%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP034-4 : 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 : n014.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 08:41:11 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(closure,axiom,
product(X,Y,multiply(X,Y)),
file('theBenchmark.p',closure) ).
cnf(left_identity,axiom,
product(identity,X,X),
file('theBenchmark.p',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('theBenchmark.p',right_identity) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('theBenchmark.p',right_inverse) ).
cnf(associativity1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('theBenchmark.p',associativity1) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('theBenchmark.p',associativity2) ).
cnf(closure_of_subgroup,axiom,
( subgroup_member(C)
| ~ product(B,inverse(A),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('theBenchmark.p',closure_of_subgroup) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('theBenchmark.p',a_is_in_subgroup) ).
cnf(prove_inverse_is_in_subgroup,negated_conjecture,
~ subgroup_member(inverse(a)),
file('theBenchmark.p',prove_inverse_is_in_subgroup) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP034-4 : 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
% 0.08/0.36 % Computer : n014.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 08:34:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------