%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM183-1 : 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 : n009.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 08:51:49 AM UTC 2026
% Result : Unsatisfiable 130.44s 130.75s
% Output : Proof 130.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 23 unt; 2 nHn; 28 RR)
% Number of literals : 49 ( 8 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X,universal_class),
file('SET004-0.ax',class_elements_are_sets) ).
cnf(intersection3,axiom,
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('SET004-0.ax',intersection3) ).
cnf(complement2,axiom,
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('SET004-0.ax',complement2) ).
cnf(limit_ordinals,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('NUM004-0.ax',limit_ordinals) ).
cnf(prove_ordinals_are_kind_1_or_limit_1,negated_conjecture,
member(x,ordinal_numbers),
file('theBenchmark.p',prove_ordinals_are_kind_1_or_limit_1) ).
cnf(prove_ordinals_are_kind_1_or_limit_2,negated_conjecture,
~ member(x,kind_1_ordinals),
file('theBenchmark.p',prove_ordinals_are_kind_1_or_limit_2) ).
cnf(prove_ordinals_are_kind_1_or_limit_3,negated_conjecture,
~ member(x,limit_ordinals),
file('theBenchmark.p',prove_ordinals_are_kind_1_or_limit_3) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_49,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(x,kind_1_ordinals),
inference(start,[status(thm),parent(0:0)],[prove_ordinals_are_kind_1_or_limit_2]) ).
cnf(t2,plain,
( member(x,complement(kind_1_ordinals))
| ~ member(x,universal_class)
| member(x,kind_1_ordinals) ),
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(x,ordinal_numbers)
| ~ subclass(ordinal_numbers,universal_class)
| member(x,universal_class) ),
inference(extension,[status(thm),parent(t2:2)],[subclass_members]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subclass(ordinal_numbers,universal_class),
inference(extension,[status(thm),parent(t4:2)],[class_elements_are_sets]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
member(x,ordinal_numbers),
inference(extension,[status(thm),parent(t4:3)],[prove_ordinals_are_kind_1_or_limit_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ member(x,ordinal_numbers)
| member(x,intersection(complement(kind_1_ordinals),ordinal_numbers))
| ~ member(x,complement(kind_1_ordinals)) ),
inference(extension,[status(thm),parent(t2:3)],[intersection3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( intersection(complement(kind_1_ordinals),ordinal_numbers) != limit_ordinals
| member(x,limit_ordinals)
| x != x
| ~ member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)) ),
inference(extension,[status(thm),parent(t10:2)],[equality_49]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
x = x,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
~ member(x,limit_ordinals),
inference(extension,[status(thm),parent(t12:3)],[prove_ordinals_are_kind_1_or_limit_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(extension,[status(thm),parent(t12:4)],[limit_ordinals]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
member(x,ordinal_numbers),
inference(extension,[status(thm),parent(t10:3)],[prove_ordinals_are_kind_1_or_limit_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM183-1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 17:54:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 130.44/130.75 % SZS status Unsatisfiable for theBenchmark
% 130.44/130.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------