%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET069-6 : 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 : n005.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 : Unsatisfiable 15.98s 4.88s
% Output : CNFRefutation 15.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 29
% Syntax : Number of formulae : 162 ( 50 unt; 2 def)
% Number of atoms : 596 ( 150 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 286 ( 102 ~; 184 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 153 ( 0 sgn 153 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(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(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(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f30,axiom,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',image) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',sum_class_definition) ).
fof(f55,axiom,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',sum_class2) ).
fof(f66,axiom,
! [X0,X1] :
( member(image(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ function(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',replacement) ).
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(f71,axiom,
! [X0,X1] : sum_class(image(X0,singleton(X1))) = apply(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',apply) ).
fof(f72,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',choice1) ).
fof(f73,axiom,
! [X0] :
( member(apply(choice,X0),X0)
| X0 = null_class
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',choice2) ).
fof(f74,plain,
! [X0] :
( member(apply(choice,X0),X0)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(reorient_equations,[],[f73]) ).
fof(f101,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unordered_pair_equals_singleton1_1) ).
fof(f102,negated_conjecture,
unordered_pair(x,y) != singleton(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unordered_pair_equals_singleton1_2) ).
fof(f103,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f104,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f105,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f104,f28]) ).
fof(f106,plain,
! [X0,X1] : apply(X0,X1) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f71,f103,f105,f12]) ).
fof(f120,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f130,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f55,f103]) ).
fof(f138,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),universal_class)
| ~ member(X1,universal_class)
| ~ function(X0) ),
inference(definition_unfolding,[],[f66,f105]) ).
fof(f139,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X0)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f74,f106]) ).
fof(f151,plain,
unordered_pair(x,y) != unordered_pair(x,x),
inference(definition_unfolding,[],[f102,f12]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_145,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_161,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] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != null_class ) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_183,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_194,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_195,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_196,plain,
function(choice),
inference(cnf_transformation,[],[f72]) ).
tcf(c_197,plain,
! [X0: $i] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X0)
| ( X0 = null_class )
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_217,negated_conjecture,
~ member(y,universal_class),
inference(cnf_transformation,[],[f101]) ).
tcf(c_218,negated_conjecture,
unordered_pair(x,y) != unordered_pair(x,x),
inference(cnf_transformation,[],[f151]) ).
tcf(c_2644,definition,
iPr_def_10 = unordered_pair(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2645,definition,
iPr_def_11 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2646,negated_conjecture,
iPr_def_10 != iPr_def_11,
inference(demodulation,[status(thm)],[c_218,c_2645,c_2644]) ).
tcf(c_2647,negated_conjecture,
~ member(y,universal_class),
inference(demodulation,[status(thm)],[c_217]) ).
tcf(c_3400,plain,
member(iPr_def_10,universal_class),
inference(superposition,[status(thm)],[c_2644,c_152]) ).
tcf(c_3437,plain,
( member(x,iPr_def_10)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_2644,c_150]) ).
tcf(c_3438,plain,
( member(x,iPr_def_11)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm)],[c_2645,c_150]) ).
tcf(c_3453,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_143,c_160]) ).
tcf(c_4091,plain,
! [X0: $i] :
( ( X0 = x )
| ( X0 = y )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2644,c_149]) ).
tcf(c_7104,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_3453,c_144]) ).
tcf(c_7267,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_195,c_7104]) ).
tcf(c_7400,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_7267,c_148]) ).
tcf(c_7477,plain,
! [X0: $i] : intersection(null_class,X0) = null_class,
inference(superposition,[status(thm)],[c_7104,c_7400]) ).
tcf(c_7504,plain,
! [X0: $i] : ~ member(X0,domain_of(null_class)),
inference(superposition,[status(thm)],[c_7477,c_166]) ).
tcf(c_7629,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm)],[c_194,c_7504]) ).
tcf(c_7646,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(demodulation,[status(thm)],[c_7504,c_7629]) ).
tcf(c_8823,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = y )
| ~ member(iPr_def_10,universal_class) ),
inference(superposition,[status(thm)],[c_197,c_4091]) ).
tcf(c_8883,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = y ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8823,c_3400]) ).
tcf(c_32796,plain,
( member(y,universal_class)
| ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))),universal_class) ),
inference(superposition,[status(thm)],[c_8883,c_183]) ).
tcf(c_32802,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class)))),universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32796,c_2647]) ).
tcf(c_34147,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ~ function(choice)
| ~ member(unordered_pair(iPr_def_10,iPr_def_10),universal_class) ),
inference(superposition,[status(thm)],[c_193,c_32802]) ).
tcf(c_34148,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34147,c_196,c_152]) ).
tcf(c_37659,plain,
member(iPr_def_10,universal_class),
inference(superposition,[status(thm)],[c_2644,c_152]) ).
tcf(c_37740,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_143,c_160]) ).
tcf(c_37750,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_143,c_161]) ).
tcf(c_37797,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,X2)
| member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_143,c_142]) ).
tcf(c_37798,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,universal_class)
| ~ subclass(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_150,c_142]) ).
tcf(c_37802,plain,
! [X0: $i,X1: $i] :
( member(regular(X0),X1)
| ( X0 = null_class )
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_194,c_142]) ).
tcf(c_37857,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = null_class )
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_195,c_160]) ).
tcf(c_37896,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_37857,c_7646]) ).
tcf(c_37898,plain,
! [X0: $i] : subclass(null_class,X0),
inference(superposition,[status(thm)],[c_143,c_37896]) ).
tcf(c_38136,plain,
! [X0: $i] :
( ( X0 = x )
| ( X0 = y )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2644,c_149]) ).
tcf(c_38137,plain,
! [X0: $i] :
( ( X0 = x )
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2645,c_149]) ).
tcf(c_38171,plain,
! [X0: $i] :
( ~ member(x,domain_of(X0))
| ( intersection(X0,cross_product(iPr_def_11,universal_class)) != null_class ) ),
inference(superposition,[status(thm)],[c_2645,c_166]) ).
tcf(c_38190,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| ( not_subclass_element(iPr_def_11,X0) = x ) ),
inference(superposition,[status(thm)],[c_143,c_38137]) ).
tcf(c_38191,plain,
( ( null_class = iPr_def_11 )
| ( regular(iPr_def_11) = x ) ),
inference(superposition,[status(thm)],[c_194,c_38137]) ).
tcf(c_38203,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( not_subclass_element(iPr_def_11,X0) = x )
| ~ subclass(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_38190,c_148]) ).
tcf(c_38215,plain,
( member(x,iPr_def_11)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_38191,c_194]) ).
tcf(c_38224,plain,
! [X0: $i] :
( member(x,X0)
| ( null_class = iPr_def_11 )
| ~ subclass(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_38215,c_142]) ).
tcf(c_38747,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,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_197,c_149]) ).
tcf(c_38777,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38747,c_152]) ).
tcf(c_38860,plain,
( member(x,universal_class)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_145,c_38224]) ).
tcf(c_38954,plain,
( ( unordered_pair(x,y) = null_class )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(x,y),unordered_pair(x,y)),universal_class)),universal_class))))))) = y ) ),
inference(superposition,[status(thm)],[c_2644,c_38777]) ).
tcf(c_38990,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = y ) ),
inference(light_normalisation,[status(thm)],[c_38954,c_2644]) ).
tcf(c_39322,plain,
( ( null_class = iPr_def_10 )
| ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(iPr_def_10,iPr_def_10),universal_class)),universal_class))))))) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_38990,c_34148]) ).
tcf(c_39335,plain,
( member(x,iPr_def_10)
| ( null_class = iPr_def_10 )
| ~ member(iPr_def_10,universal_class) ),
inference(superposition,[status(thm)],[c_39322,c_197]) ).
tcf(c_39336,plain,
( member(x,iPr_def_10)
| ( null_class = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39335,c_37659]) ).
tcf(c_39923,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ),
inference(superposition,[status(thm)],[c_37740,c_163]) ).
tcf(c_40541,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_37797,c_37896]) ).
tcf(c_40615,plain,
! [X0: $i,X1: $i] :
( ( X0 = null_class )
| ~ subclass(X0,complement(X1))
| ~ member(regular(X0),X1) ),
inference(superposition,[status(thm)],[c_37802,c_163]) ).
tcf(c_40797,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| ( not_subclass_element(iPr_def_11,null_class) = x ) ),
inference(superposition,[status(thm)],[c_38190,c_40541]) ).
tcf(c_40921,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( not_subclass_element(iPr_def_11,null_class) = x )
| ~ subclass(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_40797,c_148]) ).
tcf(c_41135,plain,
! [X0: $i] :
( subclass(iPr_def_10,X0)
| ( not_subclass_element(iPr_def_10,X0) = x )
| ( not_subclass_element(iPr_def_10,X0) = y ) ),
inference(superposition,[status(thm)],[c_143,c_38136]) ).
tcf(c_42247,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,complement(X0)) ),
inference(superposition,[status(thm)],[c_194,c_40615]) ).
tcf(c_54016,plain,
subclass(iPr_def_11,universal_class),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_57469,plain,
subclass(iPr_def_10,universal_class),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_57727,plain,
! [X0: $i] :
( member(x,X0)
| ~ member(x,universal_class)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_2644,c_37798]) ).
tcf(c_66799,plain,
! [X0: $i,X1: $i] : subclass(intersection(complement(X0),X0),X1),
inference(superposition,[status(thm)],[c_37750,c_39923]) ).
tcf(c_68067,plain,
! [X0: $i] : intersection(complement(X0),X0) = null_class,
inference(superposition,[status(thm)],[c_66799,c_42247]) ).
tcf(c_68391,plain,
~ member(x,domain_of(complement(cross_product(iPr_def_11,universal_class)))),
inference(superposition,[status(thm)],[c_68067,c_38171]) ).
tcf(c_73293,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( not_subclass_element(iPr_def_11,iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y ) ),
inference(superposition,[status(thm)],[c_41135,c_38203]) ).
tcf(c_73345,plain,
( ( not_subclass_element(iPr_def_11,iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_73293,c_2646]) ).
tcf(c_75083,plain,
( subclass(iPr_def_11,iPr_def_10)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y )
| ~ member(x,iPr_def_10) ),
inference(superposition,[status(thm)],[c_73345,c_144]) ).
tcf(c_75084,plain,
( subclass(iPr_def_11,iPr_def_10)
| member(x,iPr_def_11)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y ) ),
inference(superposition,[status(thm)],[c_73345,c_143]) ).
tcf(c_75085,plain,
! [X0: $i] :
( subclass(iPr_def_11,iPr_def_10)
| member(x,X0)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y )
| ~ subclass(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_73345,c_37797]) ).
tcf(c_75104,plain,
( subclass(iPr_def_11,iPr_def_10)
| member(x,universal_class)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y )
| ~ subclass(iPr_def_11,universal_class) ),
inference(instantiation,[status(thm)],[c_75085]) ).
tcf(c_75639,plain,
( subclass(iPr_def_11,iPr_def_10)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_75084,c_3437,c_54016,c_75083,c_75104]) ).
tcf(c_75640,plain,
( subclass(iPr_def_11,iPr_def_10)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y ) ),
inference(renaming,[status(thm)],[c_75639]) ).
tcf(c_75648,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y )
| ~ subclass(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_75640,c_148]) ).
tcf(c_75651,plain,
( ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y )
| ~ subclass(iPr_def_10,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75648,c_2646]) ).
tcf(c_76080,plain,
( ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = y ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75651,c_41135]) ).
tcf(c_76089,plain,
( subclass(iPr_def_10,iPr_def_11)
| member(y,iPr_def_10)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(superposition,[status(thm)],[c_76080,c_143]) ).
tcf(c_76090,plain,
! [X0: $i] :
( subclass(iPr_def_10,iPr_def_11)
| member(y,X0)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_76080,c_37797]) ).
tcf(c_76105,plain,
( subclass(iPr_def_10,iPr_def_11)
| member(y,universal_class)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ subclass(iPr_def_10,universal_class) ),
inference(instantiation,[status(thm)],[c_76090]) ).
tcf(c_76330,plain,
( subclass(iPr_def_10,iPr_def_11)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(global_subsumption_just,[status(thm)],[c_76089,c_217,c_57469,c_76105]) ).
tcf(c_76337,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ subclass(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_76330,c_148]) ).
tcf(c_76338,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( not_subclass_element(iPr_def_11,null_class) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(superposition,[status(thm)],[c_76330,c_40921]) ).
tcf(c_76341,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( not_subclass_element(iPr_def_11,iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(superposition,[status(thm)],[c_76330,c_38203]) ).
tcf(c_76344,plain,
( ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ subclass(iPr_def_11,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_76337,c_2646]) ).
tcf(c_76356,plain,
( ( not_subclass_element(iPr_def_11,iPr_def_10) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_76341,c_2646]) ).
tcf(c_76359,plain,
( ( not_subclass_element(iPr_def_11,null_class) = x )
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_76338,c_2646]) ).
tcf(c_82420,plain,
( subclass(iPr_def_11,iPr_def_10)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ member(x,iPr_def_10) ),
inference(superposition,[status(thm)],[c_76356,c_144]) ).
tcf(c_82422,plain,
! [X0: $i] :
( subclass(iPr_def_11,iPr_def_10)
| member(x,X0)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ subclass(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_76356,c_37797]) ).
tcf(c_82437,plain,
( subclass(iPr_def_11,iPr_def_10)
| member(x,universal_class)
| ( not_subclass_element(iPr_def_10,iPr_def_11) = x )
| ~ subclass(iPr_def_11,universal_class) ),
inference(instantiation,[status(thm)],[c_82422]) ).
tcf(c_82443,plain,
not_subclass_element(iPr_def_10,iPr_def_11) = x,
inference(global_subsumption_just,[status(thm)],[c_76359,c_3437,c_54016,c_76344,c_82420,c_82437]) ).
tcf(c_82448,plain,
( subclass(iPr_def_10,iPr_def_11)
| ~ member(x,iPr_def_11) ),
inference(superposition,[status(thm)],[c_82443,c_144]) ).
tcf(c_82449,plain,
( subclass(iPr_def_10,iPr_def_11)
| member(x,iPr_def_10) ),
inference(superposition,[status(thm)],[c_82443,c_143]) ).
tcf(c_82450,plain,
! [X0: $i] :
( subclass(iPr_def_10,iPr_def_11)
| member(x,X0)
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_82443,c_37797]) ).
tcf(c_82461,plain,
( subclass(iPr_def_10,iPr_def_11)
| member(x,universal_class)
| ~ subclass(iPr_def_10,universal_class) ),
inference(instantiation,[status(thm)],[c_82450]) ).
tcf(c_82463,plain,
subclass(iPr_def_10,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_82449,c_3438,c_57469,c_82448,c_82461]) ).
tcf(c_82466,plain,
( ( iPr_def_10 = iPr_def_11 )
| ~ subclass(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_82463,c_148]) ).
tcf(c_82470,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( not_subclass_element(iPr_def_11,iPr_def_10) = x ) ),
inference(superposition,[status(thm)],[c_82463,c_38203]) ).
tcf(c_82473,plain,
~ subclass(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_82466,c_2646]) ).
tcf(c_82478,plain,
not_subclass_element(iPr_def_11,iPr_def_10) = x,
inference(forward_subsumption_resolution,[status(thm)],[c_82470,c_2646]) ).
tcf(c_82483,plain,
( subclass(iPr_def_11,iPr_def_10)
| ~ member(x,iPr_def_10) ),
inference(superposition,[status(thm)],[c_82478,c_144]) ).
tcf(c_82487,plain,
~ member(x,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_82483,c_82473]) ).
tcf(c_82494,plain,
null_class = iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_39336,c_82487]) ).
tcf(c_82597,plain,
( member(x,universal_class)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_38860,c_82494]) ).
tcf(c_82613,plain,
! [X0: $i] : subclass(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_37898,c_82494]) ).
tcf(c_82626,plain,
! [X0: $i] :
( member(x,X0)
| ~ member(x,universal_class) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57727,c_82613]) ).
tcf(c_82655,plain,
member(x,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[c_82597,c_2646]) ).
tcf(c_82656,plain,
! [X0: $i] : member(x,X0),
inference(backward_subsumption_resolution,[status(thm)],[c_82626,c_82655]) ).
tcf(c_82659,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_68391,c_82656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET069-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.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 09:33:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 15.98/4.88 % SZS status Started for theBenchmark.p
% 15.98/4.88 % SZS status Unsatisfiable for theBenchmark.p
% 15.98/4.88
% 15.98/4.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.98/4.88
% 15.98/4.88 % ------ iProver source info
% 15.98/4.88
% 15.98/4.88 % git: date: 2026-07-19 20:42:38 +0200
% 15.98/4.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.98/4.88 % git: non_committed_changes: false
% 15.98/4.88
% 15.98/4.88 % ------ Parsing...% successful
% 15.98/4.88
% 15.98/4.88
% 15.98/4.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.98/4.88
% 15.98/4.88 % ------ 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 %
% 15.98/4.88
% 15.98/4.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.98/4.88
% 15.98/4.88 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.98/4.88 % ------ Proving...
% 15.98/4.88 % ------ Problem Properties
% 15.98/4.88
% 15.98/4.88 %
% 15.98/4.88 % clauses 71
% 15.98/4.88 % conjectures 2
% 15.98/4.88 % EPR 14
% 15.98/4.88 % Horn 63
% 15.98/4.88 % unary 19
% 15.98/4.88 % binary 32
% 15.98/4.88 % lits 149
% 15.98/4.88 % lits eq 23
% 15.98/4.88 % fd_pure 0
% 15.98/4.88 % fd_pseudo 0
% 15.98/4.88 % fd_cond 3
% 15.98/4.88 % fd_pseudo_cond 3
% 15.98/4.88 % AC symbols 0
% 15.98/4.88
% 15.98/4.88 % ------ Schedule dynamic 5 is on
% 15.98/4.88
% 15.98/4.88 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.98/4.88
% 15.98/4.88
% 15.98/4.88 % ------
% 15.98/4.88 % Current options:
% 15.98/4.88 % ------
% 15.98/4.88
% 15.98/4.88
% 15.98/4.88 %
% 15.98/4.88
% 15.98/4.88 % ------ Proving...
% 15.98/4.88 %
% 15.98/4.88
% 15.98/4.88 % SZS status Unsatisfiable for theBenchmark.p
% 15.98/4.88
% 15.98/4.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.98/4.89
% 15.98/4.89
%------------------------------------------------------------------------------