%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET098-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:46:35 PM UTC 2026
% Result : Unsatisfiable 32.97s 8.52s
% Output : CNFRefutation 32.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of formulae : 116 ( 44 unt; 0 def)
% Number of atoms : 203 ( 57 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 175 ( 88 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 157 ( 0 sgn 157 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f30,axiom,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).
fof(f63,axiom,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function1) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
fof(f102,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
fof(f103,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f102]) ).
fof(f104,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
fof(f105,plain,
null_class != x,
inference(reorient_equations,[],[f104]) ).
fof(f110,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f14,f110]) ).
fof(f122,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f123,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(f154,plain,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x),
inference(definition_unfolding,[],[f101,f12]) ).
fof(f155,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f103,f12]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_146,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_167,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,[],[f123]) ).
tcf(c_191,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_195,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_218,negated_conjecture,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x),
inference(cnf_transformation,[],[f154]) ).
tcf(c_219,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[],[f155]) ).
tcf(c_220,negated_conjecture,
x != null_class,
inference(cnf_transformation,[],[f105]) ).
tcf(c_3421,plain,
( member(regular(x),x)
| ( x = null_class ) ),
inference(instantiation,[status(thm)],[c_195]) ).
tcf(c_3495,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_144,c_162]) ).
tcf(c_3506,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_195,c_164]) ).
tcf(c_3507,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_3506]) ).
tcf(c_4222,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c_162,c_144]) ).
tcf(c_4251,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_3495,c_145]) ).
tcf(c_4267,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c_164,c_144]) ).
tcf(c_4277,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c_143,c_146]) ).
tcf(c_4323,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(resolution,[status(thm)],[c_4277,c_144]) ).
tcf(c_4550,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(resolution,[status(thm)],[c_4267,c_4323]) ).
tcf(c_4583,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(resolution,[status(thm)],[c_4550,c_143]) ).
tcf(c_4592,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(resolution,[status(thm)],[c_4583,c_195]) ).
tcf(c_4593,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_4592]) ).
tcf(c_4612,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4592,c_3507,c_4593]) ).
tcf(c_5236,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_144,c_164]) ).
tcf(c_5237,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_195,c_164]) ).
tcf(c_5256,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_153,c_143]) ).
tcf(c_5430,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X0)
| ~ subclass(universal_class,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_5256,c_154]) ).
tcf(c_5439,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_191,c_5430]) ).
tcf(c_5446,plain,
! [X0: $i] :
( subclass(complement(universal_class),X0)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_5439,c_5236]) ).
tcf(c_5447,plain,
( ( complement(universal_class) = null_class )
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_5439,c_5237]) ).
tcf(c_5448,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(global_subsumption_just,[status(thm)],[c_5446,c_4550]) ).
tcf(c_5451,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_5447,c_4612]) ).
tcf(c_5453,plain,
! [X0: $i] : subclass(null_class,X0),
inference(demodulation,[status(thm)],[c_5448,c_5451]) ).
tcf(c_5463,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_5453,c_149]) ).
tcf(c_5480,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,domain_of(X1))
| ( intersection(cross_product(unordered_pair(X0,X0),universal_class),X1) != null_class ) ),
inference(superposition,[status(thm)],[c_166,c_167]) ).
tcf(c_5507,plain,
! [X0: $i] : intersection(X0,null_class) = null_class,
inference(superposition,[status(thm)],[c_4251,c_5463]) ).
tcf(c_5550,plain,
! [X0: $i] : ~ member(X0,domain_of(null_class)),
inference(superposition,[status(thm)],[c_5507,c_5480]) ).
tcf(c_5555,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm)],[c_195,c_5550]) ).
tcf(c_5559,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(demodulation,[status(thm)],[c_5550,c_5555]) ).
tcf(c_5898,plain,
subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[c_4222,c_218]) ).
tcf(c_5949,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(resolution,[status(thm)],[c_5898,c_143]) ).
tcf(c_5958,plain,
! [X0: $i] : ~ member(X0,intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)),
inference(global_subsumption_just,[status(thm)],[c_5949,c_5559,c_5949]) ).
tcf(c_6060,plain,
! [X0: $i] :
( ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(resolution,[status(thm)],[c_163,c_5958]) ).
tcf(c_6237,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[c_6060,c_165]) ).
tcf(c_6322,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6237,c_4277]) ).
tcf(c_15162,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = null_class )
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_196,c_161]) ).
tcf(c_15182,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_15162,c_5559]) ).
tcf(c_15185,plain,
! [X0: $i] : subclass(null_class,X0),
inference(superposition,[status(thm)],[c_144,c_15182]) ).
tcf(c_15187,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_15185,c_149]) ).
tcf(c_15291,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X1),X2)
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X1 )
| ( not_subclass_element(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_144,c_150]) ).
tcf(c_15784,plain,
subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(superposition,[status(thm)],[c_3495,c_218]) ).
tcf(c_15789,plain,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(superposition,[status(thm)],[c_15784,c_15187]) ).
tcf(c_15799,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_15789,c_163]) ).
tcf(c_15803,plain,
! [X0: $i] :
( ~ member(X0,x)
| ~ member(X0,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15799,c_15182]) ).
tcf(c_15886,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_165,c_15803]) ).
tcf(c_15895,plain,
! [X0: $i] :
( member(X0,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(global_subsumption_just,[status(thm)],[c_15886,c_6322]) ).
tcf(c_15901,plain,
! [X0: $i] :
( ( not_subclass_element(x,null_class) = X0 )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_15895,c_150]) ).
tcf(c_15928,plain,
( ( x = null_class )
| ( not_subclass_element(x,null_class) = regular(x) ) ),
inference(superposition,[status(thm)],[c_195,c_15901]) ).
tcf(c_15936,plain,
not_subclass_element(x,null_class) = regular(x),
inference(forward_subsumption_resolution,[status(thm)],[c_15928,c_220]) ).
tcf(c_15942,plain,
! [X0: $i] :
( member(X0,unordered_pair(regular(x),regular(x)))
| ~ member(X0,x) ),
inference(demodulation,[status(thm)],[c_15895,c_15936]) ).
tcf(c_15945,plain,
unordered_pair(regular(x),regular(x)) != x,
inference(demodulation,[status(thm)],[c_219,c_15936]) ).
tcf(c_15947,plain,
( subclass(x,null_class)
| member(regular(x),x) ),
inference(superposition,[status(thm)],[c_15936,c_144]) ).
tcf(c_15949,plain,
member(regular(x),x),
inference(global_subsumption_just,[status(thm)],[c_15947,c_220,c_3421]) ).
tcf(c_15985,plain,
! [X0: $i] :
( subclass(X0,unordered_pair(regular(x),regular(x)))
| ~ member(not_subclass_element(X0,unordered_pair(regular(x),regular(x))),x) ),
inference(superposition,[status(thm)],[c_15942,c_145]) ).
tcf(c_16535,plain,
subclass(x,unordered_pair(regular(x),regular(x))),
inference(superposition,[status(thm)],[c_144,c_15985]) ).
tcf(c_16566,plain,
( ( unordered_pair(regular(x),regular(x)) = x )
| ~ subclass(unordered_pair(regular(x),regular(x)),x) ),
inference(superposition,[status(thm)],[c_16535,c_149]) ).
tcf(c_16568,plain,
~ subclass(unordered_pair(regular(x),regular(x)),x),
inference(forward_subsumption_resolution,[status(thm)],[c_16566,c_15945]) ).
tcf(c_16582,plain,
not_subclass_element(unordered_pair(regular(x),regular(x)),x) = regular(x),
inference(superposition,[status(thm)],[c_15291,c_16568]) ).
tcf(c_16614,plain,
( subclass(unordered_pair(regular(x),regular(x)),x)
| ~ member(regular(x),x) ),
inference(superposition,[status(thm)],[c_16582,c_145]) ).
tcf(c_16617,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16614,c_16568,c_15949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET098-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.43 % Computer : n026.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 09:49:54 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.23/0.51
% 0.23/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.51
% 0.23/0.51 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 32.97/8.52 % SZS status Started for theBenchmark.p
% 32.97/8.52 % SZS status Unsatisfiable for theBenchmark.p
% 32.97/8.52
% 32.97/8.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.97/8.52
% 32.97/8.52 % ------ iProver source info
% 32.97/8.52
% 32.97/8.52 % git: date: 2026-07-19 20:42:38 +0200
% 32.97/8.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.97/8.52 % git: non_committed_changes: false
% 32.97/8.52
% 32.97/8.52 % ------ Parsing...% successful
% 32.97/8.52
% 32.97/8.52
% 32.97/8.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.97/8.52
% 32.97/8.52 % ------ 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 %
% 32.97/8.52
% 32.97/8.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 32.97/8.52
% 32.97/8.52 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.97/8.52 % ------ Proving...
% 32.97/8.52 % ------ Problem Properties
% 32.97/8.52
% 32.97/8.52 %
% 32.97/8.52 % clauses 70
% 32.97/8.52 % conjectures 3
% 32.97/8.52 % EPR 13
% 32.97/8.52 % Horn 62
% 32.97/8.52 % unary 18
% 32.97/8.52 % binary 32
% 32.97/8.52 % lits 148
% 32.97/8.52 % lits eq 22
% 32.97/8.52 % fd_pure 0
% 32.97/8.52 % fd_pseudo 0
% 32.97/8.52 % fd_cond 3
% 32.97/8.52 % fd_pseudo_cond 3
% 32.97/8.52 % AC symbols 0
% 32.97/8.52
% 32.97/8.52 % ------ Input Options Time Limit: Unbounded
% 32.97/8.52
% 32.97/8.52
% 32.97/8.52 % ------
% 32.97/8.52 % Current options:
% 32.97/8.52 % ------
% 32.97/8.52
% 32.97/8.52
% 32.97/8.52 %
% 32.97/8.52
% 32.97/8.52 % ------ Proving...
% 32.97/8.52 %
% 32.97/8.52
% 32.97/8.52 % SZS status Unsatisfiable for theBenchmark.p
% 32.97/8.52
% 32.97/8.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.97/8.53
% 32.97/8.53
%------------------------------------------------------------------------------