%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 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 : 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 08:56:23 AM UTC 2026
% Result : Unsatisfiable 1.28s 6.68s
% Output : Proof 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 19 ( 13 unt; 2 nHn; 18 RR)
% Number of literals : 29 ( 4 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cartesian_product3,axiom,
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('SET004-0.ax',cartesian_product3) ).
cnf(null_unordered_pair,axiom,
( member(Y,universal_class)
| member(X,universal_class)
| unordered_pair(X,Y) = null_class ),
file('theBenchmark.p',null_unordered_pair) ).
cnf(corollary_to_unordered_pair_axiom3,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
cnf(prove_corollary_2_to_ordered_pairs_are_sets_1,negated_conjecture,
member(x,cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_1) ).
cnf(prove_corollary_2_to_ordered_pairs_are_sets_2,negated_conjecture,
~ member(x,universal_class),
file('theBenchmark.p',prove_corollary_2_to_ordered_pairs_are_sets_2) ).
cnf(t1,plain,
( unordered_pair(x,x) != null_class
| ~ member(ordered_pair(x,x),cross_product(cross_product(universal_class,universal_class),cross_product(universal_class,universal_class))) ),
inference(start,[status(thm),parent(0:0)],[corollary_to_unordered_pair_axiom3]) ).
cnf(t2,plain,
( ~ member(x,cross_product(universal_class,universal_class))
| ~ member(x,cross_product(universal_class,universal_class))
| member(ordered_pair(x,x),cross_product(cross_product(universal_class,universal_class),cross_product(universal_class,universal_class))) ),
inference(extension,[status(thm),parent(t1:1)],[cartesian_product3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
member(x,cross_product(universal_class,universal_class)),
inference(extension,[status(thm),parent(t2:2)],[prove_corollary_2_to_ordered_pairs_are_sets_1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
member(x,cross_product(universal_class,universal_class)),
inference(extension,[status(thm),parent(t2:3)],[prove_corollary_2_to_ordered_pairs_are_sets_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( member(x,universal_class)
| member(x,universal_class)
| unordered_pair(x,x) = null_class ),
inference(extension,[status(thm),parent(t1:2)],[null_unordered_pair]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:2]) ).
cnf(t10,plain,
~ member(x,universal_class),
inference(extension,[status(thm),parent(t8:2)],[prove_corollary_2_to_ordered_pairs_are_sets_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(l5,lemma,
~ member(x,universal_class),
inference(lemma,[status(cth),parent(t8:2),below(t1:2)],[t8:2]) ).
cnf(t12,plain,
~ member(x,universal_class),
inference(lemma_extension,[status(thm),parent(t8:3)],[l5:1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.45 % Computer : n014.cluster.edu
% 0.10/5.45 % Model : x86_64 x86_64
% 0.10/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.45 % Memory : 8046.5625MB
% 0.10/5.45 % OS : Linux 6.8.0-71-generic
% 0.10/5.45 % CPULimit : 300
% 0.10/5.45 % WCLimit : 300
% 0.10/5.45 % DateTime : Sat Sep 19 21:46:56 UTC 2026
% 0.10/5.46 % CPUTime :
% 1.28/6.68 % SZS status Unsatisfiable for theBenchmark
% 1.28/6.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------