TSTP Solution File: GRP017-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 10:32:16 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 61 ( 30 unt; 0 nHn; 46 RR)
% Number of literals : 107 ( 45 equ; 48 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 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(a_times_b_is_identity,hypothesis,
product(a,b,identity) ).
cnf(a_times_c_is_identity,hypothesis,
product(a,c,identity) ).
cnf(prove_b_equals_c,negated_conjecture,
b != c ).
cnf(refute_0_0,plain,
product(X_84,X_85,multiply(X_84,X_85)),
inference(subst,[],[total_function1:[bind(X,$fot(X_84)),bind(Y,$fot(X_85))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_84,X_85,X_86)
| ~ product(X_84,X_85,multiply(X_84,X_85))
| X_86 = multiply(X_84,X_85) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_84,X_85))),bind(X,$fot(X_84)),bind(Y,$fot(X_85)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_84,X_85,X_86)
| X_86 = multiply(X_84,X_85) ),
inference(resolve,[$cnf( product(X_84,X_85,multiply(X_84,X_85)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(b,identity,c)
| c = multiply(b,identity) ),
inference(subst,[],[refute_0_2:[bind(X_84,$fot(b)),bind(X_85,$fot(identity)),bind(X_86,$fot(c))]]) ).
cnf(refute_0_4,plain,
product(identity,X_149,multiply(identity,X_149)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(X_149))]]) ).
cnf(refute_0_5,plain,
product(inverse(X_131),X_131,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(X_131))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_131,X_132,X_128)
| ~ product(identity,X_132,X_129)
| ~ product(inverse(X_131),X_131,identity)
| product(inverse(X_131),X_128,X_129) ),
inference(subst,[],[associativity1:[bind(U,$fot(identity)),bind(V,$fot(X_128)),bind(W,$fot(X_129)),bind(X,$fot(inverse(X_131))),bind(Y,$fot(X_131)),bind(Z,$fot(X_132))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_131,X_132,X_128)
| ~ product(identity,X_132,X_129)
| product(inverse(X_131),X_128,X_129) ),
inference(resolve,[$cnf( product(inverse(X_131),X_131,identity) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(X_148,X_149,X_146)
| ~ product(identity,X_149,multiply(identity,X_149))
| product(inverse(X_148),X_146,multiply(identity,X_149)) ),
inference(subst,[],[refute_0_7:[bind(X_128,$fot(X_146)),bind(X_129,$fot(multiply(identity,X_149))),bind(X_131,$fot(X_148)),bind(X_132,$fot(X_149))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_148,X_149,X_146)
| product(inverse(X_148),X_146,multiply(identity,X_149)) ),
inference(resolve,[$cnf( product(identity,X_149,multiply(identity,X_149)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
product(identity,X_91,multiply(identity,X_91)),
inference(subst,[],[total_function1:[bind(X,$fot(identity)),bind(Y,$fot(X_91))]]) ).
cnf(refute_0_11,plain,
product(identity,X_83,X_83),
inference(subst,[],[left_identity:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_12,plain,
( ~ product(identity,X_83,X_83)
| ~ product(identity,X_83,X_86)
| X_86 = X_83 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_83)),bind(X,$fot(identity)),bind(Y,$fot(X_83)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_13,plain,
( ~ product(identity,X_83,X_86)
| X_86 = X_83 ),
inference(resolve,[$cnf( product(identity,X_83,X_83) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ product(identity,X_91,multiply(identity,X_91))
| multiply(identity,X_91) = X_91 ),
inference(subst,[],[refute_0_13:[bind(X_83,$fot(X_91)),bind(X_86,$fot(multiply(identity,X_91)))]]) ).
cnf(refute_0_15,plain,
multiply(identity,X_91) = X_91,
inference(resolve,[$cnf( product(identity,X_91,multiply(identity,X_91)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(identity,X_149) = X_149,
inference(subst,[],[refute_0_15:[bind(X_91,$fot(X_149))]]) ).
cnf(refute_0_17,plain,
( multiply(identity,X_149) != X_149
| ~ product(inverse(X_148),X_146,multiply(identity,X_149))
| product(inverse(X_148),X_146,X_149) ),
introduced(tautology,[equality,[$cnf( product(inverse(X_148),X_146,multiply(identity,X_149)) ),[2],$fot(X_149)]]) ).
cnf(refute_0_18,plain,
( ~ product(inverse(X_148),X_146,multiply(identity,X_149))
| product(inverse(X_148),X_146,X_149) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_149),X_149) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ product(X_148,X_149,X_146)
| product(inverse(X_148),X_146,X_149) ),
inference(resolve,[$cnf( product(inverse(X_148),X_146,multiply(identity,X_149)) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ product(a,c,identity)
| product(inverse(a),identity,c) ),
inference(subst,[],[refute_0_19:[bind(X_146,$fot(identity)),bind(X_148,$fot(a)),bind(X_149,$fot(c))]]) ).
cnf(refute_0_21,plain,
product(inverse(a),identity,c),
inference(resolve,[$cnf( product(a,c,identity) )],[a_times_c_is_identity,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ product(inverse(a),identity,b)
| b = multiply(inverse(a),identity) ),
inference(subst,[],[refute_0_2:[bind(X_84,$fot(inverse(a))),bind(X_85,$fot(identity)),bind(X_86,$fot(b))]]) ).
cnf(refute_0_23,plain,
( ~ product(a,b,identity)
| product(inverse(a),identity,b) ),
inference(subst,[],[refute_0_19:[bind(X_146,$fot(identity)),bind(X_148,$fot(a)),bind(X_149,$fot(b))]]) ).
cnf(refute_0_24,plain,
product(inverse(a),identity,b),
inference(resolve,[$cnf( product(a,b,identity) )],[a_times_b_is_identity,refute_0_23]) ).
cnf(refute_0_25,plain,
b = multiply(inverse(a),identity),
inference(resolve,[$cnf( product(inverse(a),identity,b) )],[refute_0_24,refute_0_22]) ).
cnf(refute_0_26,plain,
product(X_94,identity,multiply(X_94,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_94)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_27,plain,
product(X_83,identity,X_83),
inference(subst,[],[right_identity:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_28,plain,
( ~ product(X_83,identity,X_83)
| ~ product(X_83,identity,X_86)
| X_86 = X_83 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_83)),bind(X,$fot(X_83)),bind(Y,$fot(identity)),bind(Z,$fot(X_86))]]) ).
cnf(refute_0_29,plain,
( ~ product(X_83,identity,X_86)
| X_86 = X_83 ),
inference(resolve,[$cnf( product(X_83,identity,X_83) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ product(X_94,identity,multiply(X_94,identity))
| multiply(X_94,identity) = X_94 ),
inference(subst,[],[refute_0_29:[bind(X_83,$fot(X_94)),bind(X_86,$fot(multiply(X_94,identity)))]]) ).
cnf(refute_0_31,plain,
multiply(X_94,identity) = X_94,
inference(resolve,[$cnf( product(X_94,identity,multiply(X_94,identity)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(inverse(a),identity) = inverse(a),
inference(subst,[],[refute_0_31:[bind(X_94,$fot(inverse(a)))]]) ).
cnf(refute_0_33,plain,
( multiply(inverse(a),identity) != inverse(a)
| b != multiply(inverse(a),identity)
| b = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(b,multiply(inverse(a),identity)) ),[1],$fot(inverse(a))]]) ).
cnf(refute_0_34,plain,
( b != multiply(inverse(a),identity)
| b = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
b = inverse(a),
inference(resolve,[$cnf( $equal(b,multiply(inverse(a),identity)) )],[refute_0_25,refute_0_34]) ).
cnf(refute_0_36,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_37,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_38,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( b != inverse(a)
| inverse(a) = b ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(a)))]]) ).
cnf(refute_0_40,plain,
inverse(a) = b,
inference(resolve,[$cnf( $equal(b,inverse(a)) )],[refute_0_35,refute_0_39]) ).
cnf(refute_0_41,plain,
( inverse(a) != b
| ~ product(inverse(a),identity,c)
| product(b,identity,c) ),
introduced(tautology,[equality,[$cnf( product(inverse(a),identity,c) ),[0],$fot(b)]]) ).
cnf(refute_0_42,plain,
( ~ product(inverse(a),identity,c)
| product(b,identity,c) ),
inference(resolve,[$cnf( $equal(inverse(a),b) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
product(b,identity,c),
inference(resolve,[$cnf( product(inverse(a),identity,c) )],[refute_0_21,refute_0_42]) ).
cnf(refute_0_44,plain,
c = multiply(b,identity),
inference(resolve,[$cnf( product(b,identity,c) )],[refute_0_43,refute_0_3]) ).
cnf(refute_0_45,plain,
multiply(b,identity) = b,
inference(subst,[],[refute_0_31:[bind(X_94,$fot(b))]]) ).
cnf(refute_0_46,plain,
( multiply(b,identity) != b
| c != multiply(b,identity)
| c = b ),
introduced(tautology,[equality,[$cnf( $equal(c,multiply(b,identity)) ),[1],$fot(b)]]) ).
cnf(refute_0_47,plain,
( c != multiply(b,identity)
| c = b ),
inference(resolve,[$cnf( $equal(multiply(b,identity),b) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
c = b,
inference(resolve,[$cnf( $equal(c,multiply(b,identity)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( c != b
| b = c ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(c)),bind(Y0,$fot(b))]]) ).
cnf(refute_0_50,plain,
c != b,
inference(resolve,[$cnf( $equal(b,c) )],[refute_0_49,prove_b_equals_c]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(c,b) )],[refute_0_48,refute_0_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP017-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 12:45:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45
% 0.19/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.45
%------------------------------------------------------------------------------