%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP028-2 : TPTP v9.3.1. Released v1.1.0.
% 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 : n009.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 08:41:09 AM UTC 2026
% Result : Unsatisfiable 0.77s 1.05s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 13 ( 11 unt; 0 nHn; 8 RR)
% Number of literals : 19 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP002-0.ax',associativity2) ).
cnf(left_soln,hypothesis,
product(left_solution(X,Y),X,Y),
file('theBenchmark.p',left_soln) ).
cnf(right_soln,hypothesis,
product(X,right_solution(X,Y),Y),
file('theBenchmark.p',right_soln) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product(not_identity(X),X,not_identity(X)),
file('theBenchmark.p',prove_there_is_a_right_identity) ).
cnf(t1,plain,
~ product(not_identity(right_solution(U_313,U_313)),right_solution(U_313,U_313),not_identity(right_solution(U_313,U_313))),
inference(start,[status(thm),parent(0:0)],[prove_there_is_a_right_identity]) ).
cnf(t2,plain,
( ~ product(U_313,right_solution(U_313,U_313),U_313)
| ~ product(left_solution(U_313,not_identity(right_solution(U_313,U_313))),U_313,not_identity(right_solution(U_313,U_313)))
| ~ product(left_solution(U_313,not_identity(right_solution(U_313,U_313))),U_313,not_identity(right_solution(U_313,U_313)))
| product(not_identity(right_solution(U_313,U_313)),right_solution(U_313,U_313),not_identity(right_solution(U_313,U_313))) ),
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(left_solution(U_313,not_identity(right_solution(U_313,U_313))),U_313,not_identity(right_solution(U_313,U_313))),
inference(extension,[status(thm),parent(t2:2)],[left_soln]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
product(left_solution(U_313,not_identity(right_solution(U_313,U_313))),U_313,not_identity(right_solution(U_313,U_313))),
inference(extension,[status(thm),parent(t2:3)],[left_soln]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
product(U_313,right_solution(U_313,U_313),U_313),
inference(extension,[status(thm),parent(t2:4)],[right_soln]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP028-2 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 08:34:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.77/1.05 % SZS status Unsatisfiable for theBenchmark
% 0.77/1.05 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------