%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP033-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 10:32:34 EDT 2022
% Result : Unsatisfiable 0.78s 0.95s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 28 ( 0 equ; 17 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 11 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X) ).
cnf(right_identity,axiom,
product(X,identity,X) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity) ).
cnf(closure_of_product_and_inverse,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a) ).
cnf(prove_subgr2,negated_conjecture,
( ~ product(j(A),A,j(A))
| ~ product(A,j(A),j(A))
| ~ subgroup_member(A) ) ).
cnf(refute_0_0,plain,
product(X_76,inverse(X_76),identity),
inference(subst,[],[right_inverse:[bind(X,$fot(X_76))]]) ).
cnf(refute_0_1,plain,
( ~ product(X_76,inverse(X_76),identity)
| ~ subgroup_member(X_76)
| subgroup_member(identity) ),
inference(subst,[],[closure_of_product_and_inverse:[bind(A,$fot(X_76)),bind(B,$fot(X_76)),bind(C,$fot(identity))]]) ).
cnf(refute_0_2,plain,
( ~ subgroup_member(X_76)
| subgroup_member(identity) ),
inference(resolve,[$cnf( product(X_76,inverse(X_76),identity) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
product(j(identity),identity,j(identity)),
inference(subst,[],[right_identity:[bind(X,$fot(j(identity)))]]) ).
cnf(refute_0_4,plain,
( ~ product(identity,j(identity),j(identity))
| ~ product(j(identity),identity,j(identity))
| ~ subgroup_member(identity) ),
inference(subst,[],[prove_subgr2:[bind(A,$fot(identity))]]) ).
cnf(refute_0_5,plain,
( ~ product(identity,j(identity),j(identity))
| ~ subgroup_member(identity) ),
inference(resolve,[$cnf( product(j(identity),identity,j(identity)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
product(identity,j(identity),j(identity)),
inference(subst,[],[left_identity:[bind(X,$fot(j(identity)))]]) ).
cnf(refute_0_7,plain,
~ subgroup_member(identity),
inference(resolve,[$cnf( product(identity,j(identity),j(identity)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
~ subgroup_member(X_76),
inference(resolve,[$cnf( subgroup_member(identity) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
~ subgroup_member(a),
inference(subst,[],[refute_0_8:[bind(X_76,$fot(a))]]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( subgroup_member(a) )],[a_is_in_subgroup,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP033-4 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.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 23:40:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.78/0.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.95
% 0.78/0.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.78/0.95
%------------------------------------------------------------------------------