TPTP Problem File: GRP033-4.p
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%--------------------------------------------------------------------------
% File : GRP033-4 : TPTP v9.0.0. Released v1.0.0.
% Domain : Group Theory (Subgroups)
% Problem : In subgroups, the identity is the group identity
% Version : [Wos65] axioms.
% English :
% Refs : [Wos65] Wos (1965), Unpublished Note
% Source : [SPRFN]
% Names : Problem 13 [Wos65]
% Status : Unsatisfiable
% Rating : 0.08 v9.0.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.1.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.7.0, 0.00 v2.0.0
% Syntax : Number of clauses : 12 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 26 ( 1 equ; 15 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments :
%--------------------------------------------------------------------------
%----Include group theory axioms
include('Axioms/GRP003-0.ax').
%----Include sub-group theory axioms
include('Axioms/GRP003-2.ax').
%--------------------------------------------------------------------------
%----j(A) is an element for which A is identity. In a subgroup this can
%----be any element.
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a) ).
cnf(subgr2_clause1,hypothesis,
( ~ subgroup_member(A)
| subgroup_member(j(A)) ) ).
cnf(prove_subgr2,negated_conjecture,
( ~ product(j(A),A,j(A))
| ~ product(A,j(A),j(A))
| ~ subgroup_member(A) ) ).
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