%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 10:32:35 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 13 RR)
% Number of literals : 31 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity) ).
cnf(closure_of_subgroup,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(B,inverse(A),C)
| subgroup_member(C) ) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a) ).
cnf(prove_inverse_is_in_subgroup,negated_conjecture,
~ subgroup_member(inverse(a)) ).
cnf(refute_0_0,plain,
product(identity,inverse(X_51),inverse(X_51)),
inference(subst,[],[left_identity:[bind(X,$fot(inverse(X_51)))]]) ).
cnf(refute_0_1,plain,
( ~ product(identity,inverse(X_51),inverse(X_51))
| ~ subgroup_member(X_51)
| ~ subgroup_member(identity)
| subgroup_member(inverse(X_51)) ),
inference(subst,[],[closure_of_subgroup:[bind(A,$fot(X_51)),bind(B,$fot(identity)),bind(C,$fot(inverse(X_51)))]]) ).
cnf(refute_0_2,plain,
( ~ subgroup_member(X_51)
| ~ subgroup_member(identity)
| subgroup_member(inverse(X_51)) ),
inference(resolve,[$cnf( product(identity,inverse(X_51),inverse(X_51)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
product(X_51,inverse(X_51),identity),
inference(subst,[],[right_inverse:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_4,plain,
( ~ product(X_51,inverse(X_51),identity)
| ~ subgroup_member(X_51)
| subgroup_member(identity) ),
inference(subst,[],[closure_of_subgroup:[bind(A,$fot(X_51)),bind(B,$fot(X_51)),bind(C,$fot(identity))]]) ).
cnf(refute_0_5,plain,
( ~ subgroup_member(X_51)
| subgroup_member(identity) ),
inference(resolve,[$cnf( product(X_51,inverse(X_51),identity) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ subgroup_member(a)
| subgroup_member(identity) ),
inference(subst,[],[refute_0_5:[bind(X_51,$fot(a))]]) ).
cnf(refute_0_7,plain,
subgroup_member(identity),
inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ subgroup_member(X_51)
| subgroup_member(inverse(X_51)) ),
inference(resolve,[$cnf( subgroup_member(identity) )],[refute_0_7,refute_0_2]) ).
cnf(refute_0_9,plain,
( ~ subgroup_member(a)
| subgroup_member(inverse(a)) ),
inference(subst,[],[refute_0_8:[bind(X_51,$fot(a))]]) ).
cnf(refute_0_10,plain,
subgroup_member(inverse(a)),
inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_9]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( subgroup_member(inverse(a)) )],[refute_0_10,prove_inverse_is_in_subgroup]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.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 : Tue Jun 14 10:18:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------