%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET101-7 : 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 08:56:20 AM UTC 2026
% Result : Unsatisfiable 123.56s 123.89s
% Output : Proof 123.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 14 RR)
% Number of literals : 25 ( 4 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 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(subclass_members,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('SET004-0.ax',subclass_members) ).
cnf(equal_implies_subclass1,axiom,
( subclass(X,Y)
| X != Y ),
file('SET004-0.ax',equal_implies_subclass1) ).
cnf(unordered_pair2,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('SET004-0.ax',unordered_pair2) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('SET004-0.ax',ordered_pair) ).
cnf(singletons_are_sets,axiom,
member(singleton(X),universal_class),
file('theBenchmark.p',singletons_are_sets) ).
cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
~ member(singleton(x),ordered_pair(x,y)),
file('theBenchmark.p',prove_singleton_member_of_ordered_pair_1) ).
cnf(t1,plain,
~ member(singleton(x),ordered_pair(x,y)),
inference(start,[status(thm),parent(0:0)],[prove_singleton_member_of_ordered_pair_1]) ).
cnf(t2,plain,
( ~ member(singleton(x),unordered_pair(singleton(x),unordered_pair(x,singleton(y))))
| ~ subclass(unordered_pair(singleton(x),unordered_pair(x,singleton(y))),ordered_pair(x,y))
| member(singleton(x),ordered_pair(x,y)) ),
inference(extension,[status(thm),parent(t1:1)],[subclass_members]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( unordered_pair(singleton(x),unordered_pair(x,singleton(y))) != ordered_pair(x,y)
| subclass(unordered_pair(singleton(x),unordered_pair(x,singleton(y))),ordered_pair(x,y)) ),
inference(extension,[status(thm),parent(t2:2)],[equal_implies_subclass1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
unordered_pair(singleton(x),unordered_pair(x,singleton(y))) = ordered_pair(x,y),
inference(extension,[status(thm),parent(t4:2)],[ordered_pair]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ member(singleton(x),universal_class)
| member(singleton(x),unordered_pair(singleton(x),unordered_pair(x,singleton(y)))) ),
inference(extension,[status(thm),parent(t2:3)],[unordered_pair2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
member(singleton(x),universal_class),
inference(extension,[status(thm),parent(t8:2)],[singletons_are_sets]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET101-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 21:44:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 123.56/123.89 % SZS status Unsatisfiable for theBenchmark
% 123.56/123.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------