%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET234-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n020.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 08:56:37 AM UTC 2026
% Result : Unsatisfiable 95.04s 100.33s
% Output : Proof 95.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 13 unt; 2 nHn; 19 RR)
% Number of literals : 33 ( 8 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_subclass_members1,axiom,
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('SET004-0.ax',not_subclass_members1) ).
cnf(not_subclass_members2,axiom,
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('SET004-0.ax',not_subclass_members2) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('SET004-0.ax',cartesian_product4) ).
cnf(prove_cross_product_property9_1,negated_conjecture,
member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z),
file('theBenchmark.p',prove_cross_product_property9_1) ).
cnf(prove_cross_product_property9_2,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('theBenchmark.p',prove_cross_product_property9_2) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_39,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ subclass(cross_product(x,y),z),
inference(start,[status(thm),parent(0:0)],[prove_cross_product_property9_2]) ).
cnf(t2,plain,
( ~ member(not_subclass_element(cross_product(x,y),z),z)
| subclass(cross_product(x,y),z) ),
inference(extension,[status(thm),parent(t1:1)],[not_subclass_members2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( z != z
| ~ member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z)
| ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z)
| member(not_subclass_element(cross_product(x,y),z),z) ),
inference(extension,[status(thm),parent(t2:2)],[equality_39]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(not_subclass_element(cross_product(x,y),z),cross_product(x,y))
| ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) = not_subclass_element(cross_product(x,y),z) ),
inference(extension,[status(thm),parent(t4:2)],[cartesian_product4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( subclass(cross_product(x,y),z)
| member(not_subclass_element(cross_product(x,y),z),cross_product(x,y)) ),
inference(extension,[status(thm),parent(t6:2)],[not_subclass_members1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
member(ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),z),
inference(extension,[status(thm),parent(t4:3)],[prove_cross_product_property9_1]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t4:3]) ).
cnf(t13,plain,
z = z,
inference(extension,[status(thm),parent(t4:4)],[equality_1]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t4:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET234-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_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
% 0.09/5.37 % Computer : n020.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 22:00:39 UTC 2026
% 0.09/5.38 % CPUTime :
% 95.04/100.33 % SZS status Unsatisfiable for theBenchmark
% 95.04/100.33 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------