%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP021-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 16 ( 10 unt; 0 nHn; 11 RR)
% Number of literals : 25 ( 14 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_inverse,axiom,
product(X,inverse(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(prove_X_times_inverse_X_is_id,negated_conjecture,
multiply(a,inverse(a)) != identity ).
cnf(refute_0_0,plain,
product(X_56,inverse(X_56),multiply(X_56,inverse(X_56))),
inference(subst,[],[total_function1:[bind(X,$fot(X_56)),bind(Y,$fot(inverse(X_56)))]]) ).
cnf(refute_0_1,plain,
product(X_53,inverse(X_53),identity),
inference(subst,[],[right_inverse:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_2,plain,
( ~ product(X_53,inverse(X_53),X_55)
| ~ product(X_53,inverse(X_53),identity)
| X_55 = identity ),
inference(subst,[],[total_function2:[bind(W,$fot(identity)),bind(X,$fot(X_53)),bind(Y,$fot(inverse(X_53))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_3,plain,
( ~ product(X_53,inverse(X_53),X_55)
| X_55 = identity ),
inference(resolve,[$cnf( product(X_53,inverse(X_53),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(X_56,inverse(X_56),multiply(X_56,inverse(X_56)))
| multiply(X_56,inverse(X_56)) = identity ),
inference(subst,[],[refute_0_3:[bind(X_53,$fot(X_56)),bind(X_55,$fot(multiply(X_56,inverse(X_56))))]]) ).
cnf(refute_0_5,plain,
multiply(X_56,inverse(X_56)) = identity,
inference(resolve,[$cnf( product(X_56,inverse(X_56),multiply(X_56,inverse(X_56))) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(a,inverse(a)) = identity,
inference(subst,[],[refute_0_5:[bind(X_56,$fot(a))]]) ).
cnf(refute_0_7,plain,
( multiply(a,inverse(a)) != identity
| identity != identity
| multiply(a,inverse(a)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,inverse(a)),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_8,plain,
( identity != identity
| multiply(a,inverse(a)) = identity ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),identity) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
identity != identity,
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),identity) )],[refute_0_8,prove_X_times_inverse_X_is_id]) ).
cnf(refute_0_10,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_10,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP021-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n014.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 13:31:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------