%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET097-6 : 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 15.77s 3.27s
% Output : CNFRefutation 15.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 132 ( 39 unt; 0 def)
% Number of atoms : 265 ( 67 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 253 ( 120 ~; 133 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 152 ( 0 sgn 152 !; 0 ?; 106 :)
% 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(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(f63,axiom,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',function1) ).
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(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).
fof(f102,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).
fof(f103,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f102]) ).
fof(f104,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).
fof(f105,plain,
null_class != x,
inference(reorient_equations,[],[f104]) ).
fof(f110,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f110]) ).
fof(f154,plain,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(definition_unfolding,[],[f101,f12,f12]) ).
fof(f155,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f103,f12]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(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_153,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
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_191,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_195,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_218,negated_conjecture,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(cnf_transformation,[],[f154]) ).
tcf(c_219,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[],[f155]) ).
tcf(c_220,negated_conjecture,
x != null_class,
inference(cnf_transformation,[],[f105]) ).
tcf(c_2103,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2882,plain,
! [X0: $i] :
( ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) = x )
| ( x != X0 )
| ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2105]) ).
tcf(c_2885,plain,
( ( x = null_class )
| ~ subclass(null_class,x)
| ~ subclass(x,null_class) ),
inference(instantiation,[status(thm)],[c_149]) ).
tcf(c_2893,plain,
! [X0: $i] :
( ( x = X0 )
| ~ subclass(x,X0)
| ~ subclass(X0,x) ),
inference(instantiation,[status(thm)],[c_149]) ).
tcf(c_3264,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = X1 )
| ( X1 != X0 )
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) != X0 ) ),
inference(instantiation,[status(thm)],[c_2105]) ).
tcf(c_3342,plain,
! [X0: $i] :
( subclass(X0,null_class)
| member(not_subclass_element(X0,null_class),X0) ),
inference(instantiation,[status(thm)],[c_144]) ).
tcf(c_3355,plain,
( ( x = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) )
| ~ subclass(x,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ subclass(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x) ),
inference(instantiation,[status(thm)],[c_2893]) ).
tcf(c_3439,plain,
! [X0: $i] :
( ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = X0 )
| ( X0 != null_class )
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) != null_class ) ),
inference(instantiation,[status(thm)],[c_3264]) ).
tcf(c_3544,plain,
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_144,c_218]) ).
tcf(c_3546,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_144,c_161]) ).
tcf(c_3556,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_144,c_162]) ).
tcf(c_3586,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_195,c_164]) ).
tcf(c_3587,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_3586]) ).
tcf(c_3846,plain,
( ( 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_3544,c_149]) ).
tcf(c_3892,plain,
( subclass(x,null_class)
| member(not_subclass_element(x,null_class),x) ),
inference(instantiation,[status(thm)],[c_3342]) ).
tcf(c_3981,plain,
( ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) = x )
| ( x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) )
| ( unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) ) ),
inference(instantiation,[status(thm)],[c_2882]) ).
tcf(c_4154,plain,
( ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_163,c_218]) ).
tcf(c_4312,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),universal_class)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(superposition,[status(thm)],[c_165,c_4154]) ).
tcf(c_4583,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_3546,c_145]) ).
tcf(c_4683,plain,
subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[c_218,c_144]) ).
tcf(c_4861,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c_164,c_144]) ).
tcf(c_4877,plain,
subclass(x,universal_class),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_4911,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c_143,c_146]) ).
tcf(c_4917,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(resolution,[status(thm)],[c_143,c_4683]) ).
tcf(c_4962,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_3556,c_145]) ).
tcf(c_5089,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(resolution,[status(thm)],[c_4911,c_144]) ).
tcf(c_5340,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_196,c_4583]) ).
tcf(c_5382,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(null_class,X0)
| ~ subclass(X0,null_class) ),
inference(instantiation,[status(thm)],[c_149]) ).
tcf(c_5432,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(resolution,[status(thm)],[c_4861,c_5089]) ).
tcf(c_5482,plain,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(superposition,[status(thm)],[c_5340,c_3846]) ).
tcf(c_5499,plain,
subclass(null_class,x),
inference(superposition,[status(thm)],[c_5482,c_4962]) ).
tcf(c_5629,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(resolution,[status(thm)],[c_5432,c_143]) ).
tcf(c_5637,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(resolution,[status(thm)],[c_5629,c_195]) ).
tcf(c_5638,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_5637]) ).
tcf(c_5646,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_5637,c_3587,c_5638]) ).
tcf(c_6439,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(resolution,[status(thm)],[c_163,c_4917]) ).
tcf(c_6463,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),X0)
| ~ subclass(x,X0)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(instantiation,[status(thm)],[c_143]) ).
tcf(c_6465,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),universal_class)
| ~ subclass(x,universal_class)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(instantiation,[status(thm)],[c_6463]) ).
tcf(c_6712,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_3846,c_5482]) ).
tcf(c_6723,plain,
! [X0: $i] :
( member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_6712,c_161]) ).
tcf(c_6747,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),X0) ),
inference(superposition,[status(thm)],[c_6723,c_143]) ).
tcf(c_6770,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_146,c_6747]) ).
tcf(c_6778,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),universal_class)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(superposition,[status(thm)],[c_165,c_4154]) ).
tcf(c_6809,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(global_subsumption_just,[status(thm)],[c_6778,c_4312,c_4877,c_6465]) ).
tcf(c_7168,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[c_6439,c_165]) ).
tcf(c_7340,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7168,c_4911]) ).
tcf(c_7502,plain,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) = unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(instantiation,[status(thm)],[c_2103]) ).
tcf(c_24687,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_3846,c_5482]) ).
tcf(c_24709,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_24710,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_195,c_164]) ).
tcf(c_24717,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_153,c_143]) ).
tcf(c_24751,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),universal_class)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(superposition,[status(thm)],[c_165,c_4154]) ).
tcf(c_24778,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(global_subsumption_just,[status(thm)],[c_24751,c_6809]) ).
tcf(c_24781,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),X0)
| ~ subclass(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),X0)
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(superposition,[status(thm)],[c_24778,c_143]) ).
tcf(c_24786,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),X0)
| ~ member(not_subclass_element(null_class,null_class),x)
| ~ subclass(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),X0) ),
inference(superposition,[status(thm)],[c_24687,c_24781]) ).
tcf(c_24810,plain,
! [X0: $i] :
( member(X0,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_24687,c_163]) ).
tcf(c_24820,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_165,c_24810]) ).
tcf(c_24827,plain,
! [X0: $i] :
( member(X0,null_class)
| member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(global_subsumption_just,[status(thm)],[c_24820,c_7340]) ).
tcf(c_24830,plain,
! [X0: $i] :
( subclass(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| member(not_subclass_element(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),null_class)
| ~ member(not_subclass_element(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) ),
inference(superposition,[status(thm)],[c_24827,c_145]) ).
tcf(c_24856,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_25337,plain,
( subclass(x,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| member(not_subclass_element(x,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),null_class) ),
inference(superposition,[status(thm)],[c_144,c_24830]) ).
tcf(c_25629,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ subclass(universal_class,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_24717,c_155]) ).
tcf(c_25671,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_191,c_25629]) ).
tcf(c_26144,plain,
! [X0: $i] :
( subclass(complement(universal_class),X0)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_25671,c_24709]) ).
tcf(c_26153,plain,
( ( complement(universal_class) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_25671,c_24710]) ).
tcf(c_26173,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(global_subsumption_just,[status(thm)],[c_26144,c_5432]) ).
tcf(c_26177,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_26153,c_5646]) ).
tcf(c_26193,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_26177,c_164]) ).
tcf(c_26194,plain,
! [X0: $i] : subclass(null_class,X0),
inference(superposition,[status(thm)],[c_26177,c_26173]) ).
tcf(c_26226,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_26193,c_6770,c_26193]) ).
tcf(c_26249,plain,
subclass(x,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),
inference(superposition,[status(thm)],[c_25337,c_26226]) ).
tcf(c_26274,plain,
! [X0: $i] :
( subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),X0)
| member(not_subclass_element(null_class,X0),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_24687,c_3546]) ).
tcf(c_26313,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),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) = X0 )
| ~ subclass(X0,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm)],[c_26274,c_149]) ).
tcf(c_26332,plain,
! [X0: $i] :
( member(not_subclass_element(null_class,X0),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) = X0 )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_24687,c_26313]) ).
tcf(c_26334,plain,
! [X0: $i] :
( ~ subclass(X0,null_class)
| ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_26332,c_3439,c_5382,c_5482,c_26194]) ).
tcf(c_26335,plain,
! [X0: $i] :
( ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = X0 )
| ~ subclass(X0,null_class) ),
inference(renaming,[status(thm)],[c_26334]) ).
tcf(c_26342,plain,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = complement(universal_class),
inference(superposition,[status(thm)],[c_26173,c_26335]) ).
tcf(c_26390,plain,
( ~ member(not_subclass_element(complement(universal_class),null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x) ),
inference(superposition,[status(thm)],[c_26342,c_4154]) ).
tcf(c_26507,plain,
( ~ member(not_subclass_element(null_class,null_class),x)
| ~ subclass(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x)
| ~ member(not_subclass_element(complement(universal_class),null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_24786,c_26390]) ).
tcf(c_26595,plain,
~ subclass(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x),
inference(global_subsumption_just,[status(thm)],[c_26507,c_219,c_3355,c_3981,c_7502,c_26249]) ).
tcf(c_26597,plain,
not_subclass_element(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x) = not_subclass_element(x,null_class),
inference(superposition,[status(thm)],[c_24856,c_26595]) ).
tcf(c_26600,plain,
( subclass(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),x)
| ~ member(not_subclass_element(x,null_class),x) ),
inference(superposition,[status(thm)],[c_26597,c_145]) ).
tcf(c_26603,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_26600,c_26249,c_7502,c_5499,c_3981,c_3892,c_3355,c_2885,c_219,c_220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET097-6 : 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 09:46:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 15.77/3.27 % SZS status Started for theBenchmark.p
% 15.77/3.27 % SZS status Unsatisfiable for theBenchmark.p
% 15.77/3.27
% 15.77/3.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.77/3.27
% 15.77/3.27 % ------ iProver source info
% 15.77/3.27
% 15.77/3.27 % git: date: 2026-07-19 20:42:38 +0200
% 15.77/3.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.77/3.27 % git: non_committed_changes: false
% 15.77/3.27
% 15.77/3.27 % ------ Parsing...% successful
% 15.77/3.27
% 15.77/3.27
% 15.77/3.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.77/3.27
% 15.77/3.27 % ------ 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 %
% 15.77/3.27
% 15.77/3.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.77/3.27
% 15.77/3.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.77/3.27 % ------ Proving...
% 15.77/3.27 % ------ Problem Properties
% 15.77/3.27
% 15.77/3.27 %
% 15.77/3.27 % clauses 70
% 15.77/3.27 % conjectures 3
% 15.77/3.27 % EPR 13
% 15.77/3.27 % Horn 62
% 15.77/3.27 % unary 18
% 15.77/3.27 % binary 32
% 15.77/3.27 % lits 148
% 15.77/3.27 % lits eq 22
% 15.77/3.27 % fd_pure 0
% 15.77/3.27 % fd_pseudo 0
% 15.77/3.27 % fd_cond 3
% 15.77/3.27 % fd_pseudo_cond 3
% 15.77/3.27 % AC symbols 0
% 15.77/3.27
% 15.77/3.27 % ------ Input Options Time Limit: Unbounded
% 15.77/3.27
% 15.77/3.27
% 15.77/3.27 % ------
% 15.77/3.27 % Current options:
% 15.77/3.27 % ------
% 15.77/3.27
% 15.77/3.27
% 15.77/3.27 %
% 15.77/3.27
% 15.77/3.27 % ------ Proving...
% 15.77/3.27 %
% 15.77/3.27
% 15.77/3.27 % SZS status Unsatisfiable for theBenchmark.p
% 15.77/3.27
% 15.77/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.77/3.27
% 15.77/3.27
%------------------------------------------------------------------------------