%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET069+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 02:46:22 PM UTC 2026
% Result : Theorem 36.57s 13.92s
% Output : CNFRefutation 36.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 22
% Syntax : Number of formulae : 160 ( 47 unt; 2 def)
% Number of atoms : 463 ( 111 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 395 ( 156 ~; 173 |; 53 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 252 ( 0 sgn 243 !; 9 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f11,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
<=> ( member(X0,X1)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',element_relation_defn) ).
fof(f13,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',intersection) ).
fof(f14,axiom,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',complement) ).
fof(f15,axiom,
! [X0,X1,X2] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',restrict_defn) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(f25,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
<=> ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',successor_relation_defn2) ).
fof(f26,axiom,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inverse_defn) ).
fof(f27,axiom,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',range_of_defn) ).
fof(f28,axiom,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',image_defn) ).
fof(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(f42,axiom,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',apply_defn) ).
fof(f43,axiom,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| X1 = null_class ) )
& function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',choice) ).
fof(f44,conjecture,
! [X0,X1] :
( ~ member(X1,universal_class)
=> unordered_pair(X0,X1) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pair_contains_only_other2) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ~ member(X1,universal_class)
=> unordered_pair(X0,X1) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f57,plain,
! [X0] :
( null_class = X0
| ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f58,plain,
? [X0] :
( ! [X1] :
( ~ member(X1,universal_class)
| member(apply(X0,X1),X1)
| X1 = null_class )
& function(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f59,plain,
? [X0] :
( ! [X1] :
( ~ member(X1,universal_class)
| member(apply(X0,X1),X1)
| X1 = null_class )
& function(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
? [X0,X1] :
( ~ member(X1,universal_class)
& unordered_pair(X0,X1) != singleton(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
! [X0,X1] :
( ( ~ subclass(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( ( ~ subclass(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subclass(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ subclass(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( X0 != X1
| ( subclass(X1,X0)
& subclass(X0,X1) ) )
& ( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 != X1
| ( subclass(X1,X0)
& subclass(X0,X1) ) )
& ( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f66]) ).
fof(f70,plain,
! [X0,X1] :
( ( ~ member(ordered_pair(X0,X1),element_relation)
| ( member(X0,X1)
& member(X1,universal_class) ) )
& ( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(ordered_pair(X0,X1),element_relation) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f71,plain,
! [X0,X1] :
( ( ~ member(ordered_pair(X0,X1),element_relation)
| ( member(X0,X1)
& member(X1,universal_class) ) )
& ( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(ordered_pair(X0,X1),element_relation) ) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( ~ member(X1,complement(X0))
| ( ~ member(X1,X0)
& member(X1,universal_class) ) )
& ( member(X1,X0)
| ~ member(X1,universal_class)
| member(X1,complement(X0)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f75,plain,
! [X0,X1] :
( ( ~ member(X1,complement(X0))
| ( ~ member(X1,X0)
& member(X1,universal_class) ) )
& ( member(X1,X0)
| ~ member(X1,universal_class)
| member(X1,complement(X0)) ) ),
inference(flattening,[],[f74]) ).
fof(f84,plain,
! [X0,X1] :
( ( ~ member(ordered_pair(X0,X1),successor_relation)
| ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) )
& ( successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| member(ordered_pair(X0,X1),successor_relation) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ member(ordered_pair(X0,X1),successor_relation)
| ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) )
& ( successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| member(ordered_pair(X0,X1),successor_relation) ) ),
inference(flattening,[],[f84]) ).
fof(f101,plain,
! [X0] :
( null_class = X0
| ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f102,plain,
( ! [X1] :
( ~ member(X1,universal_class)
| member(apply(sK5,X1),X1)
| X1 = null_class )
& function(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f59]) ).
fof(f103,plain,
( ~ member(sK7,universal_class)
& unordered_pair(sK6,sK7) != singleton(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f104,plain,
! [X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f107,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f110,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f67]) ).
fof(f114,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f115,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f71]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(X1,complement(X0))
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f133,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(X1,universal_class)
| member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f134,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f15]) ).
fof(f135,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f154,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),successor_relation)
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f85]) ).
fof(f156,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f26]) ).
fof(f157,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f158,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f28]) ).
fof(f186,plain,
! [X0] :
( null_class = X0
| member(sK4(X0),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f187,plain,
! [X0] :
( null_class = X0
| member(sK4(X0),universal_class) ),
inference(cnf_transformation,[],[f101]) ).
fof(f188,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f42]) ).
fof(f189,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(apply(sK5,X1),X1)
| null_class = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f191,plain,
~ member(sK7,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
unordered_pair(sK6,sK7) != singleton(sK6),
inference(cnf_transformation,[],[f103]) ).
fof(f193,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f117,f116,f116]) ).
fof(f194,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f157,f156]) ).
fof(f195,plain,
! [X0,X1] : image(X1,X0) = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f158,f194,f134]) ).
fof(f197,plain,
! [X0,X1] : apply(X0,X1) = sum_class(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f188,f195,f116]) ).
fof(f204,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f126,f193]) ).
fof(f216,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f154,f193]) ).
fof(f229,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1 ),
inference(definition_unfolding,[],[f189,f197]) ).
fof(f230,plain,
unordered_pair(sK6,sK7) != unordered_pair(sK6,sK6),
inference(definition_unfolding,[],[f192,f116]) ).
fof(f233,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f114]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f107]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f115]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X1,universal_class)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_77,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f135]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_123,plain,
! [X0: $i] :
( member(sK4(X0),universal_class)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_124,plain,
! [X0: $i] :
( member(sK4(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_127,plain,
! [X0: $i] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X0)
| ( X0 = null_class )
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_128,negated_conjecture,
unordered_pair(sK6,sK6) != unordered_pair(sK6,sK7),
inference(cnf_transformation,[],[f230]) ).
tcf(c_129,negated_conjecture,
~ member(sK7,universal_class),
inference(cnf_transformation,[],[f191]) ).
tcf(c_1557,definition,
iPr_def_10 = unordered_pair(sK6,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1558,definition,
iPr_def_11 = unordered_pair(sK6,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1559,negated_conjecture,
~ member(sK7,universal_class),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_1560,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_128,c_1558,c_1557]) ).
tcf(c_2502,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1558,c_58]) ).
tcf(c_2503,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1557,c_58]) ).
tcf(c_2565,plain,
! [X0: $i,X1: $i] :
( member(sK4(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_124,c_72]) ).
tcf(c_2577,plain,
! [X0: $i,X1: $i] :
( member(sK4(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_124,c_73]) ).
tcf(c_3226,plain,
! [X0: $i] :
( ( X0 = sK7 )
| ( X0 = sK6 )
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1558,c_59]) ).
tcf(c_3227,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1557,c_59]) ).
tcf(c_5127,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X1 )
| ( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X0 )
| ~ member(unordered_pair(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_127,c_59]) ).
tcf(c_5210,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X1 )
| ( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5127,c_60]) ).
tcf(c_6753,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X1,X0) = null_class )
| ( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X0)),universal_class)),universal_class))))) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_5210]) ).
tcf(c_7118,plain,
! [X0: $i] :
( ( unordered_pair(X0,X0) = null_class )
| ( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),universal_class)),universal_class))))) = X0 ) ),
inference(equality_resolution,[status(thm)],[c_6753]) ).
tcf(c_8561,plain,
! [X0: $i] :
( member(X0,unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = null_class )
| ~ member(unordered_pair(X0,X0),universal_class) ),
inference(superposition,[status(thm)],[c_7118,c_127]) ).
tcf(c_8562,plain,
! [X0: $i] :
( member(X0,unordered_pair(X0,X0))
| ( unordered_pair(X0,X0) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8561,c_60]) ).
tcf(c_8876,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( unordered_pair(X0,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_8562,c_58]) ).
tcf(c_8908,plain,
unordered_pair(sK7,sK7) = null_class,
inference(superposition,[status(thm)],[c_8876,c_1559]) ).
tcf(c_8994,plain,
! [X0: $i] :
( member(unordered_pair(null_class,unordered_pair(sK7,unordered_pair(X0,X0))),element_relation)
| ~ member(sK7,X0)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_8908,c_67]) ).
tcf(c_9000,plain,
! [X0: $i] :
( member(sK7,universal_class)
| ~ member(unordered_pair(null_class,unordered_pair(sK7,unordered_pair(X0,X0))),successor_relation) ),
inference(superposition,[status(thm)],[c_8908,c_94]) ).
tcf(c_9042,plain,
! [X0: $i] : ~ member(unordered_pair(null_class,unordered_pair(sK7,unordered_pair(X0,X0))),successor_relation),
inference(forward_subsumption_resolution,[status(thm)],[c_9000,c_1559]) ).
tcf(c_9763,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(null_class,unordered_pair(sK7,unordered_pair(X1,X1))),X0)
| ~ member(sK7,X1)
| ~ member(X1,universal_class)
| ~ subclass(element_relation,X0) ),
inference(superposition,[status(thm)],[c_8994,c_51]) ).
tcf(c_9825,plain,
! [X0: $i] :
( ( intersection(iPr_def_10,X0) = null_class )
| ( sK4(intersection(iPr_def_10,X0)) = sK6 ) ),
inference(superposition,[status(thm)],[c_2565,c_3227]) ).
tcf(c_14585,plain,
! [X0: $i] :
( ( intersection(iPr_def_11,X0) = null_class )
| ( sK4(intersection(iPr_def_11,X0)) = sK7 )
| ( sK4(intersection(iPr_def_11,X0)) = sK6 ) ),
inference(superposition,[status(thm)],[c_2565,c_3226]) ).
tcf(c_18284,plain,
! [X0: $i] :
( ~ subclass(element_relation,successor_relation)
| ~ member(sK7,X0)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_9763,c_9042]) ).
tcf(c_18468,plain,
! [X0: $i] :
( member(sK7,universal_class)
| ~ member(sK7,X0)
| ~ subclass(X0,universal_class) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_18512,plain,
! [X0: $i] : ~ member(sK7,X0),
inference(global_subsumption_just,[status(thm)],[c_18284,c_52,c_129,c_18468]) ).
tcf(c_20833,plain,
! [X0: $i] :
( member(sK6,universal_class)
| ( intersection(iPr_def_10,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_9825,c_123]) ).
tcf(c_20836,plain,
! [X0: $i] :
( member(sK6,X0)
| ( intersection(iPr_def_10,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_9825,c_2577]) ).
tcf(c_26088,plain,
! [X0: $i] :
( member(sK7,iPr_def_11)
| ( intersection(iPr_def_11,X0) = null_class )
| ( sK4(intersection(iPr_def_11,X0)) = sK6 ) ),
inference(superposition,[status(thm)],[c_14585,c_2565]) ).
tcf(c_26093,plain,
! [X0: $i] :
( ( intersection(iPr_def_11,X0) = null_class )
| ( sK4(intersection(iPr_def_11,X0)) = sK6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26088,c_18512]) ).
tcf(c_26126,plain,
! [X0: $i] :
( member(sK6,universal_class)
| ( intersection(iPr_def_11,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_26093,c_123]) ).
tcf(c_26130,plain,
! [X0: $i] :
( member(sK6,X0)
| ( intersection(iPr_def_11,X0) = null_class ) ),
inference(superposition,[status(thm)],[c_26093,c_2577]) ).
tcf(c_28762,plain,
! [X0: $i] :
( ( intersection(iPr_def_10,complement(X0)) = null_class )
| ~ member(sK6,X0) ),
inference(superposition,[status(thm)],[c_20836,c_76]) ).
tcf(c_30777,plain,
! [X0: $i] :
( ( intersection(iPr_def_10,complement(unordered_pair(sK6,X0))) = null_class )
| ~ member(sK6,universal_class) ),
inference(superposition,[status(thm)],[c_56,c_28762]) ).
tcf(c_38047,plain,
! [X0: $i] :
( ( intersection(iPr_def_11,complement(X0)) = null_class )
| ~ member(sK6,X0) ),
inference(superposition,[status(thm)],[c_26130,c_76]) ).
tcf(c_39715,plain,
! [X0: $i] :
( ( intersection(iPr_def_11,complement(unordered_pair(sK6,X0))) = null_class )
| ~ member(sK6,universal_class) ),
inference(superposition,[status(thm)],[c_56,c_38047]) ).
tcf(c_65911,plain,
! [X0: $i] : intersection(iPr_def_10,complement(unordered_pair(sK6,X0))) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_30777,c_20833]) ).
tcf(c_65913,plain,
intersection(iPr_def_10,complement(iPr_def_11)) = null_class,
inference(superposition,[status(thm)],[c_1558,c_65911]) ).
tcf(c_65981,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,iPr_def_10)
| ~ member(X0,complement(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_65913,c_71]) ).
tcf(c_65995,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,complement(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65981,c_77]) ).
tcf(c_66058,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_74,c_65995]) ).
tcf(c_67137,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_66058,c_2503,c_66058]) ).
tcf(c_67144,plain,
! [X0: $i] :
( subclass(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_50,c_67137]) ).
tcf(c_67649,plain,
subclass(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_67144,c_49]) ).
tcf(c_67817,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subclass(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_67649,c_53]) ).
tcf(c_67820,plain,
~ subclass(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_67817,c_1560]) ).
tcf(c_96524,plain,
! [X0: $i] : intersection(iPr_def_11,complement(unordered_pair(sK6,X0))) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_39715,c_26126]) ).
tcf(c_96527,plain,
intersection(iPr_def_11,complement(iPr_def_10)) = null_class,
inference(superposition,[status(thm)],[c_1557,c_96524]) ).
tcf(c_96635,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,iPr_def_11)
| ~ member(X0,complement(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_96527,c_71]) ).
tcf(c_96649,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,complement(iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96635,c_77]) ).
tcf(c_96664,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_74,c_96649]) ).
tcf(c_97332,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_96664,c_2502,c_96664]) ).
tcf(c_97339,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_97332]) ).
tcf(c_97662,plain,
subclass(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_97339,c_49]) ).
tcf(c_97672,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_97662,c_67820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET069+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.38 % Computer : n001.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 09:39:27 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 36.57/13.92 % SZS status Started for theBenchmark.p
% 36.57/13.92 % SZS status Theorem for theBenchmark.p
% 36.57/13.92
% 36.57/13.92 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 36.57/13.92
% 36.57/13.92 % ------ iProver source info
% 36.57/13.92
% 36.57/13.92 % git: date: 2026-07-19 20:42:38 +0200
% 36.57/13.92 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 36.57/13.92 % git: non_committed_changes: false
% 36.57/13.92
% 36.57/13.92 % ------ Parsing...
% 36.57/13.92 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 36.57/13.92
% 36.57/13.92 % ------ 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: 4 0s sf_e pe_s pe_e %
% 36.57/13.92
% 36.57/13.92 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 36.57/13.92
% 36.57/13.92 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 36.57/13.92 % ------ Proving...
% 36.57/13.92 % ------ Problem Properties
% 36.57/13.92
% 36.57/13.92 %
% 36.57/13.92 % clauses 78
% 36.57/13.92 % conjectures 2
% 36.57/13.92 % EPR 9
% 36.57/13.92 % Horn 70
% 36.57/13.92 % unary 18
% 36.57/13.92 % binary 39
% 36.57/13.92 % lits 160
% 36.57/13.92 % lits eq 17
% 36.57/13.92 % fd_pure 0
% 36.57/13.92 % fd_pseudo 0
% 36.57/13.92 % fd_cond 4
% 36.57/13.92 % fd_pseudo_cond 3
% 36.57/13.92 % AC symbols 0
% 36.57/13.92
% 36.57/13.92 % ------ Schedule dynamic 5 is on
% 36.57/13.92
% 36.57/13.92 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 36.57/13.92
% 36.57/13.92
% 36.57/13.92 % ------
% 36.57/13.92 % Current options:
% 36.57/13.92 % ------
% 36.57/13.92
% 36.57/13.92
% 36.57/13.92 %
% 36.57/13.92
% 36.57/13.92 % ------ Proving...
% 36.57/13.92 %
% 36.57/13.92
% 36.57/13.92 % SZS status Theorem for theBenchmark.p
% 36.57/13.92
% 36.57/13.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 36.57/13.92
% 36.57/13.92
%------------------------------------------------------------------------------