TSTP Solution File: GRP010-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 10:32:13 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 20 unt; 0 nHn; 31 RR)
% Number of literals : 72 ( 26 equ; 33 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 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_multiply_b_is_identity,hypothesis,
product(a,b,identity) ).
cnf(prove_b_multiply_a_is_identity,negated_conjecture,
~ product(b,a,identity) ).
cnf(refute_0_0,plain,
product(inverse(a),a,identity),
inference(subst,[],[left_inverse:[bind(X,$fot(a))]]) ).
cnf(refute_0_1,plain,
product(X_7,X_8,multiply(X_7,X_8)),
inference(subst,[],[total_function1:[bind(X,$fot(X_7)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_7,X_8,X_9)
| ~ product(X_7,X_8,multiply(X_7,X_8))
| X_9 = multiply(X_7,X_8) ),
inference(subst,[],[total_function2:[bind(W,$fot(multiply(X_7,X_8))),bind(X,$fot(X_7)),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_7,X_8,X_9)
| X_9 = multiply(X_7,X_8) ),
inference(resolve,[$cnf( product(X_7,X_8,multiply(X_7,X_8)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(inverse(a),identity,b)
| b = multiply(inverse(a),identity) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(inverse(a))),bind(X_8,$fot(identity)),bind(X_9,$fot(b))]]) ).
cnf(refute_0_5,plain,
product(identity,b,b),
inference(subst,[],[left_identity:[bind(X,$fot(b))]]) ).
cnf(refute_0_6,plain,
( ~ product(X_87,b,X_89)
| ~ product(X_90,a,X_87)
| ~ product(a,b,identity)
| product(X_90,identity,X_89) ),
inference(subst,[],[associativity1:[bind(U,$fot(X_87)),bind(V,$fot(identity)),bind(W,$fot(X_89)),bind(X,$fot(X_90)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_7,plain,
( ~ product(X_87,b,X_89)
| ~ product(X_90,a,X_87)
| product(X_90,identity,X_89) ),
inference(resolve,[$cnf( product(a,b,identity) )],[a_multiply_b_is_identity,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ product(X_123,a,identity)
| ~ product(identity,b,b)
| product(X_123,identity,b) ),
inference(subst,[],[refute_0_7:[bind(X_87,$fot(identity)),bind(X_89,$fot(b)),bind(X_90,$fot(X_123))]]) ).
cnf(refute_0_9,plain,
( ~ product(X_123,a,identity)
| product(X_123,identity,b) ),
inference(resolve,[$cnf( product(identity,b,b) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ product(inverse(a),a,identity)
| product(inverse(a),identity,b) ),
inference(subst,[],[refute_0_9:[bind(X_123,$fot(inverse(a)))]]) ).
cnf(refute_0_11,plain,
product(inverse(a),identity,b),
inference(resolve,[$cnf( product(inverse(a),a,identity) )],[refute_0_0,refute_0_10]) ).
cnf(refute_0_12,plain,
b = multiply(inverse(a),identity),
inference(resolve,[$cnf( product(inverse(a),identity,b) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
product(X_11,identity,multiply(X_11,identity)),
inference(subst,[],[total_function1:[bind(X,$fot(X_11)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_14,plain,
product(X_6,identity,X_6),
inference(subst,[],[right_identity:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_15,plain,
( ~ product(X_6,identity,X_6)
| ~ product(X_6,identity,X_9)
| X_9 = X_6 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_6)),bind(X,$fot(X_6)),bind(Y,$fot(identity)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_16,plain,
( ~ product(X_6,identity,X_9)
| X_9 = X_6 ),
inference(resolve,[$cnf( product(X_6,identity,X_6) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ product(X_11,identity,multiply(X_11,identity))
| multiply(X_11,identity) = X_11 ),
inference(subst,[],[refute_0_16:[bind(X_6,$fot(X_11)),bind(X_9,$fot(multiply(X_11,identity)))]]) ).
cnf(refute_0_18,plain,
multiply(X_11,identity) = X_11,
inference(resolve,[$cnf( product(X_11,identity,multiply(X_11,identity)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(inverse(a),identity) = inverse(a),
inference(subst,[],[refute_0_18:[bind(X_11,$fot(inverse(a)))]]) ).
cnf(refute_0_20,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_21,plain,
( b != multiply(inverse(a),identity)
| b = inverse(a) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),identity),inverse(a)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
b = inverse(a),
inference(resolve,[$cnf( $equal(b,multiply(inverse(a),identity)) )],[refute_0_12,refute_0_21]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( b != inverse(a)
| inverse(a) = b ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(a)))]]) ).
cnf(refute_0_27,plain,
inverse(a) = b,
inference(resolve,[$cnf( $equal(b,inverse(a)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( inverse(a) != b
| ~ product(inverse(a),a,identity)
| product(b,a,identity) ),
introduced(tautology,[equality,[$cnf( product(inverse(a),a,identity) ),[0],$fot(b)]]) ).
cnf(refute_0_29,plain,
( ~ product(inverse(a),a,identity)
| product(b,a,identity) ),
inference(resolve,[$cnf( $equal(inverse(a),b) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
product(b,a,identity),
inference(resolve,[$cnf( product(inverse(a),a,identity) )],[refute_0_0,refute_0_29]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( product(b,a,identity) )],[refute_0_30,prove_b_multiply_a_is_identity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 10:37:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------