof(f214,plain,(
( ! [X0,X3,X1] : (~in(X3,set_intersection2(X0,X1)) | in(X3,X1)) )),
inference(equality_resolution,[],[f191])).
fof(f191,plain,(
( ! [X2,X0,X3,X1] : (in(X3,X1) | ~in(X3,X2) | set_intersection2(X0,X1) != X2) )),
inference(cnf_transformation,[],[f118])).
fof(f118,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (((in(sK8(X2,X1,X0),X2) | (in(sK8(X2,X1,X0),X0) & in(sK8(X2,X1,X0),X1))) & (~in(sK8(X2,X1,X0),X2) | ~in(sK8(X2,X1,X0),X0) | ~in(sK8(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))),
inference(skolemisation,[status(esa)],[f117])).
fof(f117,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X4] : ((in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X2) | ~in(X4,X0) | ~in(X4,X1))) | set_intersection2(X0,X1) = X2))),
inference(rectify,[],[f116])).
fof(f116,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))),
inference(flattening,[],[f115])).
fof(f115,plain,(
! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & ((~in(X3,X0) | ~in(X3,X1)) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | (~in(X3,X0) | ~in(X3,X1)))) | set_intersection2(X0,X1) = X2))),
inference(nnf_transformation,[],[f9])).
fof(f9,axiom,(
! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))),
file('Problems/SEU/SEU140+2.p',d3_xboole_0)).
% SZS output end Proof for SEU140+2
```

### Sample solution for SEU140+2

This proof uses different inference rules.
```% SZS status Theorem for SEU140+2
% SZS output start Proof for SEU140+2
fof(f1999,plain,(
\$false),
inference(unit_resulting_resolution,[],[f130,f1740,f1883,f144])).
fof(f144,plain,(
( ! [X0,X3,X1] : (~disjoint(X0,X1) | ~in(X3,X1) | ~in(X3,X0)) )),
inference(cnf_transformation,[],[f101])).
fof(f101,plain,(
! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))),
inference(skolemisation,[status(esa)],[f74])).
fof(f74,plain,(
! [X0,X1] : ((disjoint(X0,X1) | ? [X2] : (in(X2,X0) & in(X2,X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))),
inference(ennf_transformation,[],[f60])).
fof(f60,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))),
inference(flattening,[],[f58])).
fof(f58,plain,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))),
inference(rectify,[],[f43])).
fof(f43,axiom,(
! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))),
file('Problems/SEU/SEU140+2.p',t3_xboole_0)).
fof(f1883,plain,(
in(sK4(sK2,sK0),sK1)),
inference(unit_resulting_resolution,[],[f129,f1742,f1615])).
fof(f1615,plain,(
( ! [X2,X0,X1] : (~subset(X1,X2) | ~in(X0,X1) | in(X0,X2)) )),
inference(literal_reordering,[],[f1614])).
fof(f1614,plain,(
( ! [X2,X0,X1] : (in(X0,X2) | ~in(X0,X1) | ~subset(X1,X2)) )),
inference(instance_generation,[],[f184])).
fof(f184,plain,(
( ! [X2,X0,X1] : (in(X2,X1) | ~in(X2,X0) | ~subset(X0,X1)) )),
inference(cnf_transformation,[],[f114])).
fof(f114,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & ((in(sK7(X1,X0),X0) & ~in(sK7(X1,X0),X1)) | subset(X0,X1)))),
inference(skolemisation,[status(esa)],[f113])).
fof(f113,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X3] : (in(X3,X0) & ~in(X3,X1)) | subset(X0,X1)))),
inference(rectify,[],[f112])).
fof(f112,plain,(
! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))),
inference(nnf_transformation,[],[f96])).
fof(f96,plain,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))),
inference(ennf_transformation,[],[f8])).
fof(f8,axiom,(
! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))),
file('Problems/SEU/SEU140+2.p',d3_tarski)).
fof(f1742,plain,(
in(sK4(sK2,sK0),sK0)),
inference(unit_resulting_resolution,[],[f131,f1654])).
fof(f1654,plain,(
( ! [X37,X38] : (disjoint(X37,X38) | in(sK4(X38,X37),X37)) )),
inference(literal_reordering,[],[f1653])).
fof(f1653,plain,(
( ! [X37,X38] : (in(sK4(X38,X37),X37) | disjoint(X37,X38)) )),
inference(instance_generation,[],[f142])).
fof(f142,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f101])).
fof(f131,plain,(
~disjoint(sK0,sK2)),
inference(cnf_transformation,[],[f99])).
fof(f99,plain,(
subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)),
inference(skolemisation,[status(esa)],[f71])).
fof(f71,plain,(
? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))),
inference(flattening,[],[f70])).
fof(f70,plain,(
? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))),
inference(ennf_transformation,[],[f51])).
fof(f51,negated_conjecture,(
~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))),
file('Problems/SEU/SEU140+2.p',t63_xboole_1)).
fof(f129,plain,(
subset(sK0,sK1)),
inference(cnf_transformation,[],[f99])).
fof(f1740,plain,(
in(sK4(sK2,sK0),sK2)),
inference(unit_resulting_resolution,[],[f131,f1651])).
fof(f1651,plain,(
( ! [X35,X36] : (disjoint(X35,X36) | in(sK4(X36,X35),X36)) )),
inference(literal_reordering,[],[f1650])).
fof(f1650,plain,(
( ! [X35,X36] : (in(sK4(X36,X35),X36) | disjoint(X35,X36)) )),
inference(instance_generation,[],[f143])).
fof(f143,plain,(
( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )),
inference(cnf_transformation,[],[f101])).
fof(f130,plain,(
disjoint(sK1,sK2)),
inference(cnf_transformation,[],[f99])).
% SZS output end Proof for SEU140+2
```

```% SZS answers Tuple [[s__agent__m,s__experiencer__m]|_] for CSR082+1