TSTP Solution File: GRP043-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP043-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 10:32:38 EDT 2022
% Result : Unsatisfiable 0.75s 0.92s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 29 ( 14 unt; 0 nHn; 26 RR)
% Number of literals : 49 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| equalish(Z,W) ) ).
cnf(product_substitution3,axiom,
( ~ equalish(X,Y)
| ~ product(W,Z,X)
| product(W,Z,Y) ) ).
cnf(a_equals_b,hypothesis,
equalish(a,b) ).
cnf(b_equals_c,hypothesis,
equalish(b,c) ).
cnf(prove_transitivity,negated_conjecture,
~ equalish(a,c) ).
cnf(refute_0_0,plain,
product(identity,X_53,X_53),
inference(subst,[],[left_identity:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_1,plain,
( ~ product(identity,X_53,X_53)
| ~ product(identity,X_53,X_56)
| equalish(X_56,X_53) ),
inference(subst,[],[total_function2:[bind(W,$fot(X_53)),bind(X,$fot(identity)),bind(Y,$fot(X_53)),bind(Z,$fot(X_56))]]) ).
cnf(refute_0_2,plain,
( ~ product(identity,X_53,X_56)
| equalish(X_56,X_53) ),
inference(resolve,[$cnf( product(identity,X_53,X_53) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ product(identity,c,a)
| equalish(a,c) ),
inference(subst,[],[refute_0_2:[bind(X_53,$fot(c)),bind(X_56,$fot(a))]]) ).
cnf(refute_0_4,plain,
product(identity,X_111,X_111),
inference(subst,[],[left_identity:[bind(X,$fot(X_111))]]) ).
cnf(refute_0_5,plain,
( ~ equalish(X_111,X_112)
| ~ product(identity,X_111,X_111)
| product(identity,X_111,X_112) ),
inference(subst,[],[product_substitution3:[bind(W,$fot(identity)),bind(X,$fot(X_111)),bind(Y,$fot(X_112)),bind(Z,$fot(X_111))]]) ).
cnf(refute_0_6,plain,
( ~ equalish(X_111,X_112)
| product(identity,X_111,X_112) ),
inference(resolve,[$cnf( product(identity,X_111,X_111) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ equalish(c,a)
| product(identity,c,a) ),
inference(subst,[],[refute_0_6:[bind(X_111,$fot(c)),bind(X_112,$fot(a))]]) ).
cnf(refute_0_8,plain,
( ~ equalish(b,a)
| product(identity,b,a) ),
inference(subst,[],[refute_0_6:[bind(X_111,$fot(b)),bind(X_112,$fot(a))]]) ).
cnf(refute_0_9,plain,
( ~ product(identity,a,b)
| equalish(b,a) ),
inference(subst,[],[refute_0_2:[bind(X_53,$fot(a)),bind(X_56,$fot(b))]]) ).
cnf(refute_0_10,plain,
( ~ equalish(a,b)
| product(identity,a,b) ),
inference(subst,[],[refute_0_6:[bind(X_111,$fot(a)),bind(X_112,$fot(b))]]) ).
cnf(refute_0_11,plain,
product(identity,a,b),
inference(resolve,[$cnf( equalish(a,b) )],[a_equals_b,refute_0_10]) ).
cnf(refute_0_12,plain,
equalish(b,a),
inference(resolve,[$cnf( product(identity,a,b) )],[refute_0_11,refute_0_9]) ).
cnf(refute_0_13,plain,
product(identity,b,a),
inference(resolve,[$cnf( equalish(b,a) )],[refute_0_12,refute_0_8]) ).
cnf(refute_0_14,plain,
( ~ product(identity,b,W)
| ~ product(identity,b,c)
| equalish(c,W) ),
inference(subst,[],[total_function2:[bind(X,$fot(identity)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).
cnf(refute_0_15,plain,
( ~ equalish(b,c)
| product(identity,b,c) ),
inference(subst,[],[refute_0_6:[bind(X_111,$fot(b)),bind(X_112,$fot(c))]]) ).
cnf(refute_0_16,plain,
product(identity,b,c),
inference(resolve,[$cnf( equalish(b,c) )],[b_equals_c,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ product(identity,b,W)
| equalish(c,W) ),
inference(resolve,[$cnf( product(identity,b,c) )],[refute_0_16,refute_0_14]) ).
cnf(refute_0_18,plain,
( ~ product(identity,b,a)
| equalish(c,a) ),
inference(subst,[],[refute_0_17:[bind(W,$fot(a))]]) ).
cnf(refute_0_19,plain,
equalish(c,a),
inference(resolve,[$cnf( product(identity,b,a) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
product(identity,c,a),
inference(resolve,[$cnf( equalish(c,a) )],[refute_0_19,refute_0_7]) ).
cnf(refute_0_21,plain,
equalish(a,c),
inference(resolve,[$cnf( product(identity,c,a) )],[refute_0_20,refute_0_3]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( equalish(a,c) )],[refute_0_21,prove_transitivity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP043-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 17:54:44 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.75/0.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.75/0.92
% 0.75/0.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.75/0.92
%------------------------------------------------------------------------------