%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET101-6 : 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 : n016.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 40.95s 41.24s
% Output : Proof 40.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 15
% Syntax : Number of clauses : 52 ( 32 unt; 2 nHn; 46 RR)
% Number of literals : 84 ( 24 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('SET004-0.ax',subclass_members) ).
cnf(equal_implies_subclass2,axiom,
( subclass(Y,X)
| X != Y ),
file('SET004-0.ax',equal_implies_subclass2) ).
cnf(unordered_pair2,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('SET004-0.ax',unordered_pair2) ).
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(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('SET004-0.ax',ordered_pair) ).
cnf(intersection2,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('SET004-0.ax',intersection2) ).
cnf(intersection3,axiom,
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('SET004-0.ax',intersection3) ).
cnf(complement1,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('SET004-0.ax',complement1) ).
cnf(complement2,axiom,
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('SET004-0.ax',complement2) ).
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(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_11,axiom,
( intersection(Eq_x_0,Eq_x_1) = intersection(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( complement(Eq_x_0) = complement(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
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),ordered_pair(x,y)),
inference(start,[status(thm),parent(0:0)],[prove_singleton_member_of_ordered_pair_1]) ).
cnf(t2,plain,
( member(singleton(x),complement(ordered_pair(x,y)))
| ~ member(singleton(x),universal_class)
| member(singleton(x),ordered_pair(x,y)) ),
inference(extension,[status(thm),parent(t1:1)],[complement2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(singleton(x),intersection(universal_class,universal_class))
| member(singleton(x),universal_class) ),
inference(extension,[status(thm),parent(t2:2)],[intersection2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( intersection(universal_class,universal_class) != intersection(universal_class,universal_class)
| ~ member(unordered_pair(x,x),intersection(universal_class,universal_class))
| unordered_pair(x,x) != singleton(x)
| member(singleton(x),intersection(universal_class,universal_class)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_35]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
unordered_pair(x,x) = singleton(x),
inference(extension,[status(thm),parent(t6:2)],[singleton_set]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ member(unordered_pair(x,x),universal_class)
| ~ member(unordered_pair(x,x),universal_class)
| member(unordered_pair(x,x),intersection(universal_class,universal_class)) ),
inference(extension,[status(thm),parent(t6:3)],[intersection3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
member(unordered_pair(x,x),universal_class),
inference(extension,[status(thm),parent(t10:2)],[unordered_pairs_in_universal]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
member(unordered_pair(x,x),universal_class),
inference(extension,[status(thm),parent(t10:3)],[unordered_pairs_in_universal]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( universal_class != universal_class
| universal_class != universal_class
| intersection(universal_class,universal_class) = intersection(universal_class,universal_class) ),
inference(extension,[status(thm),parent(t6:4)],[equality_11]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t6:4]) ).
cnf(t18,plain,
universal_class = universal_class,
inference(extension,[status(thm),parent(t16:2)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(l9,lemma,
universal_class = universal_class,
inference(lemma,[status(cth),parent(t16:2),below(t6:4)],[t16:2]) ).
cnf(t20,plain,
universal_class = universal_class,
inference(lemma_extension,[status(thm),parent(t16:3)],[l9:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(l2,lemma,
member(singleton(x),universal_class),
inference(lemma,[status(cth),parent(t2:2),below(t1:1)],[t2:2]) ).
cnf(t22,plain,
( member(singleton(x),complement(unordered_pair(singleton(x),unordered_pair(x,singleton(y)))))
| ~ subclass(complement(ordered_pair(x,y)),complement(unordered_pair(singleton(x),unordered_pair(x,singleton(y)))))
| ~ member(singleton(x),complement(ordered_pair(x,y))) ),
inference(extension,[status(thm),parent(t2:3)],[subclass_members]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
cnf(t24,plain,
( complement(unordered_pair(singleton(x),unordered_pair(x,singleton(y)))) != complement(ordered_pair(x,y))
| subclass(complement(ordered_pair(x,y)),complement(unordered_pair(singleton(x),unordered_pair(x,singleton(y))))) ),
inference(extension,[status(thm),parent(t22:2)],[equal_implies_subclass2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( unordered_pair(singleton(x),unordered_pair(x,singleton(y))) != ordered_pair(x,y)
| complement(unordered_pair(singleton(x),unordered_pair(x,singleton(y)))) = complement(ordered_pair(x,y)) ),
inference(extension,[status(thm),parent(t24:2)],[equality_12]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
unordered_pair(singleton(x),unordered_pair(x,singleton(y))) = ordered_pair(x,y),
inference(extension,[status(thm),parent(t26:2)],[ordered_pair]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ member(singleton(x),unordered_pair(singleton(x),unordered_pair(x,singleton(y))))
| ~ member(singleton(x),complement(unordered_pair(singleton(x),unordered_pair(x,singleton(y))))) ),
inference(extension,[status(thm),parent(t22:3)],[complement1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t22:3]) ).
cnf(t32,plain,
( ~ member(singleton(x),universal_class)
| member(singleton(x),unordered_pair(singleton(x),unordered_pair(x,singleton(y)))) ),
inference(extension,[status(thm),parent(t30:2)],[unordered_pair2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
member(singleton(x),universal_class),
inference(lemma_extension,[status(thm),parent(t32:2)],[l2:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET101-6 : 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
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 21:47:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 40.95/41.24 % SZS status Unsatisfiable for theBenchmark
% 40.95/41.24 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------