%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 08:41:11 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('GRP003-0.ax',left_inverse) ).
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(associativity1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('GRP003-0.ax',associativity2) ).
cnf(closure_of_product_and_inverse,axiom,
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('GRP003-2.ax',closure_of_product_and_inverse) ).
cnf(another_left_identity,hypothesis,
( product(another_identity,A,A)
| ~ subgroup_member(A) ),
file('theBenchmark.p',another_left_identity) ).
cnf(another_right_identity,hypothesis,
( product(A,another_identity,A)
| ~ subgroup_member(A) ),
file('theBenchmark.p',another_right_identity) ).
cnf(another_right_inverse,hypothesis,
( product(A,another_inverse(A),another_identity)
| ~ subgroup_member(A) ),
file('theBenchmark.p',another_right_inverse) ).
cnf(another_left_inverse,hypothesis,
( product(another_inverse(A),A,another_identity)
| ~ subgroup_member(A) ),
file('theBenchmark.p',another_left_inverse) ).
cnf(another_inverse_in_subgroup,hypothesis,
( subgroup_member(another_inverse(A))
| ~ subgroup_member(A) ),
file('theBenchmark.p',another_inverse_in_subgroup) ).
cnf(another_identity_in_subgroup,hypothesis,
subgroup_member(another_identity),
file('theBenchmark.p',another_identity_in_subgroup) ).
cnf(prove_identity_equals_another_identity,negated_conjecture,
identity != another_identity,
file('theBenchmark.p',prove_identity_equals_another_identity) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( inverse(Eq_x_0) = inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( multiply(Eq_x_0,Eq_x_1) = multiply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( another_inverse(Eq_x_0) = another_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( product(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ product(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( subgroup_member(Eq_y_0)
| ~ subgroup_member(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP036-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 08:36:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------