%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET099-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:46:35 PM UTC 2026
% Result : Unsatisfiable 22.49s 6.85s
% Output : CNFRefutation 22.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 103 ( 30 unt; 0 def)
% Number of atoms : 215 ( 47 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 202 ( 90 ~; 112 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f101,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
fof(f102,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
fof(f104,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
fof(f106,plain,
null_class != x,
inference(reorient_equations,[],[f105]) ).
fof(f155,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(definition_unfolding,[],[f102,f12]) ).
fof(f156,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f104,f12]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_146,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_195,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_218,negated_conjecture,
not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(cnf_transformation,[],[f155]) ).
tcf(c_219,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[],[f156]) ).
tcf(c_220,negated_conjecture,
x != null_class,
inference(cnf_transformation,[],[f106]) ).
tcf(c_3420,plain,
( member(regular(x),x)
| ( x = null_class ) ),
inference(instantiation,[status(thm)],[c_195]) ).
tcf(c_3479,plain,
( subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class)
| member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_218,c_144]) ).
tcf(c_3489,plain,
( subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class)
| ~ member(not_subclass_element(x,null_class),null_class) ),
inference(superposition,[status(thm)],[c_218,c_145]) ).
tcf(c_3500,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
inference(superposition,[status(thm)],[c_3479,c_161]) ).
tcf(c_3528,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_144,c_164]) ).
tcf(c_3529,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_195,c_164]) ).
tcf(c_3571,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_146,c_143]) ).
tcf(c_3579,plain,
! [X0: $i] :
( member(X0,null_class)
| member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ member(X0,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_3500,c_143]) ).
tcf(c_3673,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class )
| ~ subclass(null_class,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_3500,c_149]) ).
tcf(c_3675,plain,
( ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class )
| ~ member(not_subclass_element(x,null_class),null_class)
| ~ subclass(null_class,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_3489,c_149]) ).
tcf(c_3739,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_144,c_3571]) ).
tcf(c_3745,plain,
! [X0: $i] :
( member(regular(X0),universal_class)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_195,c_3571]) ).
tcf(c_3747,plain,
( member(not_subclass_element(x,null_class),universal_class)
| subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
inference(superposition,[status(thm)],[c_3479,c_3571]) ).
tcf(c_3761,plain,
( member(not_subclass_element(x,null_class),universal_class)
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class )
| ~ subclass(null_class,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_3747,c_149]) ).
tcf(c_3762,plain,
! [X0: $i] :
( member(X0,null_class)
| member(not_subclass_element(x,null_class),universal_class)
| ~ member(X0,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_3747,c_143]) ).
tcf(c_3858,plain,
! [X0: $i] :
( member(X0,null_class)
| member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_163,c_3579]) ).
tcf(c_3859,plain,
! [X0: $i] :
( member(X0,null_class)
| member(not_subclass_element(x,null_class),universal_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_163,c_3762]) ).
tcf(c_4056,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_3739,c_3528]) ).
tcf(c_4064,plain,
complement(universal_class) = null_class,
inference(superposition,[status(thm)],[c_3745,c_3529]) ).
tcf(c_4107,plain,
! [X0: $i] : subclass(null_class,X0),
inference(light_normalisation,[status(thm)],[c_4056,c_4064]) ).
tcf(c_4108,plain,
( member(not_subclass_element(x,null_class),universal_class)
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3761,c_4107]) ).
tcf(c_4111,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3673,c_4107]) ).
tcf(c_4212,plain,
( ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class )
| ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))) ),
inference(superposition,[status(thm)],[c_4111,c_164]) ).
tcf(c_4215,plain,
( member(not_subclass_element(x,null_class),universal_class)
| member(not_subclass_element(x,null_class),null_class)
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class )
| ~ member(not_subclass_element(x,null_class),x) ),
inference(superposition,[status(thm)],[c_4111,c_3859]) ).
tcf(c_4234,plain,
( ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class )
| ~ member(not_subclass_element(x,null_class),universal_class) ),
inference(superposition,[status(thm)],[c_151,c_4212]) ).
tcf(c_4236,plain,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4215,c_4108,c_4234]) ).
tcf(c_5459,plain,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(global_subsumption_just,[status(thm)],[c_3675,c_4236]) ).
tcf(c_5462,plain,
not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class),
inference(demodulation,[status(thm)],[c_218,c_5459]) ).
tcf(c_5464,plain,
intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x) = null_class,
inference(demodulation,[status(thm)],[c_5459,c_5462]) ).
tcf(c_5465,plain,
unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)) != x,
inference(demodulation,[status(thm)],[c_219,c_5462]) ).
tcf(c_5479,plain,
! [X0: $i] :
( member(X0,null_class)
| member(not_subclass_element(null_class,null_class),universal_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))) ),
inference(light_normalisation,[status(thm)],[c_3859,c_5462]) ).
tcf(c_5497,plain,
! [X0: $i] :
( member(X0,null_class)
| member(not_subclass_element(null_class,null_class),complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))))
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))) ),
inference(light_normalisation,[status(thm)],[c_3858,c_5462]) ).
tcf(c_5520,plain,
( subclass(x,null_class)
| member(not_subclass_element(null_class,null_class),x) ),
inference(superposition,[status(thm)],[c_5462,c_144]) ).
tcf(c_5569,plain,
! [X0: $i] :
( member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))))
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_5464,c_161]) ).
tcf(c_5610,plain,
! [X0: $i] :
( ~ member(X0,null_class)
| ~ member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))) ),
inference(superposition,[status(thm)],[c_5569,c_164]) ).
tcf(c_5616,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_146,c_143]) ).
tcf(c_5624,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_4107,c_143]) ).
tcf(c_5654,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[c_5610,c_5624]) ).
tcf(c_5657,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5479,c_5654]) ).
tcf(c_5659,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))))
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5497,c_5654]) ).
tcf(c_5698,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| member(not_subclass_element(null_class,null_class),complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_165,c_5659]) ).
tcf(c_5700,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_165,c_5657]) ).
tcf(c_5758,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,null_class),universal_class)
| member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5700,c_5616]) ).
tcf(c_5766,plain,
! [X0: $i] :
( member(X0,universal_class)
| member(not_subclass_element(null_class,null_class),universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_5758,c_5616]) ).
tcf(c_5773,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| member(not_subclass_element(null_class,null_class),complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))))
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5698,c_5616]) ).
tcf(c_5783,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X0,x)
| ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))) ),
inference(superposition,[status(thm)],[c_5773,c_164]) ).
tcf(c_5800,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X0,x)
| ~ member(not_subclass_element(null_class,null_class),universal_class) ),
inference(superposition,[status(thm)],[c_151,c_5783]) ).
tcf(c_5817,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))) ),
inference(superposition,[status(thm)],[c_5464,c_163]) ).
tcf(c_5822,plain,
! [X0: $i] :
( ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5817,c_5654]) ).
tcf(c_5831,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X1),X2)
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X1 )
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_144,c_150]) ).
tcf(c_5880,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_165,c_5822]) ).
tcf(c_5885,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X0,x) ),
inference(global_subsumption_just,[status(thm)],[c_5880,c_5766,c_5800,c_5880]) ).
tcf(c_5891,plain,
! [X0: $i] :
( ( not_subclass_element(null_class,null_class) = X0 )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_5885,c_150]) ).
tcf(c_5902,plain,
( ( x = null_class )
| ( not_subclass_element(null_class,null_class) = regular(x) ) ),
inference(superposition,[status(thm)],[c_195,c_5891]) ).
tcf(c_5904,plain,
not_subclass_element(null_class,null_class) = regular(x),
inference(forward_subsumption_resolution,[status(thm)],[c_5902,c_220]) ).
tcf(c_5906,plain,
! [X0: $i] :
( member(X0,unordered_pair(regular(x),regular(x)))
| ~ member(X0,x) ),
inference(demodulation,[status(thm)],[c_5885,c_5904]) ).
tcf(c_5913,plain,
( subclass(x,null_class)
| member(regular(x),x) ),
inference(demodulation,[status(thm)],[c_5520,c_5904]) ).
tcf(c_5915,plain,
unordered_pair(regular(x),regular(x)) != x,
inference(demodulation,[status(thm)],[c_5465,c_5904]) ).
tcf(c_5928,plain,
member(regular(x),x),
inference(global_subsumption_just,[status(thm)],[c_5913,c_220,c_3420]) ).
tcf(c_5982,plain,
! [X0: $i] :
( subclass(X0,unordered_pair(regular(x),regular(x)))
| ~ member(not_subclass_element(X0,unordered_pair(regular(x),regular(x))),x) ),
inference(superposition,[status(thm)],[c_5906,c_145]) ).
tcf(c_6061,plain,
subclass(x,unordered_pair(regular(x),regular(x))),
inference(superposition,[status(thm)],[c_144,c_5982]) ).
tcf(c_6062,plain,
( ( unordered_pair(regular(x),regular(x)) = x )
| ~ subclass(unordered_pair(regular(x),regular(x)),x) ),
inference(superposition,[status(thm)],[c_6061,c_149]) ).
tcf(c_6064,plain,
~ subclass(unordered_pair(regular(x),regular(x)),x),
inference(forward_subsumption_resolution,[status(thm)],[c_6062,c_5915]) ).
tcf(c_6065,plain,
not_subclass_element(unordered_pair(regular(x),regular(x)),x) = regular(x),
inference(superposition,[status(thm)],[c_5831,c_6064]) ).
tcf(c_6067,plain,
( subclass(unordered_pair(regular(x),regular(x)),x)
| ~ member(regular(x),x) ),
inference(superposition,[status(thm)],[c_6065,c_145]) ).
tcf(c_6069,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6067,c_6064,c_5928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET099-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:48:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 22.49/6.85 % SZS status Started for theBenchmark.p
% 22.49/6.85 % SZS status Unsatisfiable for theBenchmark.p
% 22.49/6.85
% 22.49/6.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.49/6.85
% 22.49/6.85 % ------ iProver source info
% 22.49/6.85
% 22.49/6.85 % git: date: 2026-07-19 20:42:38 +0200
% 22.49/6.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.49/6.85 % git: non_committed_changes: false
% 22.49/6.85
% 22.49/6.85 % ------ Parsing...% successful
% 22.49/6.85
% 22.49/6.85
% 22.49/6.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.49/6.85
% 22.49/6.85 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 22.49/6.85
% 22.49/6.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.49/6.85
% 22.49/6.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.49/6.85 % ------ Proving...
% 22.49/6.85 % ------ Problem Properties
% 22.49/6.85
% 22.49/6.85 %
% 22.49/6.85 % clauses 70
% 22.49/6.85 % conjectures 3
% 22.49/6.85 % EPR 13
% 22.49/6.85 % Horn 62
% 22.49/6.85 % unary 18
% 22.49/6.85 % binary 32
% 22.49/6.85 % lits 148
% 22.49/6.85 % lits eq 23
% 22.49/6.85 % fd_pure 0
% 22.49/6.85 % fd_pseudo 0
% 22.49/6.85 % fd_cond 3
% 22.49/6.85 % fd_pseudo_cond 3
% 22.49/6.85 % AC symbols 0
% 22.49/6.85
% 22.49/6.85 % ------ Input Options Time Limit: Unbounded
% 22.49/6.85
% 22.49/6.85
% 22.49/6.85 % ------
% 22.49/6.85 % Current options:
% 22.49/6.85 % ------
% 22.49/6.85
% 22.49/6.85
% 22.49/6.85 %
% 22.49/6.85
% 22.49/6.85 % ------ Proving...
% 22.49/6.85 %
% 22.49/6.85
% 22.49/6.85 % SZS status Unsatisfiable for theBenchmark.p
% 22.49/6.85
% 22.49/6.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.49/6.86
% 22.49/6.86
%------------------------------------------------------------------------------