%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:41:05 AM UTC 2026
% Result : Unsatisfiable 0.13s 15.61s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 13 RR)
% Number of literals : 20 ( 0 equ; 8 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 : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('theBenchmark.p',right_inverse) ).
cnf(element_of_set,axiom,
an_element(a),
file('theBenchmark.p',element_of_set) ).
cnf(condition,axiom,
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
file('theBenchmark.p',condition) ).
cnf(prove_identity_is_an_element,negated_conjecture,
~ an_element(identity),
file('theBenchmark.p',prove_identity_is_an_element) ).
cnf(t1,plain,
~ an_element(identity),
inference(start,[status(thm),parent(0:0)],[prove_identity_is_an_element]) ).
cnf(t2,plain,
( ~ an_element(a)
| ~ product(a,inverse(a),identity)
| ~ an_element(a)
| an_element(identity) ),
inference(extension,[status(thm),parent(t1:1)],[condition]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
an_element(a),
inference(extension,[status(thm),parent(t2:2)],[element_of_set]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(l2,lemma,
an_element(a),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t6,plain,
product(a,inverse(a),identity),
inference(extension,[status(thm),parent(t2:3)],[right_inverse]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
an_element(a),
inference(lemma_extension,[status(thm),parent(t2:4)],[l2:1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/15.59 % Computer : n002.cluster.edu
% 0.09/15.59 % Model : x86_64 x86_64
% 0.09/15.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.59 % Memory : 8046.5625MB
% 0.09/15.59 % OS : Linux 6.8.0-71-generic
% 0.09/15.59 % CPULimit : 300
% 0.09/15.59 % WCLimit : 300
% 0.09/15.59 % DateTime : Sat Sep 19 08:33:48 UTC 2026
% 0.09/15.59 % CPUTime :
% 0.13/15.61 % SZS status Unsatisfiable for theBenchmark
% 0.13/15.61 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------