%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET288-6 : 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 : n008.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 02:47:04 PM UTC 2026
% Result : Unsatisfiable 145.94s 33.83s
% Output : CNFRefutation 145.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 104 ( 27 unt; 0 def)
% Number of atoms : 205 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 192 ( 91 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 147 ( 0 sgn 147 !; 0 ?; 84 :)
% 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(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
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(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
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(f31,axiom,
! [X0,X1] :
( member(X0,domain_of(X1))
| restrict(X1,singleton(X0),universal_class) = null_class
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain2) ).
fof(f32,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| null_class = restrict(X1,singleton(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(reorient_equations,[],[f31]) ).
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(f122,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property9_1) ).
fof(f123,negated_conjecture,
domain_of(intersection(complement(y),x)) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property9_2) ).
fof(f124,plain,
null_class = domain_of(intersection(complement(y),x)),
inference(reorient_equations,[],[f123]) ).
fof(f125,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_property9_3) ).
fof(f130,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(f139,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,f130]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f130]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f130]) ).
fof(f142,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f130]) ).
fof(f147,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f32,f28,f12]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_167,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_175,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,[],[f139]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( member(X0,domain_of(X1))
| ( intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_216,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_257,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_258,negated_conjecture,
domain_of(intersection(complement(y),x)) = null_class,
inference(cnf_transformation,[],[f124]) ).
tcf(c_259,negated_conjecture,
~ subclass(x,y),
inference(cnf_transformation,[],[f125]) ).
tcf(c_3850,plain,
( subclass(x,y)
| member(not_subclass_element(x,y),x) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_3892,plain,
! [X0: $i] :
( member(not_subclass_element(x,y),X0)
| ~ subclass(x,X0)
| ~ member(not_subclass_element(x,y),x) ),
inference(instantiation,[status(thm)],[c_164]) ).
tcf(c_3893,plain,
( member(not_subclass_element(x,y),universal_class)
| ~ subclass(x,universal_class)
| ~ member(not_subclass_element(x,y),x) ),
inference(instantiation,[status(thm)],[c_3892]) ).
tcf(c_3896,plain,
! [X0: $i] :
( member(not_subclass_element(x,y),intersection(X0,x))
| ~ member(not_subclass_element(x,y),x)
| ~ member(not_subclass_element(x,y),X0) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_3944,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_165,c_185]) ).
tcf(c_3945,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_216,c_185]) ).
tcf(c_3946,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_3945]) ).
tcf(c_4018,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_167,c_164]) ).
tcf(c_4143,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_165,c_4018]) ).
tcf(c_4361,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_4143,c_3944]) ).
tcf(c_4383,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_4361,c_164]) ).
tcf(c_4441,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(superposition,[status(thm)],[c_216,c_4383]) ).
tcf(c_4442,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_4441]) ).
tcf(c_4520,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4441,c_3946,c_4442]) ).
tcf(c_4544,plain,
! [X0: $i] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_4520,c_185]) ).
tcf(c_5127,plain,
subclass(x,universal_class),
inference(instantiation,[status(thm)],[c_167]) ).
tcf(c_6066,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_165,c_185]) ).
tcf(c_6080,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_167,c_164]) ).
tcf(c_6135,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_165,c_6080]) ).
tcf(c_6268,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_6135,c_6066]) ).
tcf(c_6279,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_6268,c_164]) ).
tcf(c_6292,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_4441,c_4520]) ).
tcf(c_6294,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(demodulation,[status(thm)],[c_6279,c_6292]) ).
tcf(c_6304,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_6294,c_4018,c_4544,c_6294]) ).
tcf(c_9106,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(X0,X1),X1)
| member(not_subclass_element(X0,X1),complement(X1))
| ~ member(not_subclass_element(X0,X1),universal_class) ),
inference(instantiation,[status(thm)],[c_186]) ).
tcf(c_9964,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_257,c_164]) ).
tcf(c_10210,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x) ),
inference(superposition,[status(thm)],[c_9964,c_175]) ).
tcf(c_10216,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x) ),
inference(superposition,[status(thm)],[c_9964,c_176]) ).
tcf(c_10381,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_9964,c_178]) ).
tcf(c_10415,plain,
! [X0: $i] :
( subclass(x,X0)
| ( unordered_pair(unordered_pair(first(not_subclass_element(x,X0)),first(not_subclass_element(x,X0))),unordered_pair(first(not_subclass_element(x,X0)),unordered_pair(second(not_subclass_element(x,X0)),second(not_subclass_element(x,X0))))) = not_subclass_element(x,X0) ) ),
inference(superposition,[status(thm)],[c_165,c_10381]) ).
tcf(c_12189,plain,
unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))) = not_subclass_element(x,y),
inference(superposition,[status(thm)],[c_10415,c_259]) ).
tcf(c_12228,plain,
( member(second(not_subclass_element(x,y)),universal_class)
| ~ member(not_subclass_element(x,y),x) ),
inference(superposition,[status(thm)],[c_12189,c_10216]) ).
tcf(c_12229,plain,
( member(first(not_subclass_element(x,y)),universal_class)
| ~ member(not_subclass_element(x,y),x) ),
inference(superposition,[status(thm)],[c_12189,c_10210]) ).
tcf(c_18688,plain,
! [X0: $i] :
( member(not_subclass_element(x,y),intersection(complement(X0),x))
| ~ member(not_subclass_element(x,y),x)
| ~ member(not_subclass_element(x,y),complement(X0)) ),
inference(instantiation,[status(thm)],[c_3896]) ).
tcf(c_24503,plain,
( subclass(x,y)
| ~ member(not_subclass_element(x,y),y) ),
inference(instantiation,[status(thm)],[c_166]) ).
tcf(c_28029,plain,
( member(not_subclass_element(x,y),y)
| member(not_subclass_element(x,y),complement(y))
| ~ member(not_subclass_element(x,y),universal_class) ),
inference(instantiation,[status(thm)],[c_9106]) ).
tcf(c_30461,plain,
( member(not_subclass_element(x,y),intersection(complement(y),x))
| ~ member(not_subclass_element(x,y),x)
| ~ member(not_subclass_element(x,y),complement(y)) ),
inference(instantiation,[status(thm)],[c_18688]) ).
tcf(c_197561,plain,
! [X0: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_257,c_164]) ).
tcf(c_197809,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x) ),
inference(superposition,[status(thm)],[c_197561,c_175]) ).
tcf(c_197843,plain,
! [X0: $i,X1: $i] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x) ),
inference(superposition,[status(thm)],[c_197561,c_176]) ).
tcf(c_197860,plain,
! [X0: $i] :
( member(X0,null_class)
| ( intersection(intersection(complement(y),x),cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_258,c_189]) ).
tcf(c_197866,plain,
! [X0: $i] :
( ( intersection(intersection(complement(y),x),cross_product(unordered_pair(X0,X0),universal_class)) = null_class )
| ~ member(X0,universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197860,c_6304]) ).
tcf(c_198067,plain,
! [X0: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_197561,c_178]) ).
tcf(c_198080,plain,
! [X0: $i] :
( subclass(x,X0)
| ( unordered_pair(unordered_pair(first(not_subclass_element(x,X0)),first(not_subclass_element(x,X0))),unordered_pair(first(not_subclass_element(x,X0)),unordered_pair(second(not_subclass_element(x,X0)),second(not_subclass_element(x,X0))))) = not_subclass_element(x,X0) ) ),
inference(superposition,[status(thm)],[c_165,c_198067]) ).
tcf(c_198681,plain,
unordered_pair(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),unordered_pair(first(not_subclass_element(x,y)),unordered_pair(second(not_subclass_element(x,y)),second(not_subclass_element(x,y))))) = not_subclass_element(x,y),
inference(superposition,[status(thm)],[c_198080,c_259]) ).
tcf(c_198702,plain,
( member(second(not_subclass_element(x,y)),universal_class)
| ~ member(not_subclass_element(x,y),x) ),
inference(superposition,[status(thm)],[c_198681,c_197843]) ).
tcf(c_198705,plain,
( member(first(not_subclass_element(x,y)),universal_class)
| ~ member(not_subclass_element(x,y),x) ),
inference(superposition,[status(thm)],[c_198681,c_197809]) ).
tcf(c_198708,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(x,y),cross_product(X0,X1))
| ~ member(second(not_subclass_element(x,y)),X1)
| ~ member(first(not_subclass_element(x,y)),X0) ),
inference(superposition,[status(thm)],[c_198681,c_177]) ).
tcf(c_198723,plain,
member(second(not_subclass_element(x,y)),universal_class),
inference(global_subsumption_just,[status(thm)],[c_198702,c_259,c_3850,c_12228]) ).
tcf(c_198728,plain,
member(first(not_subclass_element(x,y)),universal_class),
inference(global_subsumption_just,[status(thm)],[c_198705,c_259,c_3850,c_12229]) ).
tcf(c_198731,plain,
intersection(intersection(complement(y),x),cross_product(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),universal_class)) = null_class,
inference(superposition,[status(thm)],[c_198728,c_197866]) ).
tcf(c_199501,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,intersection(complement(y),x))
| ~ member(X0,cross_product(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),universal_class)) ),
inference(superposition,[status(thm)],[c_198731,c_184]) ).
tcf(c_199509,plain,
! [X0: $i] :
( ~ member(X0,intersection(complement(y),x))
| ~ member(X0,cross_product(unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y))),universal_class)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_199501,c_6304]) ).
tcf(c_199657,plain,
( ~ member(second(not_subclass_element(x,y)),universal_class)
| ~ member(not_subclass_element(x,y),intersection(complement(y),x))
| ~ member(first(not_subclass_element(x,y)),unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y)))) ),
inference(superposition,[status(thm)],[c_198708,c_199509]) ).
tcf(c_199660,plain,
( ~ member(not_subclass_element(x,y),intersection(complement(y),x))
| ~ member(first(not_subclass_element(x,y)),unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_199657,c_198723]) ).
tcf(c_199787,plain,
~ member(first(not_subclass_element(x,y)),unordered_pair(first(not_subclass_element(x,y)),first(not_subclass_element(x,y)))),
inference(global_subsumption_just,[status(thm)],[c_199660,c_259,c_3850,c_3893,c_5127,c_24503,c_28029,c_30461,c_199660]) ).
tcf(c_199789,plain,
~ member(first(not_subclass_element(x,y)),universal_class),
inference(superposition,[status(thm)],[c_172,c_199787]) ).
tcf(c_199791,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_199789,c_198728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET288-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.58 % Computer : n008.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Thu Sep 24 10:30:07 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.62 Running first-order theorem proving
% 0.15/10.63 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
% 0.15/10.64
% 0.15/10.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.64
% 0.15/10.64 % Detected problem language: tptp
% 0.15/10.65 % Proving...
% 145.94/33.83 % SZS status Started for theBenchmark.p
% 145.94/33.83 % SZS status Unsatisfiable for theBenchmark.p
% 145.94/33.83
% 145.94/33.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 145.94/33.83
% 145.94/33.83 % ------ iProver source info
% 145.94/33.83
% 145.94/33.83 % git: date: 2026-07-19 20:42:38 +0200
% 145.94/33.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 145.94/33.83 % git: non_committed_changes: false
% 145.94/33.83
% 145.94/33.83 % ------ Parsing...% successful
% 145.94/33.83
% 145.94/33.83
% 145.94/33.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 145.94/33.83
% 145.94/33.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 145.94/33.83
% 145.94/33.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 145.94/33.83
% 145.94/33.83 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 145.94/33.83 % ------ Proving...
% 145.94/33.83 % ------ Problem Properties
% 145.94/33.83
% 145.94/33.83 %
% 145.94/33.83 % clauses 84
% 145.94/33.83 % conjectures 3
% 145.94/33.83 % EPR 13
% 145.94/33.83 % Horn 76
% 145.94/33.83 % unary 23
% 145.94/33.83 % binary 40
% 145.94/33.83 % lits 172
% 145.94/33.83 % lits eq 26
% 145.94/33.83 % fd_pure 0
% 145.94/33.83 % fd_pseudo 0
% 145.94/33.83 % fd_cond 3
% 145.94/33.83 % fd_pseudo_cond 7
% 145.94/33.83 % AC symbols 0
% 145.94/33.83
% 145.94/33.83 % ------ Input Options Time Limit: Unbounded
% 145.94/33.83
% 145.94/33.83
% 145.94/33.83 % ------
% 145.94/33.83 % Current options:
% 145.94/33.83 % ------
% 145.94/33.83
% 145.94/33.83
% 145.94/33.83 %
% 145.94/33.83
% 145.94/33.83 % ------ Proving...
% 145.94/33.83 %
% 145.94/33.83
% 145.94/33.83 % SZS status Unsatisfiable for theBenchmark.p
% 145.94/33.83
% 145.94/33.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 145.94/33.83
% 145.94/33.83
%------------------------------------------------------------------------------