%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP034-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:41:10 AM UTC 2026
% Result : Unsatisfiable 1.36s 1.66s
% Output : Proof 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 29 ( 24 unt; 0 nHn; 26 RR)
% Number of literals : 44 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 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 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
product(X,identity,X),
file('GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('GRP003-0.ax',right_inverse) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity2) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(prove_a_inverse_is_in_subgroup,negated_conjecture,
~ subgroup_member(inverse(a)),
file('theBenchmark.p',prove_a_inverse_is_in_subgroup) ).
cnf(t1,plain,
~ subgroup_member(inverse(a)),
inference(start,[status(thm),parent(0:0)],[prove_a_inverse_is_in_subgroup]) ).
cnf(t2,plain,
( ~ subgroup_member(a)
| ~ product(identity,inverse(a),inverse(a))
| ~ subgroup_member(identity)
| subgroup_member(inverse(a)) ),
inference(extension,[status(thm),parent(t1:1)],[closure_of_product_and_inverse]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ subgroup_member(a)
| ~ product(a,inverse(a),identity)
| ~ subgroup_member(a)
| subgroup_member(identity) ),
inference(extension,[status(thm),parent(t2:2)],[closure_of_product_and_inverse]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subgroup_member(a),
inference(extension,[status(thm),parent(t4:2)],[a_is_in_subgroup]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l3,lemma,
subgroup_member(a),
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t8,plain,
product(a,inverse(a),identity),
inference(extension,[status(thm),parent(t4:3)],[right_inverse]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
subgroup_member(a),
inference(lemma_extension,[status(thm),parent(t4:4)],[l3:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
( ~ product(inverse(inverse(a)),inverse(a),identity)
| ~ product(inverse(a),identity,inverse(a))
| ~ product(inverse(a),inverse(inverse(a)),identity)
| product(identity,inverse(a),inverse(a)) ),
inference(extension,[status(thm),parent(t2:3)],[associativity2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
product(inverse(a),inverse(inverse(a)),identity),
inference(extension,[status(thm),parent(t12:2)],[right_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
product(inverse(a),identity,inverse(a)),
inference(extension,[status(thm),parent(t12:3)],[right_identity]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
product(inverse(inverse(a)),inverse(a),identity),
inference(extension,[status(thm),parent(t12:4)],[left_inverse]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
subgroup_member(a),
inference(extension,[status(thm),parent(t2:4)],[a_is_in_subgroup]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP034-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 08:32:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 1.36/1.66 % SZS status Unsatisfiable for theBenchmark
% 1.36/1.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------