TSTP Solution File: GRP022-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:32:18 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 43 ( 23 unt; 0 nHn; 25 RR)
% Number of literals : 75 ( 34 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ) ).
cnf(associativity1,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ) ).
cnf(prove_inverse_of_inverse_is_original,negated_conjecture,
inverse(inverse(a)) != a ).
cnf(refute_0_0,plain,
product(X_51,X_52,multiply(X_51,X_52)),
inference(subst,[],[total_function1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_51,X_52,X_53)
| ~ product(X_51,X_52,multiply(X_51,X_52))
| X_53 = multiply(X_51,X_52) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_51,X_52))),bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_51,X_52,X_53)
| X_53 = multiply(X_51,X_52) ),
inference(resolve,[$cnf( product(X_51,X_52,multiply(X_51,X_52)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(inverse(inverse(X_167)),identity,X_167)
| X_167 = multiply(inverse(inverse(X_167)),identity) ),
inference(subst,[],[refute_0_2:[bind(X_51,$fot(inverse(inverse(X_167)))),bind(X_52,$fot(identity)),bind(X_53,$fot(X_167))]]) ).
cnf(refute_0_4,plain,
product(inverse(inverse(X_165)),inverse(X_165),identity),
inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X_165)))]]) ).
cnf(refute_0_5,plain,
product(inverse(X_162),X_162,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_162))]]) ).
cnf(refute_0_6,plain,
product(identity,X_103,X_103),
inference(subst,[],[left_identity:[bind(X,$fot(X_103))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_104,X_105,identity)
| ~ product(X_105,X_103,X_102)
| ~ product(identity,X_103,X_103)
| product(X_104,X_102,X_103) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_102)),bind(W,$fot(X_103)),bind(X,$fot(X_104)),bind(Y,$fot(X_105)),bind(Z,$fot(X_103))]]) ).
cnf(refute_0_8,plain,
( ~ product(X_104,X_105,identity)
| ~ product(X_105,X_103,X_102)
| product(X_104,X_102,X_103) ),
inference(resolve,[$cnf( product(identity,X_103,X_103) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ product(X_163,inverse(X_162),identity)
| ~ product(inverse(X_162),X_162,identity)
| product(X_163,identity,X_162) ),
inference(subst,[],[refute_0_8:[bind(X_102,$fot(identity)),bind(X_103,$fot(X_162)),bind(X_104,$fot(X_163)),bind(X_105,$fot(inverse(X_162)))]]) ).
cnf(refute_0_10,plain,
( ~ product(X_163,inverse(X_162),identity)
| product(X_163,identity,X_162) ),
inference(resolve,[$cnf( product(inverse(X_162),X_162,identity) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ product(inverse(inverse(X_165)),inverse(X_165),identity)
| product(inverse(inverse(X_165)),identity,X_165) ),
inference(subst,[],[refute_0_10:[bind(X_162,$fot(X_165)),bind(X_163,$fot(inverse(inverse(X_165))))]]) ).
cnf(refute_0_12,plain,
product(inverse(inverse(X_165)),identity,X_165),
inference(resolve,[$cnf( product(inverse(inverse(X_165)),inverse(X_165),identity) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
product(inverse(inverse(X_167)),identity,X_167),
inference(subst,[],[refute_0_12:[bind(X_165,$fot(X_167))]]) ).
cnf(refute_0_14,plain,
X_167 = multiply(inverse(inverse(X_167)),identity),
inference(resolve,[$cnf( product(inverse(inverse(X_167)),identity,X_167) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
product(X_60,identity,multiply(X_60,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_60)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_16,plain,
product(X_50,identity,X_50),
inference(subst,[],[right_identity:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_17,plain,
( ~ product(X_50,identity,X_50)
| ~ product(X_50,identity,X_53)
| X_53 = X_50 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_50)),bind(X,$fot(X_50)),bind(Y,$fot(identity)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_18,plain,
( ~ product(X_50,identity,X_53)
| X_53 = X_50 ),
inference(resolve,[$cnf( product(X_50,identity,X_50) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ product(X_60,identity,multiply(X_60,identity))
| multiply(X_60,identity) = X_60 ),
inference(subst,[],[refute_0_18:[bind(X_50,$fot(X_60)),bind(X_53,$fot(multiply(X_60,identity)))]]) ).
cnf(refute_0_20,plain,
multiply(X_60,identity) = X_60,
inference(resolve,[$cnf( product(X_60,identity,multiply(X_60,identity)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(inverse(inverse(X_167)),identity) = inverse(inverse(X_167)),
inference(subst,[],[refute_0_20:[bind(X_60,$fot(inverse(inverse(X_167))))]]) ).
cnf(refute_0_22,plain,
( X_167 != multiply(inverse(inverse(X_167)),identity)
| multiply(inverse(inverse(X_167)),identity) != inverse(inverse(X_167))
| X_167 = inverse(inverse(X_167)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_167,inverse(inverse(X_167))) ),[0],$fot(multiply(inverse(inverse(X_167)),identity))]]) ).
cnf(refute_0_23,plain,
( X_167 != multiply(inverse(inverse(X_167)),identity)
| X_167 = inverse(inverse(X_167)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_167)),identity),inverse(inverse(X_167))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
X_167 = inverse(inverse(X_167)),
inference(resolve,[$cnf( $equal(X_167,multiply(inverse(inverse(X_167)),identity)) )],[refute_0_14,refute_0_23]) ).
cnf(refute_0_25,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( X_167 != inverse(inverse(X_167))
| inverse(inverse(X_167)) = X_167 ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(X_167)),bind(Y0,$fot(inverse(inverse(X_167))))]]) ).
cnf(refute_0_29,plain,
inverse(inverse(X_167)) = X_167,
inference(resolve,[$cnf( $equal(X_167,inverse(inverse(X_167))) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
inverse(inverse(a)) = a,
inference(subst,[],[refute_0_29:[bind(X_167,$fot(a))]]) ).
cnf(refute_0_31,plain,
( a != a
| inverse(inverse(a)) != a
| inverse(inverse(a)) = a ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a)),a) ),[0,0,0],$fot(a)]]) ).
cnf(refute_0_32,plain,
( a != a
| inverse(inverse(a)) = a ),
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
a != a,
inference(resolve,[$cnf( $equal(inverse(inverse(a)),a) )],[refute_0_32,prove_inverse_of_inverse_is_original]) ).
cnf(refute_0_34,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_34,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 21:40:26 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40
% 0.19/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.41
%------------------------------------------------------------------------------