TSTP Solution File: SET097+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET097+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:59:52 EDT 2024
% Result : Theorem 127.95s 17.76s
% Output : CNFRefutation 127.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 23
% Syntax : Number of formulae : 176 ( 42 unt; 0 def)
% Number of atoms : 485 ( 144 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 518 ( 209 ~; 218 |; 69 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-3 aty)
% Number of variables : 308 ( 12 sgn 183 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f13,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
<=> ( member(X4,X1)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f14,axiom,
! [X0,X4] :
( member(X4,complement(X0))
<=> ( ~ member(X4,X0)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f15,axiom,
! [X0,X5,X1] : restrict(X5,X0,X1) = intersection(X5,cross_product(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,union(X0,X1))
<=> ( member(X4,X1)
| member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f26,axiom,
! [X1] : inverse(X1) = domain_of(flip(cross_product(X1,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).
fof(f27,axiom,
! [X4] : range_of(X4) = domain_of(inverse(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
fof(f28,axiom,
! [X0,X5] : image(X5,X0) = range_of(restrict(X5,X0,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).
fof(f40,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f42,axiom,
! [X8,X1] : apply(X8,X1) = sum_class(image(X8,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
fof(f44,conjecture,
! [X0] :
( ? [X3] :
( ? [X6] : member(X6,intersection(complement(singleton(X3)),X0))
& member(X3,X0) )
| ? [X1] : singleton(X1) = X0
| null_class = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_of_elements_in_class) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( ? [X3] :
( ? [X6] : member(X6,intersection(complement(singleton(X3)),X0))
& member(X3,X0) )
| ? [X1] : singleton(X1) = X0
| null_class = X0 ),
inference(negated_conjecture,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f49,plain,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f50,plain,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f14]) ).
fof(f51,plain,
! [X0,X1,X2] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(rectify,[],[f15]) ).
fof(f55,plain,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f56,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(rectify,[],[f26]) ).
fof(f57,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(rectify,[],[f27]) ).
fof(f58,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(rectify,[],[f28]) ).
fof(f67,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f68,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(rectify,[],[f42]) ).
fof(f69,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f70,plain,
~ ! [X0] :
( ? [X1] :
( ? [X2] : member(X2,intersection(complement(singleton(X1)),X0))
& member(X1,X0) )
| ? [X3] : singleton(X3) = X0
| null_class = X0 ),
inference(rectify,[],[f45]) ).
fof(f71,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f72,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f71]) ).
fof(f82,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f67]) ).
fof(f83,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
? [X0] :
( ! [X1] :
( ! [X2] : ~ member(X2,intersection(complement(singleton(X1)),X0))
| ~ member(X1,X0) )
& ! [X3] : singleton(X3) != X0
& null_class != X0 ),
inference(ennf_transformation,[],[f70]) ).
fof(f86,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f87,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f87,f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f91,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f90]) ).
fof(f92,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,[],[f46]) ).
fof(f93,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,[],[f92]) ).
fof(f98,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,[],[f49]) ).
fof(f99,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,[],[f98]) ).
fof(f100,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,[],[f50]) ).
fof(f101,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,[],[f100]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f108]) ).
fof(f130,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0] :
( ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f82,f130]) ).
fof(f132,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
( ! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f84,f132]) ).
fof(f134,plain,
( ? [X0] :
( ! [X1] :
( ! [X2] : ~ member(X2,intersection(complement(singleton(X1)),X0))
| ~ member(X1,X0) )
& ! [X3] : singleton(X3) != X0
& null_class != X0 )
=> ( ! [X1] :
( ! [X2] : ~ member(X2,intersection(complement(singleton(X1)),sK6))
| ~ member(X1,sK6) )
& ! [X3] : singleton(X3) != sK6
& null_class != sK6 ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( ! [X1] :
( ! [X2] : ~ member(X2,intersection(complement(singleton(X1)),sK6))
| ~ member(X1,sK6) )
& ! [X3] : singleton(X3) != sK6
& null_class != sK6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f85,f134]) ).
fof(f136,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f137,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f138,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f139,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f142,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f143,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f144,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f162,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f165,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f101]) ).
fof(f166,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f51]) ).
fof(f167,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f181,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f188,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f56]) ).
fof(f189,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f57]) ).
fof(f190,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f58]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f217,plain,
! [X0] :
( member(sK4(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f218,plain,
! [X0] :
( member(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f219,plain,
! [X0] :
( disjoint(sK4(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f220,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f68]) ).
fof(f222,plain,
! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f133]) ).
fof(f223,plain,
null_class != sK6,
inference(cnf_transformation,[],[f135]) ).
fof(f224,plain,
! [X3] : singleton(X3) != sK6,
inference(cnf_transformation,[],[f135]) ).
fof(f225,plain,
! [X2,X1] :
( ~ member(X2,intersection(complement(singleton(X1)),sK6))
| ~ member(X1,sK6) ),
inference(cnf_transformation,[],[f135]) ).
fof(f227,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f189,f188]) ).
fof(f228,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,[],[f190,f227,f166]) ).
fof(f230,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,[],[f220,f228,f148]) ).
fof(f262,plain,
! [X1] :
( 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
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f222,f230]) ).
fof(f263,plain,
! [X2,X1] :
( ~ member(X2,intersection(complement(unordered_pair(X1,X1)),sK6))
| ~ member(X1,sK6) ),
inference(definition_unfolding,[],[f225,f148]) ).
fof(f264,plain,
! [X3] : sK6 != unordered_pair(X3,X3),
inference(definition_unfolding,[],[f224,f148]) ).
fof(f268,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f145]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_51,plain,
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_52,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[],[f139]) ).
cnf(c_53,plain,
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_57,plain,
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[],[f268]) ).
cnf(c_58,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_59,plain,
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_71,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_74,plain,
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_77,plain,
~ member(X0,null_class),
inference(cnf_transformation,[],[f167]) ).
cnf(c_89,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f181]) ).
cnf(c_122,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_123,plain,
( X0 = null_class
| disjoint(sK4(X0),X0) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_124,plain,
( X0 = null_class
| member(sK4(X0),X0) ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_125,plain,
( X0 = null_class
| member(sK4(X0),universal_class) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_126,plain,
( ~ member(X0,universal_class)
| X0 = null_class
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X0) ),
inference(cnf_transformation,[],[f262]) ).
cnf(c_128,negated_conjecture,
( ~ member(X0,intersection(complement(unordered_pair(X1,X1)),sK6))
| ~ member(X1,sK6) ),
inference(cnf_transformation,[],[f263]) ).
cnf(c_129,negated_conjecture,
unordered_pair(X0,X0) != sK6,
inference(cnf_transformation,[],[f264]) ).
cnf(c_130,negated_conjecture,
null_class != sK6,
inference(cnf_transformation,[],[f223]) ).
cnf(c_136,plain,
unordered_pair(universal_class,universal_class) != sK6,
inference(instantiation,[status(thm)],[c_129]) ).
cnf(c_862,plain,
( sK4(X0) != X1
| X0 != X2
| ~ member(X3,X1)
| ~ member(X3,X2)
| X0 = null_class ),
inference(resolution_lifted,[status(thm)],[c_122,c_123]) ).
cnf(c_863,plain,
( ~ member(X0,sK4(X1))
| ~ member(X0,X1)
| X1 = null_class ),
inference(unflattening,[status(thm)],[c_862]) ).
cnf(c_1578,negated_conjecture,
null_class != sK6,
inference(demodulation,[status(thm)],[c_130]) ).
cnf(c_1579,negated_conjecture,
unordered_pair(X0,X0) != sK6,
inference(demodulation,[status(thm)],[c_129]) ).
cnf(c_1580,negated_conjecture,
( ~ member(X0,intersection(complement(unordered_pair(X1,X1)),sK6))
| ~ member(X1,sK6) ),
inference(demodulation,[status(thm)],[c_128]) ).
cnf(c_1583,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2488,plain,
( ~ member(X0,sK6)
| intersection(complement(unordered_pair(X0,X0)),sK6) = null_class ),
inference(superposition,[status(thm)],[c_124,c_1580]) ).
cnf(c_2557,plain,
( intersection(complement(unordered_pair(sK4(sK6),sK4(sK6))),sK6) = null_class
| null_class = sK6 ),
inference(superposition,[status(thm)],[c_124,c_2488]) ).
cnf(c_2558,plain,
intersection(complement(unordered_pair(sK4(sK6),sK4(sK6))),sK6) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_2557,c_1578]) ).
cnf(c_2671,plain,
( ~ subclass(union(X0,X1),X2)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(superposition,[status(thm)],[c_89,c_51]) ).
cnf(c_3315,plain,
( ~ member(X0,complement(unordered_pair(sK4(sK6),sK4(sK6))))
| ~ member(X0,sK6)
| member(X0,null_class) ),
inference(superposition,[status(thm)],[c_2558,c_71]) ).
cnf(c_3323,plain,
( ~ member(X0,complement(unordered_pair(X1,X1)))
| ~ member(X0,sK6)
| ~ member(X1,sK6) ),
inference(superposition,[status(thm)],[c_71,c_1580]) ).
cnf(c_3327,plain,
( ~ member(X0,complement(unordered_pair(sK4(sK6),sK4(sK6))))
| ~ member(X0,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3315,c_77]) ).
cnf(c_3373,plain,
( sK4(unordered_pair(X0,X1)) = X0
| sK4(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(superposition,[status(thm)],[c_124,c_58]) ).
cnf(c_3394,plain,
( unordered_pair(X0,X0) != X1
| sK6 != X1
| unordered_pair(X0,X0) = sK6 ),
inference(instantiation,[status(thm)],[c_1583]) ).
cnf(c_3587,plain,
( ~ member(X0,universal_class)
| ~ member(X0,sK6)
| ~ member(X1,sK6)
| member(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_74,c_3323]) ).
cnf(c_3643,plain,
( ~ member(X0,universal_class)
| ~ member(X0,sK6)
| ~ member(X1,sK6)
| X0 = X1 ),
inference(superposition,[status(thm)],[c_3587,c_58]) ).
cnf(c_3789,plain,
( ~ member(X0,universal_class)
| ~ member(X0,sK6)
| member(X0,unordered_pair(sK4(sK6),sK4(sK6))) ),
inference(superposition,[status(thm)],[c_74,c_3327]) ).
cnf(c_3918,plain,
( unordered_pair(X0,X0) != null_class
| sK6 != null_class
| unordered_pair(X0,X0) = sK6 ),
inference(instantiation,[status(thm)],[c_3394]) ).
cnf(c_3920,plain,
( sK6 = null_class
| member(sK4(sK6),sK6) ),
inference(instantiation,[status(thm)],[c_124]) ).
cnf(c_3922,plain,
( unordered_pair(universal_class,universal_class) != null_class
| sK6 != null_class
| unordered_pair(universal_class,universal_class) = sK6 ),
inference(instantiation,[status(thm)],[c_3918]) ).
cnf(c_3948,plain,
( X0 != X1
| sK4(unordered_pair(X1,X0)) = X0
| unordered_pair(X1,X0) = null_class ),
inference(equality_factoring,[status(thm)],[c_3373]) ).
cnf(c_5050,plain,
( sK4(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = null_class ),
inference(equality_resolution,[status(thm)],[c_3948]) ).
cnf(c_5275,plain,
( ~ member(X0,universal_class)
| ~ member(X0,sK6)
| ~ member(sK6,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = X0
| null_class = sK6 ),
inference(superposition,[status(thm)],[c_126,c_3643]) ).
cnf(c_5332,plain,
( ~ member(X0,universal_class)
| ~ member(X0,sK6)
| ~ member(sK6,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_5275,c_1578]) ).
cnf(c_5708,plain,
( ~ member(sK4(sK6),universal_class)
| ~ member(sK6,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = sK4(sK6)
| null_class = sK6 ),
inference(superposition,[status(thm)],[c_124,c_5332]) ).
cnf(c_5711,plain,
( ~ member(sK4(sK6),universal_class)
| ~ member(sK6,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = sK4(sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5708,c_1578]) ).
cnf(c_5736,plain,
( ~ member(sK6,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = sK4(sK6)
| null_class = sK6 ),
inference(superposition,[status(thm)],[c_125,c_5711]) ).
cnf(c_5737,plain,
( ~ member(sK6,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = sK4(sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5736,c_1578]) ).
cnf(c_6427,plain,
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_5050,c_125]) ).
cnf(c_6428,plain,
( unordered_pair(X0,X0) = null_class
| member(X0,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_5050,c_124]) ).
cnf(c_6429,plain,
( ~ member(X0,unordered_pair(X1,X1))
| ~ member(X0,X1)
| unordered_pair(X1,X1) = null_class ),
inference(superposition,[status(thm)],[c_5050,c_863]) ).
cnf(c_6437,plain,
( unordered_pair(universal_class,universal_class) = null_class
| member(universal_class,universal_class) ),
inference(instantiation,[status(thm)],[c_6427]) ).
cnf(c_6438,plain,
( unordered_pair(universal_class,universal_class) = null_class
| member(universal_class,unordered_pair(universal_class,universal_class)) ),
inference(instantiation,[status(thm)],[c_6428]) ).
cnf(c_6439,plain,
( ~ member(universal_class,unordered_pair(universal_class,universal_class))
| ~ member(universal_class,universal_class)
| unordered_pair(universal_class,universal_class) = null_class ),
inference(instantiation,[status(thm)],[c_6429]) ).
cnf(c_6540,plain,
( sum_class(domain_of(domain_of(flip(cross_product(intersection(sK5,cross_product(unordered_pair(sK6,sK6),universal_class)),universal_class))))) = sK4(sK6)
| unordered_pair(sK6,sK6) = null_class ),
inference(superposition,[status(thm)],[c_6427,c_5737]) ).
cnf(c_6815,plain,
( ~ member(sK6,universal_class)
| unordered_pair(sK6,sK6) = null_class
| null_class = sK6
| member(sK4(sK6),sK6) ),
inference(superposition,[status(thm)],[c_6540,c_126]) ).
cnf(c_6816,plain,
( ~ member(sK6,universal_class)
| unordered_pair(sK6,sK6) = null_class
| member(sK4(sK6),sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6815,c_1578]) ).
cnf(c_6829,plain,
member(sK4(sK6),sK6),
inference(global_subsumption_just,[status(thm)],[c_6816,c_136,c_3922,c_3920,c_6437,c_6438,c_6439]) ).
cnf(c_31331,plain,
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_52,c_2671]) ).
cnf(c_181064,plain,
( ~ member(X0,sK6)
| member(X0,unordered_pair(sK4(sK6),sK4(sK6))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3789,c_31331]) ).
cnf(c_181075,plain,
( ~ member(X0,sK6)
| member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_181064,c_31331]) ).
cnf(c_284059,plain,
( ~ subclass(unordered_pair(X0,X1),X2)
| ~ member(X0,universal_class)
| member(X0,X2) ),
inference(superposition,[status(thm)],[c_57,c_51]) ).
cnf(c_285126,plain,
( ~ member(X0,complement(unordered_pair(X1,X1)))
| ~ member(X0,sK6)
| ~ member(X1,sK6) ),
inference(superposition,[status(thm)],[c_71,c_1580]) ).
cnf(c_285154,plain,
( sK0(unordered_pair(X0,X1),X2) = X0
| sK0(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50,c_58]) ).
cnf(c_285406,plain,
( ~ member(X0,universal_class)
| ~ member(X0,sK6)
| ~ member(X1,sK6)
| member(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_74,c_285126]) ).
cnf(c_286222,plain,
( ~ member(X0,sK6)
| ~ member(X1,sK6)
| member(X0,unordered_pair(X1,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_285406,c_3587,c_181075]) ).
cnf(c_286230,plain,
( ~ member(sK0(X0,unordered_pair(X1,X1)),sK6)
| ~ member(X1,sK6)
| subclass(X0,unordered_pair(X1,X1)) ),
inference(superposition,[status(thm)],[c_286222,c_49]) ).
cnf(c_286233,plain,
( ~ member(X0,sK6)
| ~ member(X1,sK6)
| member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_286222,c_59]) ).
cnf(c_286648,plain,
( ~ member(X0,sK6)
| member(X0,universal_class) ),
inference(global_subsumption_just,[status(thm)],[c_286233,c_181075]) ).
cnf(c_286656,plain,
( null_class = sK6
| member(sK4(sK6),universal_class) ),
inference(superposition,[status(thm)],[c_124,c_286648]) ).
cnf(c_286671,plain,
member(sK4(sK6),universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_286656,c_1578]) ).
cnf(c_338278,plain,
( ~ member(X0,sK6)
| subclass(sK6,unordered_pair(X0,X0)) ),
inference(superposition,[status(thm)],[c_50,c_286230]) ).
cnf(c_394317,plain,
( ~ subclass(unordered_pair(X0,X0),sK6)
| ~ member(X0,sK6)
| unordered_pair(X0,X0) = sK6 ),
inference(superposition,[status(thm)],[c_338278,c_53]) ).
cnf(c_394318,plain,
( ~ subclass(unordered_pair(X0,X0),sK6)
| ~ member(X0,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_394317,c_1579]) ).
cnf(c_397264,plain,
( ~ member(X0,sK6)
| sK0(unordered_pair(X0,X0),sK6) = X0 ),
inference(superposition,[status(thm)],[c_285154,c_394318]) ).
cnf(c_400425,plain,
( sK0(unordered_pair(sK4(sK6),sK4(sK6)),sK6) = sK4(sK6)
| null_class = sK6 ),
inference(superposition,[status(thm)],[c_124,c_397264]) ).
cnf(c_400458,plain,
sK0(unordered_pair(sK4(sK6),sK4(sK6)),sK6) = sK4(sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_400425,c_1578]) ).
cnf(c_405820,plain,
( ~ member(sK4(sK6),sK6)
| subclass(unordered_pair(sK4(sK6),sK4(sK6)),sK6) ),
inference(superposition,[status(thm)],[c_400458,c_49]) ).
cnf(c_405863,plain,
subclass(unordered_pair(sK4(sK6),sK4(sK6)),sK6),
inference(global_subsumption_just,[status(thm)],[c_405820,c_6829,c_405820]) ).
cnf(c_405867,plain,
( ~ member(sK4(sK6),universal_class)
| member(sK4(sK6),sK6) ),
inference(superposition,[status(thm)],[c_405863,c_284059]) ).
cnf(c_405869,plain,
~ member(sK4(sK6),sK6),
inference(superposition,[status(thm)],[c_405863,c_394318]) ).
cnf(c_405871,plain,
~ member(sK4(sK6),universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_405867,c_405869]) ).
cnf(c_405872,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_405871,c_286671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET097+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.08/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 20:28:42 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 127.95/17.76 % SZS status Started for theBenchmark.p
% 127.95/17.76 % SZS status Theorem for theBenchmark.p
% 127.95/17.76
% 127.95/17.76 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 127.95/17.76
% 127.95/17.76 ------ iProver source info
% 127.95/17.76
% 127.95/17.76 git: date: 2024-05-02 19:28:25 +0000
% 127.95/17.76 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 127.95/17.76 git: non_committed_changes: false
% 127.95/17.76
% 127.95/17.76 ------ Parsing...
% 127.95/17.76 ------ Clausification by vclausify_rel & Parsing by iProver...
% 127.95/17.76
% 127.95/17.76 ------ 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
% 127.95/17.76
% 127.95/17.76 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 127.95/17.76
% 127.95/17.76 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 127.95/17.76 ------ Proving...
% 127.95/17.76 ------ Problem Properties
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76 clauses 77
% 127.95/17.76 conjectures 3
% 127.95/17.76 EPR 8
% 127.95/17.76 Horn 69
% 127.95/17.76 unary 16
% 127.95/17.76 binary 40
% 127.95/17.76 lits 160
% 127.95/17.76 lits eq 16
% 127.95/17.76 fd_pure 0
% 127.95/17.76 fd_pseudo 0
% 127.95/17.76 fd_cond 4
% 127.95/17.76 fd_pseudo_cond 3
% 127.95/17.76 AC symbols 0
% 127.95/17.76
% 127.95/17.76 ------ Schedule dynamic 5 is on
% 127.95/17.76
% 127.95/17.76 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76 ------
% 127.95/17.76 Current options:
% 127.95/17.76 ------
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76 ------ Proving...
% 127.95/17.76 Proof_search_loop: time out after: 7090 full_loop iterations
% 127.95/17.76
% 127.95/17.76 ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76 ------
% 127.95/17.76 Current options:
% 127.95/17.76 ------
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76 ------ Proving...
% 127.95/17.76
% 127.95/17.76
% 127.95/17.76 % SZS status Theorem for theBenchmark.p
% 127.95/17.76
% 127.95/17.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 127.95/17.76
% 127.95/17.77
%------------------------------------------------------------------------------