%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP021-1 : 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 : n003.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 08:41:08 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 4 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('GRP003-0.ax',right_inverse) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('GRP003-0.ax',total_function1) ).
cnf(total_function2,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('GRP003-0.ax',total_function2) ).
cnf(prove_X_times_inverse_X_is_id,negated_conjecture,
multiply(a,inverse(a)) != identity,
file('theBenchmark.p',prove_X_times_inverse_X_is_id) ).
cnf(t1,plain,
multiply(a,inverse(a)) != identity,
inference(start,[status(thm),parent(0:0)],[prove_X_times_inverse_X_is_id]) ).
cnf(t2,plain,
( ~ product(a,inverse(a),identity)
| ~ product(a,inverse(a),multiply(a,inverse(a)))
| multiply(a,inverse(a)) = identity ),
inference(extension,[status(thm),parent(t1:1)],[total_function2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
product(a,inverse(a),multiply(a,inverse(a))),
inference(extension,[status(thm),parent(t2:2)],[total_function1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP021-1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n003.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 19 08:34:03 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------