%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP039-6 : 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 : n015.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 08:41:12 AM UTC 2026
% Result : Unsatisfiable 217.23s 217.51s
% Output : Proof 217.75s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(subgroup_member_substitution,axiom,
( subgroup_member(B)
| ~ subgroup_member(A)
| ~ equalish(A,B) ),
file('theBenchmark.p',subgroup_member_substitution) ).
cnf(product_substitution3,axiom,
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('theBenchmark.p',product_substitution3) ).
cnf(element_in_O2_substitution1,axiom,
( equalish(element_in_O2(C,A),element_in_O2(C,B))
| ~ equalish(A,B) ),
file('theBenchmark.p',element_in_O2_substitution1) ).
cnf(element_in_O2_substitution2,axiom,
( equalish(element_in_O2(A,C),element_in_O2(B,C))
| ~ equalish(A,B) ),
file('theBenchmark.p',element_in_O2_substitution2) ).
cnf(closure_of_inverse,axiom,
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
file('theBenchmark.p',closure_of_inverse) ).
cnf(closure_of_product,axiom,
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('theBenchmark.p',closure_of_product) ).
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(left_inverse,axiom,
product(inverse(X),X,identity),
file('theBenchmark.p',left_inverse) ).
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(well_defined,axiom,
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('theBenchmark.p',well_defined) ).
cnf(identity_is_in_subgroup,axiom,
subgroup_member(identity),
file('theBenchmark.p',identity_is_in_subgroup) ).
cnf(product_right_cancellation,axiom,
( equalish(D,B)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(product_left_cancellation,axiom,
( equalish(D,A)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('theBenchmark.p',an_element_in_O2) ).
cnf(property_of_O2,axiom,
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('theBenchmark.p',property_of_O2) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('theBenchmark.p',b_is_in_subgroup) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('theBenchmark.p',a_times_c_is_d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN 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
% 0.09/0.38 % Computer : n015.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 08:38:19 UTC 2026
% 0.09/0.38 % CPUTime :
% 217.23/217.51 % SZS status Unsatisfiable for theBenchmark
% 217.23/217.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------