%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET077-6 : 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 : n003.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 08:56:14 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.84s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 11 RR)
% Number of literals : 20 ( 8 equ; 8 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X,Y),universal_class),
file('SET004-0.ax',unordered_pairs_in_universal) ).
cnf(singleton_set,axiom,
unordered_pair(X,X) = singleton(X),
file('SET004-0.ax',singleton_set) ).
cnf(prove_singletons_are_sets_1,negated_conjecture,
~ member(singleton(x),universal_class),
file('theBenchmark.p',prove_singletons_are_sets_1) ).
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(singleton(x),universal_class),
inference(start,[status(thm),parent(0:0)],[prove_singletons_are_sets_1]) ).
cnf(t2,plain,
( universal_class != universal_class
| ~ member(unordered_pair(x,x),universal_class)
| unordered_pair(x,x) != singleton(x)
| member(singleton(x),universal_class) ),
inference(extension,[status(thm),parent(t1:1)],[equality_35]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
unordered_pair(x,x) = singleton(x),
inference(extension,[status(thm),parent(t2:2)],[singleton_set]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
member(unordered_pair(x,x),universal_class),
inference(extension,[status(thm),parent(t2:3)],[unordered_pairs_in_universal]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
universal_class = universal_class,
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET077-6 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n003.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sat Sep 19 21:39:30 UTC 2026
% 0.09/0.59 % CPUTime :
% 0.14/0.84 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.84 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------