WATCH: 0.00 CPU 0.01 WC WATCH: 5.24 CPU 3.02 WC WATCH: 10.44 CPU 6.03 WC WATCH: 15.55 CPU 9.04 WC # Garbage collection reclaimed 10 unused term cells. # Garbage collection reclaimed 74 unused term cells. # Garbage collection reclaimed 52 unused term cells. # Garbage collection reclaimed 55 unused term cells. # Garbage collection reclaimed 9 unused term cells. # Auto-Ordering is analysing problem. # Problem is type HUSMGFFSF21MM # Auto-mode selected ordering type KBO6 # Auto-mode selected ordering precedence scheme # Auto-mode selected weight ordering scheme # # Auto-Heuristic is analysing problem. # Problem is type HUSMGFFSF21MM # Auto-Mode selected heuristic H_____102_C18_F1_PI_AE_Q4_CS_SP_S1S # and selection function SelectComplexAHP. # # Initializing proof state # Scanning for AC axioms # multiplication is associative # addition is AC # AC handling enabled # Garbage collection reclaimed 255 unused term cells. # Garbage collection reclaimed 255 unused term cells. # Garbage collection reclaimed 256 unused term cells. # Garbage collection reclaimed 256 unused term cells. # Garbage collection reclaimed 255 unused term cells. # Garbage collection reclaimed 258 unused term cells. # Garbage collection reclaimed 256 unused term cells. # Garbage collection reclaimed 260 unused term cells. # Garbage collection reclaimed 256 unused term cells. # Garbage collection reclaimed 258 unused term cells. # Garbage collection reclaimed 255 unused term cells. # Garbage collection reclaimed 259 unused term cells. # Garbage collection reclaimed 257 unused term cells. # Garbage collection reclaimed 257 unused term cells. # Garbage collection reclaimed 257 unused term cells. # Garbage collection reclaimed 258 unused term cells. # Garbage collection reclaimed 261 unused term cells. # Garbage collection reclaimed 257 unused term cells. # Garbage collection reclaimed 264 unused term cells. # Proof found! # SZS status Theorem # Parsed axioms : 17 # Removed by relevancy pruning : 0 # Initial clauses : 18 # Removed in clause preprocessing : 0 # Initial clauses in saturation : 18 # Processed clauses : 17535 # ...of these trivial : 6601 # ...subsumed : 8250 # ...remaining for further processing : 2684 # Other redundant clauses eliminated : 0 # Clauses deleted for lack of memory : 0 # Backward-subsumed : 21 # Backward-rewritten : 432 # Generated clauses : 716435 # ...of the previous two non-trivial : 492514 # Contextual simplify-reflections : 0 # Paramodulations : 716434 # Factorizations : 0 # Equation resolutions : 1 # Current number of processed clauses : 2231 # Positive orientable unit clauses : 1523 # Positive unorientable unit clauses: 22 # Negative unit clauses : 0 # Non-unit-clauses : 686 # Current number of unprocessed clauses: 432012 # ...number of literals in the above : 598111 # Clause-clause subsumption calls (NU) : 132147 # Rec. Clause-clause subsumption calls : 132147 # Unit Clause-clause subsumption calls : 4381 # Rewrite failures with RHS unbound : 0 # Indexed BW rewrite attempts : 31584 # Indexed BW rewrite successes : 395 # Backwards rewriting index : 653 leaves, 5.66+/-7.284 terms/leaf # Paramod-from index : 347 leaves, 4.50+/-7.102 terms/leaf # Paramod-into index : 560 leaves, 5.46+/-7.133 terms/leaf # SZS output start CNFRefutation. fof(3, axiom,![X1]:![X2]:![X3]:addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', right_distributivity)). fof(4, axiom,![X1]:leq(addition(one,multiplication(star(X1),X1)),star(X1)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', star_unfold_left)). fof(5, axiom,![X1]:X1=multiplication(one,X1),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', multiplicative_left_identity)). fof(6, axiom,![X1]:![X2]:![X3]:(leq(multiplication(star(X1),X3),X2)<=leq(addition(multiplication(X1,X2),X3),X2)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', star_induction_left)). fof(7, axiom,![X3]:![X2]:![X1]:addition(addition(X1,X2),X3)=addition(X1,addition(X2,X3)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', additive_associativity)). fof(8, axiom,![X1]:![X2]:![X3]:addition(multiplication(X1,X3),multiplication(X2,X3))=multiplication(addition(X1,X2),X3),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', left_distributivity)). fof(9, axiom,![X1]:![X2]:(addition(X1,X2)=X2<=>leq(X1,X2)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', order)). fof(10, axiom,![X1]:leq(addition(one,multiplication(X1,star(X1))),star(X1)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', star_unfold_right)). fof(12, axiom,![X1]:X1=multiplication(X1,one),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', multiplicative_right_identity)). fof(13, axiom,![X1]:addition(X1,X1)=X1,file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', additive_idempotence)). fof(14, axiom,![X1]:![X2]:![X3]:multiplication(multiplication(X1,X2),X3)=multiplication(X1,multiplication(X2,X3)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', multiplicative_associativity)). fof(15, axiom,![X1]:![X2]:![X3]:(leq(multiplication(X3,star(X2)),X1)<=leq(addition(multiplication(X1,X2),X3),X1)),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', star_induction_right)). fof(16, axiom,![X1]:![X2]:addition(X1,X2)=addition(X2,X1),file('/CW/home-0/sutcliff/TPTP/Axioms/KLE002+0.ax', additive_commutativity)). fof(17, conjecture,leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a)),file('/CW/home-0/sutcliff/CASC/23/Problems/FEQ/FEQ073.p', a)). fof(18, negated_conjecture,~(leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a))),inference(assume_negation,[status(cth)],[17])). fof(19, plain,![X1]:![X2]:![X3]:(leq(addition(multiplication(X1,X2),X3),X2)=>leq(multiplication(star(X1),X3),X2)),inference(fof_simplification,[status(thm)],[6,theory(equality)])). fof(20, plain,![X1]:![X2]:![X3]:(leq(addition(multiplication(X1,X2),X3),X1)=>leq(multiplication(X3,star(X2)),X1)),inference(fof_simplification,[status(thm)],[15,theory(equality)])). fof(21, negated_conjecture,~(leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a))),inference(fof_simplification,[status(thm)],[18,theory(equality)])). fof(26, plain,![X4]:![X5]:![X6]:addition(multiplication(X4,X5),multiplication(X4,X6))=multiplication(X4,addition(X5,X6)),inference(variable_rename,[status(thm)],[3])). cnf(27,plain,(addition(multiplication(X1,X2),multiplication(X1,X3))=multiplication(X1,addition(X2,X3))),inference(split_conjunct,[status(thm)],[26])). fof(28, plain,![X2]:leq(addition(one,multiplication(star(X2),X2)),star(X2)),inference(variable_rename,[status(thm)],[4])). cnf(29,plain,(leq(addition(one,multiplication(star(X1),X1)),star(X1))),inference(split_conjunct,[status(thm)],[28])). fof(30, plain,![X2]:X2=multiplication(one,X2),inference(variable_rename,[status(thm)],[5])). cnf(31,plain,(X1=multiplication(one,X1)),inference(split_conjunct,[status(thm)],[30])). fof(32, plain,![X1]:![X2]:![X3]:(~(leq(addition(multiplication(X1,X2),X3),X2))|leq(multiplication(star(X1),X3),X2)),inference(fof_nnf,[status(thm)],[19])). fof(33, plain,![X4]:![X5]:![X6]:(~(leq(addition(multiplication(X4,X5),X6),X5))|leq(multiplication(star(X4),X6),X5)),inference(variable_rename,[status(thm)],[32])). cnf(34,plain,(leq(multiplication(star(X1),X2),X3)|~leq(addition(multiplication(X1,X3),X2),X3)),inference(split_conjunct,[status(thm)],[33])). fof(35, plain,![X4]:![X5]:![X6]:addition(addition(X6,X5),X4)=addition(X6,addition(X5,X4)),inference(variable_rename,[status(thm)],[7])). cnf(36,plain,(addition(addition(X1,X2),X3)=addition(X1,addition(X2,X3))),inference(split_conjunct,[status(thm)],[35])). fof(37, plain,![X4]:![X5]:![X6]:addition(multiplication(X4,X6),multiplication(X5,X6))=multiplication(addition(X4,X5),X6),inference(variable_rename,[status(thm)],[8])). cnf(38,plain,(addition(multiplication(X1,X2),multiplication(X3,X2))=multiplication(addition(X1,X3),X2)),inference(split_conjunct,[status(thm)],[37])). fof(39, plain,![X1]:![X2]:((~(addition(X1,X2)=X2)|leq(X1,X2))&(~(leq(X1,X2))|addition(X1,X2)=X2)),inference(fof_nnf,[status(thm)],[9])). fof(40, plain,![X3]:![X4]:((~(addition(X3,X4)=X4)|leq(X3,X4))&(~(leq(X3,X4))|addition(X3,X4)=X4)),inference(variable_rename,[status(thm)],[39])). cnf(41,plain,(addition(X1,X2)=X2|~leq(X1,X2)),inference(split_conjunct,[status(thm)],[40])). cnf(42,plain,(leq(X1,X2)|addition(X1,X2)!=X2),inference(split_conjunct,[status(thm)],[40])). fof(43, plain,![X2]:leq(addition(one,multiplication(X2,star(X2))),star(X2)),inference(variable_rename,[status(thm)],[10])). cnf(44,plain,(leq(addition(one,multiplication(X1,star(X1))),star(X1))),inference(split_conjunct,[status(thm)],[43])). fof(47, plain,![X2]:X2=multiplication(X2,one),inference(variable_rename,[status(thm)],[12])). cnf(48,plain,(X1=multiplication(X1,one)),inference(split_conjunct,[status(thm)],[47])). fof(49, plain,![X2]:addition(X2,X2)=X2,inference(variable_rename,[status(thm)],[13])). cnf(50,plain,(addition(X1,X1)=X1),inference(split_conjunct,[status(thm)],[49])). fof(51, plain,![X4]:![X5]:![X6]:multiplication(multiplication(X4,X5),X6)=multiplication(X4,multiplication(X5,X6)),inference(variable_rename,[status(thm)],[14])). cnf(52,plain,(multiplication(multiplication(X1,X2),X3)=multiplication(X1,multiplication(X2,X3))),inference(split_conjunct,[status(thm)],[51])). fof(53, plain,![X1]:![X2]:![X3]:(~(leq(addition(multiplication(X1,X2),X3),X1))|leq(multiplication(X3,star(X2)),X1)),inference(fof_nnf,[status(thm)],[20])). fof(54, plain,![X4]:![X5]:![X6]:(~(leq(addition(multiplication(X4,X5),X6),X4))|leq(multiplication(X6,star(X5)),X4)),inference(variable_rename,[status(thm)],[53])). cnf(55,plain,(leq(multiplication(X1,star(X2)),X3)|~leq(addition(multiplication(X3,X2),X1),X3)),inference(split_conjunct,[status(thm)],[54])). fof(56, plain,![X3]:![X4]:addition(X3,X4)=addition(X4,X3),inference(variable_rename,[status(thm)],[16])). cnf(57,plain,(addition(X1,X2)=addition(X2,X1)),inference(split_conjunct,[status(thm)],[56])). cnf(58,negated_conjecture,(~leq(multiplication(a,multiplication(a,multiplication(a,a))),star(a))),inference(split_conjunct,[status(thm)],[21])). cnf(66,plain,(leq(X1,X1)),inference(spm,[status(thm)],[42,50,theory(equality)])). cnf(69,plain,(leq(addition(one,star(one)),star(one))),inference(spm,[status(thm)],[44,31,theory(equality)])). cnf(72,plain,(addition(addition(one,multiplication(X1,star(X1))),star(X1))=star(X1)),inference(spm,[status(thm)],[41,44,theory(equality)])). cnf(93,plain,(addition(X1,addition(X2,X3))=addition(X3,addition(X1,X2))),inference(spm,[status(thm)],[57,36,theory(equality)])). cnf(98,plain,(addition(X1,X2)=addition(X1,addition(X1,X2))),inference(spm,[status(thm)],[36,50,theory(equality)])). cnf(99,plain,(addition(addition(X2,X1),X3)=addition(X1,addition(X2,X3))),inference(spm,[status(thm)],[36,57,theory(equality)])). cnf(104,plain,(addition(X2,addition(X1,X3))=addition(X1,addition(X2,X3))),inference(rw,[status(thm)],[99,36,theory(equality)])). cnf(109,plain,(leq(multiplication(X1,star(one)),X2)|~leq(addition(X2,X1),X2)),inference(spm,[status(thm)],[55,48,theory(equality)])). cnf(112,plain,(leq(multiplication(multiplication(X1,X2),star(X2)),X1)|~leq(multiplication(X1,X2),X1)),inference(spm,[status(thm)],[55,50,theory(equality)])). cnf(113,plain,(leq(multiplication(X1,star(X2)),X3)|~leq(addition(X1,multiplication(X3,X2)),X3)),inference(spm,[status(thm)],[55,57,theory(equality)])). cnf(116,plain,(leq(multiplication(X1,multiplication(X2,star(X2))),X1)|~leq(multiplication(X1,X2),X1)),inference(rw,[status(thm)],[112,52,theory(equality)])). cnf(124,plain,(leq(multiplication(star(X1),X2),X3)|~leq(addition(X2,multiplication(X1,X3)),X3)),inference(spm,[status(thm)],[34,57,theory(equality)])). cnf(129,plain,(leq(multiplication(X1,X2),multiplication(X1,X3))|multiplication(X1,addition(X2,X3))!=multiplication(X1,X3)),inference(spm,[status(thm)],[42,27,theory(equality)])). cnf(132,plain,(leq(multiplication(multiplication(X1,X2),star(X3)),X1)|~leq(multiplication(X1,addition(X3,X2)),X1)),inference(spm,[status(thm)],[55,27,theory(equality)])). cnf(137,plain,(addition(multiplication(X1,X2),X1)=multiplication(X1,addition(X2,one))),inference(spm,[status(thm)],[27,48,theory(equality)])). cnf(147,plain,(leq(multiplication(X1,multiplication(X2,star(X3))),X1)|~leq(multiplication(X1,addition(X3,X2)),X1)),inference(rw,[status(thm)],[132,52,theory(equality)])). cnf(170,plain,(addition(multiplication(X1,X2),X2)=multiplication(addition(X1,one),X2)),inference(spm,[status(thm)],[38,31,theory(equality)])). cnf(196,plain,(addition(addition(one,multiplication(star(X1),X1)),star(X1))=star(X1)),inference(spm,[status(thm)],[41,29,theory(equality)])). cnf(199,plain,(addition(one,addition(multiplication(star(X1),X1),star(X1)))=star(X1)),inference(rw,[status(thm)],[196,36,theory(equality)])). cnf(220,plain,(addition(addition(one,star(one)),star(one))=star(one)),inference(spm,[status(thm)],[41,69,theory(equality)])). cnf(221,plain,(addition(one,star(one))=star(one)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[220,36,theory(equality)]),50,theory(equality)])). cnf(223,plain,(addition(star(one),X1)=addition(one,addition(star(one),X1))),inference(spm,[status(thm)],[36,221,theory(equality)])). cnf(303,plain,(leq(one,addition(star(one),X1))),inference(spm,[status(thm)],[42,223,theory(equality)])). cnf(323,plain,(leq(X1,addition(X1,X2))),inference(spm,[status(thm)],[42,98,theory(equality)])). cnf(339,plain,(addition(X1,addition(X2,X1))=addition(X2,X1)),inference(spm,[status(thm)],[98,57,theory(equality)])). cnf(437,plain,(leq(one,addition(X1,star(one)))),inference(spm,[status(thm)],[303,57,theory(equality)])). cnf(446,plain,(leq(one,addition(X1,addition(X2,star(one))))),inference(spm,[status(thm)],[437,36,theory(equality)])). cnf(651,plain,(addition(X1,addition(X2,addition(X3,X1)))=addition(X2,addition(X3,X1))),inference(spm,[status(thm)],[98,93,theory(equality)])). cnf(678,plain,(leq(X1,addition(X2,X3))|addition(X3,addition(X1,X2))!=addition(X2,X3)),inference(spm,[status(thm)],[42,93,theory(equality)])). cnf(684,plain,(leq(X1,addition(X3,addition(X1,X2)))),inference(spm,[status(thm)],[323,93,theory(equality)])). cnf(893,plain,(addition(X1,multiplication(X1,X2))=multiplication(X1,addition(X2,one))),inference(rw,[status(thm)],[137,57,theory(equality)])). cnf(907,plain,(addition(X1,addition(multiplication(X1,X2),X3))=addition(X3,multiplication(X1,addition(X2,one)))),inference(spm,[status(thm)],[93,893,theory(equality)])). cnf(1388,plain,(addition(one,addition(star(X1),multiplication(X1,star(X1))))=star(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[72,36,theory(equality)]),57,theory(equality)])). cnf(1393,plain,(addition(one,star(X1))=star(X1)),inference(spm,[status(thm)],[98,1388,theory(equality)])). cnf(1562,plain,(addition(X2,multiplication(X1,X2))=multiplication(addition(X1,one),X2)),inference(rw,[status(thm)],[170,57,theory(equality)])). cnf(1596,plain,(multiplication(addition(X1,one),X1)=multiplication(X1,addition(X1,one))),inference(spm,[status(thm)],[893,1562,theory(equality)])). cnf(1602,plain,(addition(one,multiplication(addition(X1,one),star(X1)))=star(X1)),inference(rw,[status(thm)],[1388,1562,theory(equality)])). cnf(1673,plain,(leq(multiplication(X1,star(one)),X1)|~leq(X1,X1)),inference(spm,[status(thm)],[109,50,theory(equality)])). cnf(1686,plain,(leq(multiplication(X1,star(one)),X1)|$false),inference(rw,[status(thm)],[1673,66,theory(equality)])). cnf(1687,plain,(leq(multiplication(X1,star(one)),X1)),inference(cn,[status(thm)],[1686,theory(equality)])). cnf(1690,plain,(leq(star(one),one)),inference(spm,[status(thm)],[1687,31,theory(equality)])). cnf(1697,plain,(addition(star(one),one)=one),inference(spm,[status(thm)],[41,1690,theory(equality)])). cnf(1698,plain,(star(one)=one),inference(rw,[status(thm)],[inference(rw,[status(thm)],[1697,57,theory(equality)]),1393,theory(equality)])). cnf(1716,plain,(leq(one,addition(X1,addition(X2,one)))),inference(rw,[status(thm)],[446,1698,theory(equality)])). cnf(1807,plain,(leq(one,addition(X1,addition(one,X2)))),inference(spm,[status(thm)],[1716,57,theory(equality)])). cnf(2088,plain,(leq(one,addition(X1,star(X2)))),inference(spm,[status(thm)],[1807,1393,theory(equality)])). cnf(2129,plain,(leq(one,addition(star(X2),X1))),inference(spm,[status(thm)],[2088,57,theory(equality)])). cnf(2145,plain,(leq(one,multiplication(star(X1),addition(X2,one)))),inference(spm,[status(thm)],[2129,893,theory(equality)])). cnf(2146,plain,(leq(one,multiplication(addition(X2,one),star(X1)))),inference(spm,[status(thm)],[2129,1562,theory(equality)])). cnf(2361,plain,(addition(one,multiplication(star(X1),addition(X2,one)))=multiplication(star(X1),addition(X2,one))),inference(spm,[status(thm)],[41,2145,theory(equality)])). cnf(2365,plain,(leq(one,multiplication(star(X1),addition(one,X2)))),inference(spm,[status(thm)],[2145,57,theory(equality)])). cnf(2373,plain,(addition(one,multiplication(addition(X1,one),star(X2)))=multiplication(addition(X1,one),star(X2))),inference(spm,[status(thm)],[41,2146,theory(equality)])). cnf(2511,plain,(leq(one,multiplication(star(X1),star(X2)))),inference(spm,[status(thm)],[2365,1393,theory(equality)])). cnf(2524,plain,(addition(one,multiplication(star(X1),star(X2)))=multiplication(star(X1),star(X2))),inference(spm,[status(thm)],[41,2511,theory(equality)])). cnf(2893,plain,(leq(X1,addition(X2,multiplication(X1,addition(X3,one))))),inference(spm,[status(thm)],[684,893,theory(equality)])). cnf(2894,plain,(leq(X1,addition(X2,multiplication(addition(X3,one),X1)))),inference(spm,[status(thm)],[684,1562,theory(equality)])). cnf(3117,plain,(leq(multiplication(X1,star(X2)),X1)|~leq(multiplication(X1,addition(X2,one)),X1)),inference(spm,[status(thm)],[113,893,theory(equality)])). cnf(3216,plain,(leq(multiplication(star(addition(X1,one)),one),star(X1))|~leq(star(X1),star(X1))),inference(spm,[status(thm)],[124,1602,theory(equality)])). cnf(3227,plain,(addition(one,multiplication(addition(one,X1),star(X1)))=star(X1)),inference(spm,[status(thm)],[1602,57,theory(equality)])). cnf(3240,plain,(leq(star(addition(X1,one)),star(X1))|~leq(star(X1),star(X1))),inference(rw,[status(thm)],[3216,48,theory(equality)])). cnf(3241,plain,(leq(star(addition(X1,one)),star(X1))|$false),inference(rw,[status(thm)],[3240,66,theory(equality)])). cnf(3242,plain,(leq(star(addition(X1,one)),star(X1))),inference(cn,[status(thm)],[3241,theory(equality)])). cnf(3254,plain,(addition(star(addition(X1,one)),star(X1))=star(X1)),inference(spm,[status(thm)],[41,3242,theory(equality)])). cnf(3299,plain,(addition(star(X1),star(addition(X1,one)))=star(X1)),inference(rw,[status(thm)],[3254,57,theory(equality)])). cnf(3599,plain,(addition(one,multiplication(star(X1),addition(X1,one)))=star(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[199,57,theory(equality)]),893,theory(equality)])). cnf(4606,plain,(leq(multiplication(one,star(addition(X1,one))),star(X2))|~leq(multiplication(star(X2),addition(X1,one)),star(X2))),inference(spm,[status(thm)],[113,2361,theory(equality)])). cnf(4627,plain,(multiplication(star(X1),addition(X1,one))=star(X1)),inference(rw,[status(thm)],[3599,2361,theory(equality)])). cnf(4644,plain,(leq(star(addition(X1,one)),star(X2))|~leq(multiplication(star(X2),addition(X1,one)),star(X2))),inference(rw,[status(thm)],[4606,31,theory(equality)])). cnf(4679,plain,(addition(addition(X1,one),star(X1))=multiplication(addition(star(X1),one),addition(X1,one))),inference(spm,[status(thm)],[1562,4627,theory(equality)])). cnf(4683,plain,(leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1))|~leq(star(X1),star(X1))),inference(spm,[status(thm)],[147,4627,theory(equality)])). cnf(4695,plain,(multiplication(star(X1),addition(one,X1))=star(X1)),inference(spm,[status(thm)],[4627,57,theory(equality)])). cnf(4709,plain,(addition(X1,star(X1))=multiplication(addition(star(X1),one),addition(X1,one))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[4679,36,theory(equality)]),1393,theory(equality)])). cnf(4710,plain,(addition(X1,star(X1))=star(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4709,57,theory(equality)]),1393,theory(equality)]),4627,theory(equality)])). cnf(4714,plain,(leq(multiplication(star(X1),star(X1)),star(X1))|~leq(star(X1),star(X1))),inference(rw,[status(thm)],[4683,31,theory(equality)])). cnf(4715,plain,(leq(multiplication(star(X1),star(X1)),star(X1))|$false),inference(rw,[status(thm)],[4714,66,theory(equality)])). cnf(4716,plain,(leq(multiplication(star(X1),star(X1)),star(X1))),inference(cn,[status(thm)],[4715,theory(equality)])). cnf(4771,plain,(addition(X1,star(X2))=addition(X2,addition(X1,star(X2)))),inference(spm,[status(thm)],[104,4710,theory(equality)])). cnf(4773,plain,(leq(X1,addition(X2,star(X1)))),inference(spm,[status(thm)],[684,4710,theory(equality)])). cnf(4905,plain,(leq(multiplication(X1,X2),multiplication(X1,star(X2)))),inference(spm,[status(thm)],[129,4710,theory(equality)])). cnf(5021,plain,(leq(X1,addition(star(X1),X2))),inference(spm,[status(thm)],[4773,57,theory(equality)])). cnf(5042,plain,(leq(X1,multiplication(star(X1),addition(X2,one)))),inference(spm,[status(thm)],[5021,893,theory(equality)])). cnf(5253,plain,(addition(multiplication(star(X1),X2),star(X1))=multiplication(star(X1),addition(X2,addition(one,X1)))),inference(spm,[status(thm)],[27,4695,theory(equality)])). cnf(5280,plain,(multiplication(star(addition(X1,one)),addition(X1,one))=star(addition(X1,one))),inference(spm,[status(thm)],[4695,339,theory(equality)])). cnf(6156,plain,(addition(multiplication(star(X1),star(X1)),star(X1))=star(X1)),inference(spm,[status(thm)],[41,4716,theory(equality)])). cnf(6175,plain,(leq(X1,multiplication(star(X1),addition(one,X2)))),inference(spm,[status(thm)],[5042,57,theory(equality)])). cnf(6883,plain,(leq(X1,multiplication(star(X1),star(X2)))),inference(spm,[status(thm)],[6175,1393,theory(equality)])). cnf(6912,plain,(addition(X1,multiplication(star(X1),star(X2)))=multiplication(star(X1),star(X2))),inference(spm,[status(thm)],[41,6883,theory(equality)])). cnf(8250,plain,(addition(one,multiplication(star(X1),star(star(X1))))=star(star(X1))),inference(spm,[status(thm)],[3227,1393,theory(equality)])). cnf(8320,plain,(multiplication(star(X1),star(star(X1)))=star(star(X1))),inference(rw,[status(thm)],[8250,2524,theory(equality)])). cnf(8552,plain,(multiplication(addition(X1,one),star(X1))=star(X1)),inference(rw,[status(thm)],[1602,2373,theory(equality)])). cnf(9806,plain,(leq(multiplication(addition(X1,one),X1),star(X1))),inference(spm,[status(thm)],[4905,8552,theory(equality)])). cnf(9831,plain,(leq(multiplication(X1,addition(X1,one)),star(X1))),inference(rw,[status(thm)],[9806,1596,theory(equality)])). cnf(9902,plain,(addition(multiplication(X1,addition(X1,one)),star(X1))=star(X1)),inference(spm,[status(thm)],[41,9831,theory(equality)])). cnf(22248,plain,(leq(X1,addition(X2,multiplication(X1,addition(one,X3))))),inference(spm,[status(thm)],[2893,57,theory(equality)])). cnf(24301,plain,(leq(X1,addition(X2,multiplication(addition(one,X3),X1)))),inference(spm,[status(thm)],[2894,57,theory(equality)])). cnf(27548,plain,(multiplication(star(X1),star(X1))=star(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6156,57,theory(equality)]),893,theory(equality)]),57,theory(equality)]),1393,theory(equality)])). cnf(27551,plain,(addition(star(X1),multiplication(X2,star(X1)))=multiplication(addition(star(X1),X2),star(X1))),inference(spm,[status(thm)],[38,27548,theory(equality)])). cnf(27553,plain,(leq(multiplication(star(X1),multiplication(star(X1),star(star(X1)))),star(X1))|~leq(star(X1),star(X1))),inference(spm,[status(thm)],[116,27548,theory(equality)])). cnf(27620,plain,(multiplication(addition(X2,one),star(X1))=multiplication(addition(star(X1),X2),star(X1))),inference(rw,[status(thm)],[27551,1562,theory(equality)])). cnf(27622,plain,(leq(star(star(X1)),star(X1))|~leq(star(X1),star(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[27553,8320,theory(equality)]),8320,theory(equality)])). cnf(27623,plain,(leq(star(star(X1)),star(X1))|$false),inference(rw,[status(thm)],[27622,66,theory(equality)])). cnf(27624,plain,(leq(star(star(X1)),star(X1))),inference(cn,[status(thm)],[27623,theory(equality)])). cnf(27679,plain,(addition(star(star(X1)),star(X1))=star(X1)),inference(spm,[status(thm)],[41,27624,theory(equality)])). cnf(27699,plain,(star(star(X1))=star(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[27679,57,theory(equality)]),4710,theory(equality)])). cnf(29510,plain,(addition(star(X1),multiplication(X1,addition(X1,one)))=star(X1)),inference(rw,[status(thm)],[9902,57,theory(equality)])). cnf(29593,plain,(addition(X1,addition(multiplication(X1,X1),star(X1)))=star(X1)),inference(spm,[status(thm)],[907,29510,theory(equality)])). cnf(29687,plain,(addition(multiplication(X1,X1),star(X1))=star(X1)),inference(rw,[status(thm)],[29593,4771,theory(equality)])). cnf(29726,plain,(star(X1)=addition(star(X1),multiplication(X1,X1))),inference(spm,[status(thm)],[57,29687,theory(equality)])). cnf(29738,plain,(leq(multiplication(X1,X1),addition(star(X1),X2))|addition(X2,star(X1))!=addition(star(X1),X2)),inference(spm,[status(thm)],[678,29687,theory(equality)])). cnf(29858,plain,(leq(multiplication(X1,X1),addition(star(X1),X2))),inference(ar,[status(thm)],[29738,57,52,36,theory(equality)])). cnf(31093,plain,(multiplication(star(X1),star(X1))=multiplication(addition(star(addition(X1,one)),one),star(X1))),inference(spm,[status(thm)],[27620,3299,theory(equality)])). cnf(31212,plain,(star(X1)=multiplication(addition(star(addition(X1,one)),one),star(X1))),inference(rw,[status(thm)],[31093,27548,theory(equality)])). cnf(31213,plain,(star(X1)=multiplication(star(addition(X1,one)),star(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[31212,57,theory(equality)]),1393,theory(equality)])). cnf(41279,plain,(leq(X1,addition(X2,multiplication(X1,multiplication(star(one),star(X3)))))),inference(spm,[status(thm)],[22248,6912,theory(equality)])). cnf(41346,plain,(leq(X1,addition(X2,multiplication(X1,star(X3))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[41279,1698,theory(equality)]),31,theory(equality)])). cnf(41414,plain,(leq(X1,addition(multiplication(X1,star(X3)),X2))),inference(spm,[status(thm)],[41346,57,theory(equality)])). cnf(41600,plain,(leq(X1,star(multiplication(X1,star(X2))))),inference(spm,[status(thm)],[41414,4710,theory(equality)])). cnf(41665,plain,(addition(X1,star(multiplication(X1,star(X2))))=star(multiplication(X1,star(X2)))),inference(spm,[status(thm)],[41,41600,theory(equality)])). cnf(44698,plain,(leq(X1,addition(X2,multiplication(star(multiplication(one,star(X3))),X1)))),inference(spm,[status(thm)],[24301,41665,theory(equality)])). cnf(44780,plain,(leq(X1,addition(X2,multiplication(star(X3),X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[44698,31,theory(equality)]),27699,theory(equality)])). cnf(44873,plain,(leq(X1,addition(multiplication(star(X3),X1),X2))),inference(spm,[status(thm)],[44780,57,theory(equality)])). cnf(45210,plain,(leq(X1,star(multiplication(star(X2),X1)))),inference(spm,[status(thm)],[44873,4710,theory(equality)])). cnf(45278,plain,(addition(X1,star(multiplication(star(X2),X1)))=star(multiplication(star(X2),X1))),inference(spm,[status(thm)],[41,45210,theory(equality)])). cnf(55108,plain,(multiplication(star(X1),addition(X2,one))=multiplication(star(X1),addition(X2,addition(one,X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[5253,57,theory(equality)]),893,theory(equality)])). cnf(55264,plain,(multiplication(star(addition(X1,X2)),addition(one,addition(X1,X2)))=multiplication(star(addition(X1,X2)),addition(X2,one))),inference(spm,[status(thm)],[55108,651,theory(equality)])). cnf(55416,plain,(star(addition(X1,X2))=multiplication(star(addition(X1,X2)),addition(X2,one))),inference(rw,[status(thm)],[55264,4695,theory(equality)])). cnf(131754,plain,(addition(addition(X1,one),star(star(addition(X2,X1))))=star(star(addition(X2,X1)))),inference(spm,[status(thm)],[45278,55416,theory(equality)])). cnf(132054,plain,(addition(X1,star(addition(X2,X1)))=star(star(addition(X2,X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[131754,27699,theory(equality)]),36,theory(equality)]),1393,theory(equality)])). cnf(132055,plain,(addition(X1,star(addition(X2,X1)))=star(addition(X2,X1))),inference(rw,[status(thm)],[132054,27699,theory(equality)])). cnf(133033,plain,(leq(multiplication(X1,X1),star(addition(X2,star(X1))))),inference(spm,[status(thm)],[29858,132055,theory(equality)])). cnf(138519,plain,(leq(multiplication(star(addition(X1,one)),star(X1)),star(addition(X1,one)))|~leq(star(addition(X1,one)),star(addition(X1,one)))),inference(spm,[status(thm)],[3117,5280,theory(equality)])). cnf(138548,plain,(leq(star(X1),star(addition(X1,one)))|~leq(star(addition(X1,one)),star(addition(X1,one)))),inference(rw,[status(thm)],[138519,31213,theory(equality)])). cnf(138549,plain,(leq(star(X1),star(addition(X1,one)))|$false),inference(rw,[status(thm)],[138548,66,theory(equality)])). cnf(138550,plain,(leq(star(X1),star(addition(X1,one)))),inference(cn,[status(thm)],[138549,theory(equality)])). cnf(138582,plain,(addition(star(X1),star(addition(X1,one)))=star(addition(X1,one))),inference(spm,[status(thm)],[41,138550,theory(equality)])). cnf(138593,plain,(star(X1)=star(addition(X1,one))),inference(rw,[status(thm)],[138582,3299,theory(equality)])). cnf(262397,plain,(leq(star(X1),star(X2))|~leq(multiplication(star(X2),addition(X1,one)),star(X2))),inference(rw,[status(thm)],[4644,138593,theory(equality)])). cnf(262443,plain,(leq(star(X1),star(addition(X2,X1)))|~leq(star(addition(X2,X1)),star(addition(X2,X1)))),inference(spm,[status(thm)],[262397,55416,theory(equality)])). cnf(262472,plain,(leq(star(X1),star(addition(X2,X1)))|$false),inference(rw,[status(thm)],[262443,66,theory(equality)])). cnf(262473,plain,(leq(star(X1),star(addition(X2,X1)))),inference(cn,[status(thm)],[262472,theory(equality)])). cnf(262500,plain,(leq(star(multiplication(X1,X1)),star(star(X1)))),inference(spm,[status(thm)],[262473,29726,theory(equality)])). cnf(262644,plain,(leq(star(multiplication(X1,X1)),star(X1))),inference(rw,[status(thm)],[262500,27699,theory(equality)])). cnf(262976,plain,(addition(star(multiplication(X1,X1)),star(X1))=star(X1)),inference(spm,[status(thm)],[41,262644,theory(equality)])). cnf(265613,plain,(addition(star(X1),star(multiplication(X1,X1)))=star(X1)),inference(rw,[status(thm)],[262976,57,theory(equality)])). cnf(265951,plain,(leq(multiplication(multiplication(X1,X1),multiplication(X1,X1)),star(star(X1)))),inference(spm,[status(thm)],[133033,265613,theory(equality)])). cnf(266389,plain,(leq(multiplication(X1,multiplication(X1,multiplication(X1,X1))),star(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[265951,52,theory(equality)]),27699,theory(equality)])). cnf(1277632,negated_conjecture,($false),inference(rw,[status(thm)],[58,266389,theory(equality)])). cnf(1277633,negated_conjecture,($false),inference(cn,[status(thm)],[1277632,theory(equality)])). cnf(1277634,negated_conjecture,($false),1277633,['proof']). # SZS output end CNFRefutation WATCH: 19.04 CPU 11.14 WC FINAL WATCH: 19.04 CPU 11.14 WC