%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM095-1 : 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 : n013.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 02:23:21 PM UTC 2026
% Result : Unsatisfiable 125.43s 19.71s
% Output : CNFRefutation 125.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 150 ( 37 unt; 0 def)
% Number of atoms : 338 ( 78 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 346 ( 158 ~; 188 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 217 ( 0 sgn 217 !; 0 ?; 159 :)
% 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(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(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f63,axiom,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',function1) ).
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(f135,axiom,
! [X2,X0,X1] :
( member(least(X0,X2),X2)
| X2 = null_class
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering2) ).
fof(f136,plain,
! [X2,X0,X1] :
( member(least(X0,X2),X2)
| null_class = X2
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
inference(reorient_equations,[],[f135]) ).
fof(f137,axiom,
! [X2,X3,X0,X1] :
( member(least(X0,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).
fof(f146,axiom,
! [X2,X0,X1] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',section1) ).
fof(f174,axiom,
! [X0] :
( integer_of(X0) = null_class
| member(X0,omega) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',integer_function2) ).
fof(f175,plain,
! [X0] :
( null_class = integer_of(X0)
| member(X0,omega) ),
inference(reorient_equations,[],[f174]) ).
fof(f176,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sections_property4_1) ).
fof(f177,negated_conjecture,
section(xr,w,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sections_property4_2) ).
fof(f178,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sections_property4_3) ).
fof(f179,negated_conjecture,
y != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sections_property4_4) ).
fof(f180,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(f198,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,f180]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_214,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_223,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,[],[f198]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_259,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_263,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_264,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(least(X0,X2),X2)
| ( X2 = null_class )
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(least(X0,X3),X3)
| ~ subclass(X3,X1)
| ~ member(X2,X3)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_345,plain,
! [X0: $i] :
( member(X0,omega)
| ( integer_of(X0) = null_class ) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_346,negated_conjecture,
well_ordering(xr,y),
inference(cnf_transformation,[],[f176]) ).
tcf(c_347,negated_conjecture,
section(xr,w,y),
inference(cnf_transformation,[],[f177]) ).
tcf(c_348,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
inference(cnf_transformation,[],[f178]) ).
tcf(c_349,negated_conjecture,
y != w,
inference(cnf_transformation,[],[f179]) ).
tcf(c_484,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_320]) ).
tcf(c_2134,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X2,X1)
| ( X2 != w )
| ( X1 != y )
| ( X0 != xr ) ),
inference(resolution_lifted,[status(thm)],[c_347,c_484]) ).
tcf(c_2135,plain,
subclass(w,y),
inference(unflattening,[status(thm)],[c_2134]) ).
tcf(c_2644,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(least(X0,X2),X2)
| ( X2 = null_class )
| ~ subclass(X2,X1)
| ( X1 != y )
| ( X0 != xr ) ),
inference(resolution_lifted,[status(thm)],[c_346,c_313]) ).
tcf(c_2645,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ( X0 = null_class )
| ~ subclass(X0,y) ),
inference(unflattening,[status(thm)],[c_2644]) ).
tcf(c_4851,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_4853,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,X2)
| ~ subclass(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6075,plain,
( ( y = w )
| ~ subclass(w,y)
| ~ subclass(y,w) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_6134,plain,
( subclass(y,w)
| ~ member(not_subclass_element(y,w),w) ),
inference(instantiation,[status(thm)],[c_213]) ).
tcf(c_6135,plain,
( subclass(y,w)
| member(not_subclass_element(y,w),y) ),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_6149,plain,
y = y,
inference(instantiation,[status(thm)],[c_4851]) ).
tcf(c_6159,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,y)
| ~ subclass(X1,X2)
| ( y != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_4859]) ).
tcf(c_6305,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_263,c_232]) ).
tcf(c_6308,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_6305]) ).
tcf(c_7541,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c_232,c_212]) ).
tcf(c_7717,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c_211,c_214]) ).
tcf(c_7951,plain,
! [X0: $i] :
( member(not_subclass_element(y,w),X0)
| ~ subclass(y,X0)
| ~ member(not_subclass_element(y,w),y) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_7952,plain,
( member(not_subclass_element(y,w),universal_class)
| ~ subclass(y,universal_class)
| ~ member(not_subclass_element(y,w),y) ),
inference(instantiation,[status(thm)],[c_7951]) ).
tcf(c_8001,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(resolution,[status(thm)],[c_7717,c_212]) ).
tcf(c_8273,plain,
subclass(y,universal_class),
inference(instantiation,[status(thm)],[c_214]) ).
tcf(c_8490,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(resolution,[status(thm)],[c_7541,c_8001]) ).
tcf(c_8519,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(resolution,[status(thm)],[c_8490,c_211]) ).
tcf(c_8527,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(resolution,[status(thm)],[c_8519,c_263]) ).
tcf(c_8528,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_8527]) ).
tcf(c_8549,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_8527,c_6308,c_8528]) ).
tcf(c_8728,plain,
! [X0: $i,X1: $i] :
( subclass(X0,y)
| ~ subclass(X1,y)
| ( y != y )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6159]) ).
tcf(c_8847,plain,
! [X0: $i] :
( member(least(xr,intersection(complement(w),y)),complement(w))
| ~ member(least(xr,intersection(complement(w),y)),intersection(complement(w),X0)) ),
inference(instantiation,[status(thm)],[c_229]) ).
tcf(c_10430,plain,
( member(not_subclass_element(y,w),w)
| member(not_subclass_element(y,w),complement(w))
| ~ member(not_subclass_element(y,w),universal_class) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_14974,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_212,c_229]) ).
tcf(c_14979,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_212,c_230]) ).
tcf(c_15409,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_14974,c_213]) ).
tcf(c_15453,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_14979,c_213]) ).
tcf(c_15672,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ( X0 = null_class )
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_346,c_313]) ).
tcf(c_15742,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X0),X1)
| ( X0 = null_class )
| ~ subclass(X0,y)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_15672,c_211]) ).
tcf(c_16442,plain,
( ( intersection(complement(w),y) = null_class )
| ~ subclass(intersection(complement(w),y),y)
| ~ subclass(intersection(complement(w),y),complement(w)) ),
inference(superposition,[status(thm)],[c_15742,c_348]) ).
tcf(c_16466,plain,
intersection(complement(w),y) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_16442,c_15453,c_15409]) ).
tcf(c_17048,plain,
( member(least(xr,intersection(complement(w),y)),complement(w))
| ~ member(least(xr,intersection(complement(w),y)),intersection(complement(w),y)) ),
inference(instantiation,[status(thm)],[c_8847]) ).
tcf(c_19681,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),y)
| ~ subclass(X2,y)
| ( y != y )
| ( intersection(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_8728]) ).
tcf(c_25969,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_221,c_211]) ).
tcf(c_26366,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ( X0 = null_class )
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_346,c_313]) ).
tcf(c_26415,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X0),X1)
| ( X0 = null_class )
| ~ subclass(X0,y)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_26366,c_211]) ).
tcf(c_26419,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ subclass(complement(X0),y)
| ~ member(least(xr,complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_26366,c_232]) ).
tcf(c_26458,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X1),X1)
| ~ subclass(X1,y)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_346,c_314]) ).
tcf(c_26529,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(least(xr,X0),X0)
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_212,c_26458]) ).
tcf(c_26956,plain,
( ( intersection(complement(w),y) = null_class )
| ~ subclass(intersection(complement(w),y),y)
| ~ subclass(intersection(complement(w),y),complement(w)) ),
inference(superposition,[status(thm)],[c_26415,c_348]) ).
tcf(c_26981,plain,
intersection(complement(w),y) = null_class,
inference(global_subsumption_just,[status(thm)],[c_26956,c_16466]) ).
tcf(c_26985,plain,
~ member(least(xr,null_class),complement(w)),
inference(demodulation,[status(thm)],[c_348,c_26981]) ).
tcf(c_26989,plain,
! [X0: $i] :
( member(X0,y)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_26981,c_230]) ).
tcf(c_26990,plain,
! [X0: $i] :
( member(X0,complement(w))
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_26981,c_229]) ).
tcf(c_27037,plain,
! [X0: $i] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),y) ),
inference(superposition,[status(thm)],[c_212,c_26989]) ).
tcf(c_27063,plain,
! [X0: $i,X1: $i] :
( member(X1,X0)
| ~ member(X1,null_class)
| ~ subclass(complement(w),X0) ),
inference(superposition,[status(thm)],[c_26990,c_211]) ).
tcf(c_27068,plain,
~ member(least(xr,null_class),null_class),
inference(superposition,[status(thm)],[c_26990,c_26985]) ).
tcf(c_27084,plain,
! [X0: $i] :
( subclass(null_class,X0)
| ~ subclass(null_class,y) ),
inference(superposition,[status(thm)],[c_26529,c_27068]) ).
tcf(c_30690,plain,
! [X0: $i] :
( subclass(intersection(complement(w),y),y)
| ~ subclass(X0,y)
| ( y != y )
| ( intersection(complement(w),y) != X0 ) ),
inference(instantiation,[status(thm)],[c_19681]) ).
tcf(c_30817,plain,
subclass(null_class,y),
inference(superposition,[status(thm)],[c_27037,c_213]) ).
tcf(c_30842,plain,
! [X0: $i] : subclass(null_class,X0),
inference(backward_subsumption_resolution,[status(thm)],[c_27084,c_30817]) ).
tcf(c_31607,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ subclass(universal_class,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_25969,c_223]) ).
tcf(c_32441,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_259,c_31607]) ).
tcf(c_32676,plain,
( ( complement(universal_class) = null_class )
| ~ function(universal_class)
| ~ subclass(complement(universal_class),y) ),
inference(superposition,[status(thm)],[c_32441,c_26419]) ).
tcf(c_33755,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_214,c_27063]) ).
tcf(c_42793,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_32676,c_8549]) ).
tcf(c_42815,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_42793,c_232]) ).
tcf(c_43085,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_42815,c_33755,c_42815]) ).
tcf(c_53207,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_212,c_229]) ).
tcf(c_53222,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_53207,c_213]) ).
tcf(c_53232,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_212,c_230]) ).
tcf(c_53286,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_53232,c_213]) ).
tcf(c_53378,plain,
( member(least(xr,intersection(complement(w),y)),w)
| ~ member(least(xr,intersection(complement(w),y)),universal_class) ),
inference(superposition,[status(thm)],[c_233,c_348]) ).
tcf(c_53503,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = null_class )
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_264,c_229]) ).
tcf(c_53558,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_53503,c_43085]) ).
tcf(c_53737,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_231,c_211]) ).
tcf(c_53950,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ( X0 = null_class )
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_346,c_313]) ).
tcf(c_53960,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X1),X1)
| ~ subclass(X1,y)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_346,c_314]) ).
tcf(c_54004,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X0),X1)
| ( X0 = null_class )
| ~ subclass(X0,y)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_53950,c_211]) ).
tcf(c_54404,plain,
( ( intersection(complement(w),y) = null_class )
| ~ subclass(intersection(complement(w),y),y)
| ~ subclass(intersection(complement(w),y),complement(w)) ),
inference(superposition,[status(thm)],[c_54004,c_348]) ).
tcf(c_54430,plain,
intersection(complement(w),y) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[c_54404,c_53286,c_53222]) ).
tcf(c_54432,plain,
( member(least(xr,null_class),w)
| ~ member(least(xr,null_class),universal_class) ),
inference(demodulation,[status(thm)],[c_53378,c_54430]) ).
tcf(c_56729,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_214,c_53737]) ).
tcf(c_68634,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_56729,c_7717]) ).
tcf(c_68639,plain,
! [X0: $i] :
( member(X0,universal_class)
| ( integer_of(X0) = null_class ) ),
inference(superposition,[status(thm)],[c_345,c_68634]) ).
tcf(c_70712,plain,
( member(least(xr,null_class),w)
| ( integer_of(least(xr,null_class)) = null_class ) ),
inference(superposition,[status(thm)],[c_68639,c_54432]) ).
tcf(c_72443,plain,
( member(least(xr,w),w)
| ( integer_of(least(xr,null_class)) = null_class )
| ~ subclass(w,y) ),
inference(superposition,[status(thm)],[c_70712,c_53960]) ).
tcf(c_72449,plain,
( member(least(xr,w),w)
| ( integer_of(least(xr,null_class)) = null_class ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72443,c_2135]) ).
tcf(c_72497,plain,
! [X0: $i] :
( member(least(xr,w),X0)
| ( integer_of(least(xr,null_class)) = null_class )
| ~ subclass(w,X0) ),
inference(superposition,[status(thm)],[c_72449,c_211]) ).
tcf(c_81382,plain,
! [X0: $i,X1: $i] :
( member(least(xr,X1),X1)
| ~ well_ordering(xr,y)
| ~ subclass(X1,y)
| ~ member(X0,X1) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_83158,plain,
! [X0: $i] :
( member(not_subclass_element(y,w),intersection(X0,y))
| ~ member(not_subclass_element(y,w),y)
| ~ member(not_subclass_element(y,w),X0) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_86824,plain,
! [X0: $i] :
( member(least(xr,intersection(complement(w),y)),intersection(complement(w),y))
| ~ well_ordering(xr,y)
| ~ subclass(intersection(complement(w),y),y)
| ~ member(X0,intersection(complement(w),y)) ),
inference(instantiation,[status(thm)],[c_81382]) ).
tcf(c_92683,plain,
! [X0: $i,X1: $i] :
( ( intersection(complement(w),y) = X1 )
| ( X1 != X0 )
| ( intersection(complement(w),y) != X0 ) ),
inference(instantiation,[status(thm)],[c_4853]) ).
tcf(c_95130,plain,
( member(least(xr,intersection(complement(w),y)),intersection(complement(w),y))
| ~ well_ordering(xr,y)
| ~ subclass(intersection(complement(w),y),y)
| ~ member(not_subclass_element(y,w),intersection(complement(w),y)) ),
inference(instantiation,[status(thm)],[c_86824]) ).
tcf(c_95131,plain,
( member(not_subclass_element(y,w),intersection(complement(w),y))
| ~ member(not_subclass_element(y,w),y)
| ~ member(not_subclass_element(y,w),complement(w)) ),
inference(instantiation,[status(thm)],[c_83158]) ).
tcf(c_107822,plain,
! [X0: $i] :
( ( intersection(complement(w),y) = X0 )
| ( X0 != null_class )
| ( intersection(complement(w),y) != null_class ) ),
inference(instantiation,[status(thm)],[c_92683]) ).
tcf(c_108259,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ( integer_of(least(xr,null_class)) = null_class )
| ~ subclass(w,X0)
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_72497,c_53960]) ).
tcf(c_108299,plain,
! [X0: $i] :
( member(least(xr,X0),X0)
| ~ subclass(X0,y) ),
inference(global_subsumption_just,[status(thm)],[c_108259,c_346,c_349,c_348,c_2135,c_2645,c_6075,c_6135,c_6134,c_6149,c_7952,c_8273,c_10430,c_16466,c_17048,c_30690,c_95130,c_95131,c_107822]) ).
tcf(c_108334,plain,
~ subclass(null_class,y),
inference(superposition,[status(thm)],[c_108299,c_53558]) ).
tcf(c_108340,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_108334,c_30842]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM095-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n013.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 02:52:58 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 0.22/0.52
% 0.22/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.53
% 0.22/0.53 % Detected problem language: tptp
% 0.22/0.54 % Proving...
% 125.43/19.71 % SZS status Started for theBenchmark.p
% 125.43/19.71 % SZS status Unsatisfiable for theBenchmark.p
% 125.43/19.71
% 125.43/19.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 125.43/19.71
% 125.43/19.71 % ------ iProver source info
% 125.43/19.71
% 125.43/19.71 % git: date: 2026-07-19 20:42:38 +0200
% 125.43/19.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 125.43/19.71 % git: non_committed_changes: false
% 125.43/19.71
% 125.43/19.71 % ------ Parsing...% successful
% 125.43/19.71
% 125.43/19.71
% 125.43/19.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 125.43/19.71
% 125.43/19.71 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 125.43/19.71
% 125.43/19.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 125.43/19.71
% 125.43/19.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 125.43/19.71 % ------ Proving...
% 125.43/19.71 % ------ Problem Properties
% 125.43/19.71
% 125.43/19.71 %
% 125.43/19.71 % clauses 119
% 125.43/19.71 % conjectures 3
% 125.43/19.71 % EPR 17
% 125.43/19.71 % Horn 107
% 125.43/19.71 % unary 30
% 125.43/19.71 % binary 58
% 125.43/19.71 % lits 253
% 125.43/19.71 % lits eq 40
% 125.43/19.71 % fd_pure 0
% 125.43/19.71 % fd_pseudo 0
% 125.43/19.71 % fd_cond 5
% 125.43/19.71 % fd_pseudo_cond 10
% 125.43/19.71 % AC symbols 0
% 125.43/19.71
% 125.43/19.71 % ------ Input Options Time Limit: Unbounded
% 125.43/19.71
% 125.43/19.71
% 125.43/19.71 % ------
% 125.43/19.71 % Current options:
% 125.43/19.71 % ------
% 125.43/19.71
% 125.43/19.71
% 125.43/19.71 %
% 125.43/19.71
% 125.43/19.71 % ------ Proving...
% 125.43/19.71 %
% 125.43/19.71
% 125.43/19.71 % SZS status Unsatisfiable for theBenchmark.p
% 125.43/19.71
% 125.43/19.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 125.43/19.71
% 125.43/19.71
%------------------------------------------------------------------------------