%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP033-4 : 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 : n020.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 17.15s 17.40s
% Output : Proof 17.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 33 ( 26 unt; 0 nHn; 30 RR)
% Number of literals : 52 ( 0 equ; 21 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 13 ( 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_subgr2,negated_conjecture,
( ~ subgroup_member(A)
| ~ product(A,j(A),j(A))
| ~ product(j(A),A,j(A)) ),
file('theBenchmark.p',prove_subgr2) ).
cnf(t1,plain,
( ~ product(identity,j(identity),j(identity))
| ~ subgroup_member(identity)
| ~ product(j(identity),identity,j(identity)) ),
inference(start,[status(thm),parent(0:0)],[prove_subgr2]) ).
cnf(t2,plain,
( ~ product(identity,identity,identity)
| ~ product(j(identity),identity,j(identity))
| ~ product(j(identity),identity,j(identity))
| product(j(identity),identity,j(identity)) ),
inference(extension,[status(thm),parent(t1:1)],[associativity2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
product(j(identity),identity,j(identity)),
inference(extension,[status(thm),parent(t2:2)],[right_identity]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
product(j(identity),identity,j(identity)),
inference(extension,[status(thm),parent(t2:3)],[right_identity]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
product(identity,identity,identity),
inference(extension,[status(thm),parent(t2:4)],[right_identity]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
( ~ subgroup_member(a)
| ~ product(a,inverse(a),identity)
| ~ subgroup_member(a)
| subgroup_member(identity) ),
inference(extension,[status(thm),parent(t1:2)],[closure_of_product_and_inverse]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
subgroup_member(a),
inference(extension,[status(thm),parent(t10:2)],[a_is_in_subgroup]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(l6,lemma,
subgroup_member(a),
inference(lemma,[status(cth),parent(t10:2),below(t1:2)],[t10:2]) ).
cnf(t14,plain,
product(a,inverse(a),identity),
inference(extension,[status(thm),parent(t10:3)],[right_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
subgroup_member(a),
inference(lemma_extension,[status(thm),parent(t10:4)],[l6:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
cnf(t18,plain,
( ~ product(inverse(j(identity)),j(identity),identity)
| ~ product(j(identity),identity,j(identity))
| ~ product(j(identity),inverse(j(identity)),identity)
| product(identity,j(identity),j(identity)) ),
inference(extension,[status(thm),parent(t1:3)],[associativity2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t1:3]) ).
cnf(t20,plain,
product(j(identity),inverse(j(identity)),identity),
inference(extension,[status(thm),parent(t18:2)],[right_inverse]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
product(j(identity),identity,j(identity)),
inference(extension,[status(thm),parent(t18:3)],[right_identity]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
product(inverse(j(identity)),j(identity),identity),
inference(extension,[status(thm),parent(t18:4)],[left_inverse]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP033-4 : 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
% 0.10/0.38 % Computer : n020.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 08:35:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 17.15/17.40 % SZS status Unsatisfiable for theBenchmark
% 17.15/17.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------