%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP023-1 : TPTP v8.1.0. Released v1.0.0.
% 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 10:32:18 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 12 RR)
% Number of literals : 26 ( 15 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| Z = W ) ).
cnf(prove_inverse_of_id_is_id,negated_conjecture,
inverse(identity) != identity ).
cnf(refute_0_0,plain,
product(identity,inverse(identity),identity),
inference(subst,[],[right_inverse:[bind(X,$fot(identity))]]) ).
cnf(refute_0_1,plain,
product(identity,X_49,X_49),
inference(subst,[],[left_identity:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_2,plain,
( ~ product(identity,X_49,X_49)
| ~ product(identity,X_49,X_52)
| X_52 = X_49 ),
inference(subst,[],[total_function2:[bind(W,$fot(X_49)),bind(X,$fot(identity)),bind(Y,$fot(X_49)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_3,plain,
( ~ product(identity,X_49,X_52)
| X_52 = X_49 ),
inference(resolve,[$cnf( product(identity,X_49,X_49) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ product(identity,inverse(identity),identity)
| identity = inverse(identity) ),
inference(subst,[],[refute_0_3:[bind(X_49,$fot(inverse(identity))),bind(X_52,$fot(identity))]]) ).
cnf(refute_0_5,plain,
identity = inverse(identity),
inference(resolve,[$cnf( product(identity,inverse(identity),identity) )],[refute_0_0,refute_0_4]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(identity)),bind(Y0,$fot(inverse(identity)))]]) ).
cnf(refute_0_10,plain,
identity != inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_9,prove_inverse_of_id_is_id]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_5,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP023-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 08:28:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------