%------------------------------------------------------------------------------ % File : NLP005^7 : TPTP v7.0.0. Released v5.5.0. % Domain : Natural Language Processing % Problem : "The old dirty white Chevy" problem 5 % Version : [Ben12] axioms. % English : % Refs : [Bos00] Bos (2000), DORIS: Discourse Oriented Representation an % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe % Source : [Ben12] % Names : s4-cumul-NLP005+1 [Ben12] % Status : CounterSatisfiable % Rating : 0.67 v5.5.0 % Syntax : Number of formulae : 119 ( 0 unit; 56 type; 32 defn) % Number of atoms : 1001 ( 36 equality; 409 variable) % Maximal formula depth : 58 ( 7 average) % Number of connectives : 871 ( 5 ~; 5 |; 9 &; 842 @) % ( 0 <=>; 10 =>; 0 <=; 0 <~>) % ( 0 ~|; 0 ~&) % Number of type conns : 223 ( 223 >; 0 *; 0 +; 0 <<) % Number of symbols : 60 ( 56 :; 0 =) % Number of variables : 186 ( 2 sgn; 34 !; 7 ?; 145 ^) % ( 186 :; 0 !>; 0 ?*) % ( 0 @-; 0 @+) % SPC : TH0_CSA_EQU_NAR % Comments : %------------------------------------------------------------------------------ %----Include axioms for Modal logic S4 under cumulative domains include('Axioms/LCL015^0.ax'). include('Axioms/LCL013^5.ax'). include('Axioms/LCL015^1.ax'). %------------------------------------------------------------------------------ thf(young_type,type,( young: mu > $i > $o )). thf(man_type,type,( man: mu > $i > $o )). thf(fellow_type,type,( fellow: mu > $i > $o )). thf(in_type,type,( in: mu > mu > $i > $o )). thf(down_type,type,( down: mu > mu > $i > $o )). thf(barrel_type,type,( barrel: mu > mu > $i > $o )). thf(lonely_type,type,( lonely: mu > $i > $o )). thf(way_type,type,( way: mu > $i > $o )). thf(street_type,type,( street: mu > $i > $o )). thf(old_type,type,( old: mu > $i > $o )). thf(dirty_type,type,( dirty: mu > $i > $o )). thf(white_type,type,( white: mu > $i > $o )). thf(car_type,type,( car: mu > $i > $o )). thf(chevy_type,type,( chevy: mu > $i > $o )). thf(event_type,type,( event: mu > $i > $o )). thf(city_type,type,( city: mu > $i > $o )). thf(hollywood_type,type,( hollywood: mu > $i > $o )). thf(front_type,type,( front: mu > $i > $o )). thf(furniture_type,type,( furniture: mu > $i > $o )). thf(seat_type,type,( seat: mu > $i > $o )). thf(reflexivity,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( qmltpeq @ X @ X ) ) )). thf(symmetry,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) )). thf(transitivity,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mforall_ind @ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) )). thf(barrel_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mforall_ind @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( barrel @ A @ C ) ) @ ( barrel @ B @ C ) ) ) ) ) )). thf(barrel_substitution_2,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mforall_ind @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( barrel @ C @ A ) ) @ ( barrel @ C @ B ) ) ) ) ) )). thf(car_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( car @ A ) ) @ ( car @ B ) ) ) ) )). thf(chevy_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( chevy @ A ) ) @ ( chevy @ B ) ) ) ) )). thf(city_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( city @ A ) ) @ ( city @ B ) ) ) ) )). thf(dirty_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( dirty @ A ) ) @ ( dirty @ B ) ) ) ) )). thf(down_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mforall_ind @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( down @ A @ C ) ) @ ( down @ B @ C ) ) ) ) ) )). thf(down_substitution_2,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mforall_ind @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( down @ C @ A ) ) @ ( down @ C @ B ) ) ) ) ) )). thf(event_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( event @ A ) ) @ ( event @ B ) ) ) ) )). thf(fellow_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( fellow @ A ) ) @ ( fellow @ B ) ) ) ) )). thf(front_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( front @ A ) ) @ ( front @ B ) ) ) ) )). thf(furniture_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( furniture @ A ) ) @ ( furniture @ B ) ) ) ) )). thf(hollywood_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( hollywood @ A ) ) @ ( hollywood @ B ) ) ) ) )). thf(in_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mforall_ind @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) )). thf(in_substitution_2,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mforall_ind @ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) )). thf(lonely_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( lonely @ A ) ) @ ( lonely @ B ) ) ) ) )). thf(man_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( man @ A ) ) @ ( man @ B ) ) ) ) )). thf(old_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( old @ A ) ) @ ( old @ B ) ) ) ) )). thf(seat_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( seat @ A ) ) @ ( seat @ B ) ) ) ) )). thf(street_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( street @ A ) ) @ ( street @ B ) ) ) ) )). thf(way_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( way @ A ) ) @ ( way @ B ) ) ) ) )). thf(white_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( white @ A ) ) @ ( white @ B ) ) ) ) )). thf(young_substitution_1,axiom, ( mvalid @ ( mforall_ind @ ^ [A: mu] : ( mforall_ind @ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( young @ A ) ) @ ( young @ B ) ) ) ) )). thf(co1,conjecture, ( mvalid @ ( mand @ ( mimplies @ ( mexists_ind @ ^ [U: mu] : ( mexists_ind @ ^ [V: mu] : ( mexists_ind @ ^ [W: mu] : ( mexists_ind @ ^ [X: mu] : ( mexists_ind @ ^ [Y: mu] : ( mexists_ind @ ^ [Z: mu] : ( mexists_ind @ ^ [X1: mu] : ( mexists_ind @ ^ [X3: mu] : ( mexists_ind @ ^ [X4: mu] : ( mand @ ( seat @ U ) @ ( mand @ ( furniture @ U ) @ ( mand @ ( front @ U ) @ ( mand @ ( hollywood @ V ) @ ( mand @ ( city @ V ) @ ( mand @ ( event @ W ) @ ( mand @ ( chevy @ X ) @ ( mand @ ( car @ X ) @ ( mand @ ( white @ X ) @ ( mand @ ( dirty @ X ) @ ( mand @ ( old @ X ) @ ( mand @ ( street @ Y ) @ ( mand @ ( way @ Y ) @ ( mand @ ( lonely @ Y ) @ ( mand @ ( barrel @ W @ X ) @ ( mand @ ( down @ W @ Y ) @ ( mand @ ( in @ W @ V ) @ ( mand @ ( mnot @ ( qmltpeq @ Z @ X1 ) ) @ ( mand @ ( fellow @ Z ) @ ( mand @ ( man @ Z ) @ ( mand @ ( young @ Z ) @ ( mand @ ( fellow @ X1 ) @ ( mand @ ( man @ X1 ) @ ( mand @ ( young @ X1 ) @ ( mand @ ( qmltpeq @ Z @ X3 ) @ ( mand @ ( in @ X3 @ U ) @ ( mand @ ( qmltpeq @ X1 @ X4 ) @ ( in @ X4 @ U ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( mexists_ind @ ^ [X5: mu] : ( mexists_ind @ ^ [X6: mu] : ( mexists_ind @ ^ [X7: mu] : ( mexists_ind @ ^ [X8: mu] : ( mexists_ind @ ^ [X9: mu] : ( mexists_ind @ ^ [X10: mu] : ( mexists_ind @ ^ [X11: mu] : ( mexists_ind @ ^ [X12: mu] : ( mexists_ind @ ^ [X14: mu] : ( mexists_ind @ ^ [X15: mu] : ( mand @ ( seat @ X5 ) @ ( mand @ ( furniture @ X5 ) @ ( mand @ ( front @ X5 ) @ ( mand @ ( seat @ X6 ) @ ( mand @ ( furniture @ X6 ) @ ( mand @ ( front @ X6 ) @ ( mand @ ( hollywood @ X7 ) @ ( mand @ ( city @ X7 ) @ ( mand @ ( event @ X8 ) @ ( mand @ ( street @ X9 ) @ ( mand @ ( way @ X9 ) @ ( mand @ ( lonely @ X9 ) @ ( mand @ ( chevy @ X10 ) @ ( mand @ ( car @ X10 ) @ ( mand @ ( white @ X10 ) @ ( mand @ ( dirty @ X10 ) @ ( mand @ ( old @ X10 ) @ ( mand @ ( barrel @ X8 @ X10 ) @ ( mand @ ( down @ X8 @ X9 ) @ ( mand @ ( in @ X8 @ X7 ) @ ( mand @ ( mnot @ ( qmltpeq @ X11 @ X12 ) ) @ ( mand @ ( fellow @ X11 ) @ ( mand @ ( man @ X11 ) @ ( mand @ ( young @ X11 ) @ ( mand @ ( fellow @ X12 ) @ ( mand @ ( man @ X12 ) @ ( mand @ ( young @ X12 ) @ ( mand @ ( qmltpeq @ X11 @ X14 ) @ ( mand @ ( in @ X14 @ X5 ) @ ( mand @ ( qmltpeq @ X12 @ X15 ) @ ( in @ X15 @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( mimplies @ ( mexists_ind @ ^ [X16: mu] : ( mexists_ind @ ^ [X17: mu] : ( mexists_ind @ ^ [X18: mu] : ( mexists_ind @ ^ [X19: mu] : ( mexists_ind @ ^ [X20: mu] : ( mexists_ind @ ^ [X21: mu] : ( mexists_ind @ ^ [X22: mu] : ( mexists_ind @ ^ [X23: mu] : ( mexists_ind @ ^ [X25: mu] : ( mexists_ind @ ^ [X26: mu] : ( mand @ ( seat @ X16 ) @ ( mand @ ( furniture @ X16 ) @ ( mand @ ( front @ X16 ) @ ( mand @ ( seat @ X17 ) @ ( mand @ ( furniture @ X17 ) @ ( mand @ ( front @ X17 ) @ ( mand @ ( hollywood @ X18 ) @ ( mand @ ( city @ X18 ) @ ( mand @ ( event @ X19 ) @ ( mand @ ( street @ X20 ) @ ( mand @ ( way @ X20 ) @ ( mand @ ( lonely @ X20 ) @ ( mand @ ( chevy @ X21 ) @ ( mand @ ( car @ X21 ) @ ( mand @ ( white @ X21 ) @ ( mand @ ( dirty @ X21 ) @ ( mand @ ( old @ X21 ) @ ( mand @ ( barrel @ X19 @ X21 ) @ ( mand @ ( down @ X19 @ X20 ) @ ( mand @ ( in @ X19 @ X18 ) @ ( mand @ ( mnot @ ( qmltpeq @ X22 @ X23 ) ) @ ( mand @ ( fellow @ X22 ) @ ( mand @ ( man @ X22 ) @ ( mand @ ( young @ X22 ) @ ( mand @ ( fellow @ X23 ) @ ( mand @ ( man @ X23 ) @ ( mand @ ( young @ X23 ) @ ( mand @ ( qmltpeq @ X22 @ X25 ) @ ( mand @ ( in @ X25 @ X16 ) @ ( mand @ ( qmltpeq @ X23 @ X26 ) @ ( in @ X26 @ X17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( mexists_ind @ ^ [X27: mu] : ( mexists_ind @ ^ [X28: mu] : ( mexists_ind @ ^ [X29: mu] : ( mexists_ind @ ^ [X30: mu] : ( mexists_ind @ ^ [X31: mu] : ( mexists_ind @ ^ [X32: mu] : ( mexists_ind @ ^ [X33: mu] : ( mexists_ind @ ^ [X35: mu] : ( mexists_ind @ ^ [X36: mu] : ( mand @ ( seat @ X27 ) @ ( mand @ ( furniture @ X27 ) @ ( mand @ ( front @ X27 ) @ ( mand @ ( hollywood @ X28 ) @ ( mand @ ( city @ X28 ) @ ( mand @ ( event @ X29 ) @ ( mand @ ( chevy @ X30 ) @ ( mand @ ( car @ X30 ) @ ( mand @ ( white @ X30 ) @ ( mand @ ( dirty @ X30 ) @ ( mand @ ( old @ X30 ) @ ( mand @ ( street @ X31 ) @ ( mand @ ( way @ X31 ) @ ( mand @ ( lonely @ X31 ) @ ( mand @ ( barrel @ X29 @ X30 ) @ ( mand @ ( down @ X29 @ X31 ) @ ( mand @ ( in @ X29 @ X28 ) @ ( mand @ ( mnot @ ( qmltpeq @ X32 @ X33 ) ) @ ( mand @ ( fellow @ X32 ) @ ( mand @ ( man @ X32 ) @ ( mand @ ( young @ X32 ) @ ( mand @ ( fellow @ X33 ) @ ( mand @ ( man @ X33 ) @ ( mand @ ( young @ X33 ) @ ( mand @ ( qmltpeq @ X32 @ X35 ) @ ( mand @ ( in @ X35 @ X27 ) @ ( mand @ ( qmltpeq @ X33 @ X36 ) @ ( in @ X36 @ X27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )). %------------------------------------------------------------------------------