%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET052-6 : 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 : n018.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 08:56:05 AM UTC 2026
% Result : Unsatisfiable 31.07s 31.38s
% Output : Proof 31.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 13 RR)
% Number of literals : 20 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X,universal_class),
file('SET004-0.ax',class_elements_are_sets) ).
cnf(cartesian_product1,axiom,
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('SET004-0.ax',cartesian_product1) ).
cnf(prove_corollary_1_to_cartesian_product_1,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('theBenchmark.p',prove_corollary_1_to_cartesian_product_1) ).
cnf(prove_corollary_1_to_cartesian_product_2,negated_conjecture,
~ member(u,universal_class),
file('theBenchmark.p',prove_corollary_1_to_cartesian_product_2) ).
cnf(t1,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(start,[status(thm),parent(0:0)],[prove_corollary_1_to_cartesian_product_1]) ).
cnf(t2,plain,
( member(u,x)
| ~ member(ordered_pair(u,v),cross_product(x,y)) ),
inference(extension,[status(thm),parent(t1:1)],[cartesian_product1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( member(u,universal_class)
| ~ subclass(x,universal_class)
| ~ member(u,x) ),
inference(extension,[status(thm),parent(t2:2)],[subclass_members]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subclass(x,universal_class),
inference(extension,[status(thm),parent(t4:2)],[class_elements_are_sets]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
~ member(u,universal_class),
inference(extension,[status(thm),parent(t4:3)],[prove_corollary_1_to_cartesian_product_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET052-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 21:37:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 31.07/31.38 % SZS status Unsatisfiable for theBenchmark
% 31.07/31.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------