%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : n013.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 08:56:13 AM UTC 2026
% Result : Unsatisfiable 31.05s 31.36s
% Output : Proof 31.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 13 unt; 0 nHn; 16 RR)
% Number of literals : 25 ( 8 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_2_to_unordered_pair,axiom,
( member(Y,unordered_pair(X,Y))
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('theBenchmark.p',corollary_2_to_unordered_pair) ).
cnf(existence_of_null_class,axiom,
~ member(Z,null_class),
file('theBenchmark.p',existence_of_null_class) ).
cnf(prove_corollary_to_unordered_pair_axiom3_1,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
cnf(prove_corollary_to_unordered_pair_axiom3_2,negated_conjecture,
unordered_pair(x,y) = null_class,
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_35,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,
member(ordered_pair(x,y),cross_product(u,v)),
inference(start,[status(thm),parent(0:0)],[prove_corollary_to_unordered_pair_axiom3_1]) ).
cnf(t2,plain,
( member(y,unordered_pair(x,y))
| ~ member(ordered_pair(x,y),cross_product(u,v)) ),
inference(extension,[status(thm),parent(t1:1)],[corollary_2_to_unordered_pair]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( unordered_pair(x,y) != null_class
| member(y,null_class)
| y != y
| ~ member(y,unordered_pair(x,y)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_35]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
y = y,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
~ member(y,null_class),
inference(extension,[status(thm),parent(t4:3)],[existence_of_null_class]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
unordered_pair(x,y) = null_class,
inference(extension,[status(thm),parent(t4:4)],[prove_corollary_to_unordered_pair_axiom3_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET075-7 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 21:36:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 31.05/31.36 % SZS status Unsatisfiable for theBenchmark
% 31.05/31.36 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------