%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP028-2 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:32:32 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 5 RR)
% Number of literals : 20 ( 0 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ) ).
cnf(left_soln,hypothesis,
product(left_solution(X,Y),X,Y) ).
cnf(right_soln,hypothesis,
product(X,right_solution(X,Y),Y) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_identity(X),X,not_identity(X)) ).
cnf(refute_0_0,plain,
~ product(not_identity(right_solution(X_111,X_111)),right_solution(X_111,X_111),not_identity(right_solution(X_111,X_111))),
inference(subst,[],[prove_there_is_a_right_identity:[bind(X,$fot(right_solution(X_111,X_111)))]]) ).
cnf(refute_0_1,plain,
product(X_108,right_solution(X_108,X_108),X_108),
inference(subst,[],[right_soln:[bind(X,$fot(X_108)),bind(Y,$fot(X_108))]]) ).
cnf(refute_0_2,plain,
product(left_solution(X_105,X_103),X_105,X_103),
inference(subst,[],[left_soln:[bind(X,$fot(X_105)),bind(Y,$fot(X_103))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_105,X_106,X_105)
| ~ product(left_solution(X_105,X_103),X_105,X_103)
| product(X_103,X_106,X_103) ),
inference(subst,[],[associativity2:[bind(U,$fot(X_103)),bind(V,$fot(X_105)),bind(W,$fot(X_103)),bind(X,$fot(left_solution(X_105,X_103))),bind(Y,$fot(X_105)),bind(Z,$fot(X_106))]]) ).
cnf(refute_0_4,plain,
( ~ product(X_105,X_106,X_105)
| product(X_103,X_106,X_103) ),
inference(resolve,[$cnf( product(left_solution(X_105,X_103),X_105,X_103) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ product(X_108,right_solution(X_108,X_108),X_108)
| product(X_107,right_solution(X_108,X_108),X_107) ),
inference(subst,[],[refute_0_4:[bind(X_103,$fot(X_107)),bind(X_105,$fot(X_108)),bind(X_106,$fot(right_solution(X_108,X_108)))]]) ).
cnf(refute_0_6,plain,
product(X_107,right_solution(X_108,X_108),X_107),
inference(resolve,[$cnf( product(X_108,right_solution(X_108,X_108),X_108) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
product(not_identity(right_solution(X_111,X_111)),right_solution(X_111,X_111),not_identity(right_solution(X_111,X_111))),
inference(subst,[],[refute_0_6:[bind(X_107,$fot(not_identity(right_solution(X_111,X_111)))),bind(X_108,$fot(X_111))]]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( product(not_identity(right_solution(X_111,X_111)),right_solution(X_111,X_111),not_identity(right_solution(X_111,X_111))) )],[refute_0_7,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP028-2 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n008.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 15:23:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41
% 0.18/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41
%------------------------------------------------------------------------------