%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM534+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:25:52 PM UTC 2026
% Result : Theorem 28.80s 4.72s
% Output : CNFRefutation 28.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 224 ( 33 unt; 6 def)
% Number of atoms : 1009 ( 184 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 1092 ( 446 ~; 499 |; 116 &)
% ( 22 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 415 ( 0 sgn 402 !; 13 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f13,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
fof(f15,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).
fof(f19,conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(flattening,[],[f20]) ).
fof(f28,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f30,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f33,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f34]) ).
fof(f38,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f40]) ).
fof(f48,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) ) )
& ( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f53,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK5(X0,X1),X1)
& ~ aElementOf0(sK5(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f54]) ).
fof(f56,plain,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( ( sdtpldt0(X0,X1) != X2
| sP0(X2,X0,X1) )
& ( ~ sP0(X2,X0,X1)
| X2 = sdtpldt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ! [X2] :
( ( sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) )
& ( ~ sP0(X2,X1,X0)
| sdtpldt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f56]) ).
fof(f62,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtmndt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtmndt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f62]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f69,plain,
! [X2,X0] :
( slcrc0 != X0
| ~ aElementOf0(X2,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X0] :
( slcrc0 != X0
| aSet0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X0] :
( aElementOf0(sK4(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f78,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f105,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f106,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f107,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(cnf_transformation,[],[f25]) ).
fof(f108,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f70]) ).
fof(f109,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f69]) ).
fof(f110,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f81]) ).
fof(f112,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f93]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_50,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),X0)
| ( X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_51,plain,
aSet0(slcrc0),
inference(cnf_transformation,[],[f108]) ).
tcf(c_52,plain,
! [X0: $i] : ~ aElementOf0(X0,slcrc0),
inference(cnf_transformation,[],[f109]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_59,plain,
! [X0: $i] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(X1,X2) = X0 )
| ~ sP3(X2,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_86,plain,
aSet0(xS),
inference(cnf_transformation,[],[f105]) ).
tcf(c_87,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f106]) ).
tcf(c_88,negated_conjecture,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(cnf_transformation,[],[f107]) ).
tcf(c_90,plain,
( aSubsetOf0(slcrc0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_101,plain,
( ( slcrc0 = slcrc0 )
| ~ aSet0(slcrc0)
| ~ aSubsetOf0(slcrc0,slcrc0) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_56,c_60]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1) ),
inference(renaming,[status(thm)],[c_106]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(sdtpldt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_63]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_601]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP2(sdtmndt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_75]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_635]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sdtmndt0(X0,X2) = X4 )
| ~ aSet0(X1)
| ~ aElement0(X3)
| ~ sP2(X4,X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_85]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtmndt0(X1,X2) = X0 )
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ sP2(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_647]) ).
tcf(c_4618,definition,
iPr_def_10 = sdtmndt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4619,definition,
iPr_def_11 = sdtpldt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4620,negated_conjecture,
iPr_def_11 != xS,
inference(demodulation,[status(thm)],[c_88,c_4618,c_4619]) ).
tcf(c_4621,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_4623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5213,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_87,c_49]) ).
tcf(c_5214,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_5213,c_86]) ).
tcf(c_5293,plain,
( sP0(iPr_def_11,iPr_def_10,xx)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_4619,c_602]) ).
tcf(c_5300,plain,
( sP0(iPr_def_11,iPr_def_10,xx)
| ~ aSet0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5293,c_5214]) ).
tcf(c_5498,plain,
( sP2(iPr_def_10,xS,xx)
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_4618,c_636]) ).
tcf(c_5506,plain,
sP2(iPr_def_10,xS,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_5498,c_86,c_5214]) ).
tcf(c_5659,plain,
! [X0: $i] :
( ( iPr_def_11 = xS )
| ( iPr_def_11 != X0 )
| ( xS != X0 ) ),
inference(instantiation,[status(thm)],[c_4623]) ).
tcf(c_5662,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ~ aElementOf0(xx,xS)
| ( X1 != xS )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_4625]) ).
tcf(c_5772,plain,
( aSubsetOf0(xS,iPr_def_11)
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS)
| ~ aElementOf0(sK5(iPr_def_11,xS),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_5802,plain,
( aElementOf0(sK4(xS),xS)
| ( xS = slcrc0 )
| ~ aSet0(xS) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_5803,plain,
! [X0: $i] :
( ( xS = X0 )
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0)
| ~ aSubsetOf0(X0,xS) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_6116,plain,
~ aElementOf0(xx,slcrc0),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_6121,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X1)
| ~ aElementOf0(xx,X2)
| ( X1 != X2 )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_4625]) ).
tcf(c_6265,plain,
! [X0: $i] :
( aElementOf0(xx,X0)
| ~ aElementOf0(xx,xS)
| ( xx != xx )
| ( X0 != xS ) ),
inference(instantiation,[status(thm)],[c_5662]) ).
tcf(c_6266,plain,
xx = xx,
inference(instantiation,[status(thm)],[c_4621]) ).
tcf(c_6267,plain,
( aElementOf0(xx,slcrc0)
| ~ aElementOf0(xx,xS)
| ( xx != xx )
| ( slcrc0 != xS ) ),
inference(instantiation,[status(thm)],[c_6265]) ).
tcf(c_6501,plain,
( aSubsetOf0(iPr_def_11,xS)
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS)
| ~ aElementOf0(sK5(xS,iPr_def_11),xS) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_6710,plain,
( ( iPr_def_11 = xS )
| ( iPr_def_11 != iPr_def_11 )
| ( xS != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_5659]) ).
tcf(c_6711,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_4621]) ).
tcf(c_7090,plain,
! [X0: $i,X1: $i] :
( ( X0 = xS )
| ( xS != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_4623]) ).
tcf(c_7091,plain,
( ( slcrc0 = xS )
| ( xS != slcrc0 )
| ( slcrc0 != slcrc0 ) ),
inference(instantiation,[status(thm)],[c_7090]) ).
tcf(c_8349,plain,
( aElement0(sK4(xS))
| ~ aSet0(xS)
| ~ aElementOf0(sK4(xS),xS) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_8596,plain,
xS = xS,
inference(instantiation,[status(thm)],[c_4621]) ).
tcf(c_8906,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ~ aElementOf0(xx,iPr_def_11)
| ( X1 != iPr_def_11 )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_6121]) ).
tcf(c_11989,plain,
( ( xS = iPr_def_11 )
| ~ aSet0(iPr_def_11)
| ~ aSubsetOf0(iPr_def_11,xS)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_5803]) ).
tcf(c_13810,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElementOf0(xx,iPr_def_11)
| ( iPr_def_11 != iPr_def_11 )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_8906]) ).
tcf(c_15728,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(xx,xS)
| ( xS != xS )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_5662]) ).
tcf(c_28599,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aSet0(xS)
| ~ aElementOf0(X0,xS) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_29246,plain,
( aElementOf0(sK5(xS,iPr_def_11),xS)
| ~ aElementOf0(xx,xS)
| ( xS != xS )
| ( sK5(xS,iPr_def_11) != xx ) ),
inference(instantiation,[status(thm)],[c_15728]) ).
tcf(c_39615,plain,
( aElementOf0(sK5(iPr_def_11,xS),iPr_def_11)
| ~ aElementOf0(xx,iPr_def_11)
| ( iPr_def_11 != iPr_def_11 )
| ( sK5(iPr_def_11,xS) != xx ) ),
inference(instantiation,[status(thm)],[c_13810]) ).
fof(f42,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f43,definition,
! [X1,X0] :
( ~ sP1(X1,X0)
| ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> sP0(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f39,f43,f42]) ).
fof(f45,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f46,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f41,f46,f45]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ( ~ sP0(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( ( X3 = X1
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP0(X2,X0,X1) ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( X2 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& ( ( X2 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( ( X2 = X3
| aElementOf0(X3,X1) )
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| ( X2 != X3
& ~ aElementOf0(X3,X1) )
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ~ sP0(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( ( X2 = X4
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& ( ( X2 != X4
& ~ aElementOf0(X4,X1) )
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK6(X0,X1,X2),X0)
| ( ( sK6(X0,X1,X2) = X2
| aElementOf0(sK6(X0,X1,X2),X1) )
& aElement0(sK6(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK6(X0,X1,X2),X0)
| ( sK6(X0,X1,X2) != X2
& ~ aElementOf0(sK6(X0,X1,X2),X1) )
| ~ aElement0(sK6(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f60]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( X2 != X3
& aElementOf0(X3,X1)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| X2 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK7(X0,X1,X2),X0)
| ( sK7(X0,X1,X2) != X2
& aElementOf0(sK7(X0,X1,X2),X1)
& aElement0(sK7(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK7(X0,X1,X2),X0)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| ~ aElement0(sK7(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f66]) ).
fof(f83,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| X2 = X4
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f84,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElement0(X4) ),
inference(cnf_transformation,[],[f61]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| X2 != X4
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f89,plain,
! [X2,X0,X1] :
( aElementOf0(sK6(X0,X1,X2),X0)
| aElement0(sK6(X0,X1,X2))
| ~ aSet0(X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f95,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| X2 != X4 ),
inference(cnf_transformation,[],[f67]) ).
fof(f96,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f97,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElement0(X4) ),
inference(cnf_transformation,[],[f67]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f101,plain,
! [X2,X0,X1] :
( aElementOf0(sK7(X0,X1,X2),X0)
| aElementOf0(sK7(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f85]) ).
fof(f113,plain,
! [X0,X1,X4] :
( ~ sP2(X0,X1,X4)
| ~ aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f95]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| aElement0(sK6(X0,X1,X2))
| aElementOf0(sK6(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,X0)
| ~ aElement0(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElement0(X3)
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ( X2 = X3 )
| ~ aElementOf0(X3,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X0,X1,X2)
| aElementOf0(sK7(X0,X1,X2),X1)
| aElementOf0(sK7(X0,X1,X2),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( aSet0(X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X0)
| ( X2 = X3 )
| ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElement0(X3)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ aElementOf0(X2,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| aElement0(sK6(X0,X1,X2))
| ~ aSet0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_49]) ).
tcf(c_1552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( aElementOf0(X5,X2)
| ~ aSet0(X0)
| ~ aElement0(X5)
| ~ aElement0(X1)
| ~ aElementOf0(X5,X3)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sdtpldt0(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_602]) ).
tcf(c_1553,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X0,X1) ),
inference(unflattening,[status(thm)],[c_1552]) ).
tcf(c_1554,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_1553,c_49,c_1553]) ).
tcf(c_5314,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aSet0(iPr_def_10)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_5300,c_71]) ).
tcf(c_5315,plain,
( aElementOf0(xx,iPr_def_11)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_5300,c_70]) ).
tcf(c_5316,plain,
( aSet0(iPr_def_11)
| ~ aSet0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5300,c_68]) ).
tcf(c_5319,plain,
( aElementOf0(xx,iPr_def_11)
| ~ aSet0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5315,c_5214]) ).
tcf(c_5415,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_602,c_69]) ).
tcf(c_5518,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5506,c_83]) ).
tcf(c_5521,plain,
aSet0(iPr_def_10),
inference(superposition,[status(thm)],[c_5506,c_80]) ).
tcf(c_5527,plain,
aSet0(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_5316,c_5521]) ).
tcf(c_5528,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5314,c_5521]) ).
tcf(c_5529,plain,
sP0(iPr_def_11,iPr_def_10,xx),
inference(backward_subsumption_resolution,[status(thm)],[c_5300,c_5521]) ).
tcf(c_5541,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtpldt0(X1,X2))
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5415,c_1554]) ).
tcf(c_5551,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4619,c_5541]) ).
tcf(c_5560,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5551,c_5521,c_5214]) ).
tcf(c_5610,plain,
! [X0: $i,X1: $i] :
( sP2(slcrc0,X0,X1)
| aElementOf0(sK7(slcrc0,X0,X1),X0)
| ~ aSet0(slcrc0) ),
inference(superposition,[status(thm)],[c_78,c_52]) ).
tcf(c_5612,plain,
! [X0: $i,X1: $i] :
( sP2(X0,X0,X1)
| aElementOf0(sK7(X0,X0,X1),X0)
| ~ aSet0(X0) ),
inference(equality_factoring,[status(thm)],[c_78]) ).
tcf(c_5617,plain,
! [X0: $i,X1: $i] :
( sP2(slcrc0,X0,X1)
| aElementOf0(sK7(slcrc0,X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5610,c_51]) ).
tcf(c_5676,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_5506,c_81]) ).
tcf(c_5698,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_5529,c_72]) ).
tcf(c_5781,plain,
! [X0: $i,X1: $i] :
( sP2(X0,iPr_def_10,X1)
| aElementOf0(sK7(X0,iPr_def_10,X1),xS)
| aElementOf0(sK7(X0,iPr_def_10,X1),X0)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_78,c_5518]) ).
tcf(c_5886,plain,
! [X0: $i] : sP2(slcrc0,slcrc0,X0),
inference(superposition,[status(thm)],[c_5617,c_52]) ).
tcf(c_6197,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_10)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_55,c_5698]) ).
tcf(c_6219,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),iPr_def_10)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6197,c_5527]) ).
tcf(c_6516,plain,
! [X0: $i] :
( sP2(iPr_def_11,iPr_def_11,X0)
| aElement0(sK7(iPr_def_11,iPr_def_11,X0))
| ~ aSet0(iPr_def_11) ),
inference(superposition,[status(thm)],[c_5612,c_5528]) ).
tcf(c_6523,plain,
! [X0: $i] :
( sP2(iPr_def_11,iPr_def_11,X0)
| aElement0(sK7(iPr_def_11,iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6516,c_5527]) ).
tcf(c_6839,plain,
( aElementOf0(sK4(xS),iPr_def_10)
| ( slcrc0 = xS )
| ( sK4(xS) = xx )
| ~ aSet0(xS)
| ~ aElement0(sK4(xS)) ),
inference(superposition,[status(thm)],[c_50,c_5676]) ).
tcf(c_6854,plain,
( aElementOf0(sK4(xS),iPr_def_10)
| ( slcrc0 = xS )
| ( sK4(xS) = xx )
| ~ aElement0(sK4(xS)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6839,c_86]) ).
tcf(c_8100,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,X0) = slcrc0 )
| ~ aSet0(slcrc0)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_5886,c_648]) ).
tcf(c_8101,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,X0) = slcrc0 )
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8100,c_51]) ).
tcf(c_8252,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| ( sdtmndt0(slcrc0,sK6(X0,X1,X2)) = slcrc0 )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_151,c_8101]) ).
tcf(c_8710,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X1)
| ( sdtmndt0(slcrc0,sK6(X1,X2,X0)) = slcrc0 )
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_8252,c_70]) ).
tcf(c_16275,plain,
! [X0: $i] :
( aSubsetOf0(iPr_def_11,X0)
| aElementOf0(sK5(X0,iPr_def_11),xS)
| ( sK5(X0,iPr_def_11) = xx )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_6219,c_5518]) ).
tcf(c_17770,plain,
( aElementOf0(sK4(xS),iPr_def_10)
| ( sK4(xS) = xx ) ),
inference(global_subsumption_just,[status(thm)],[c_6854,c_86,c_51,c_87,c_90,c_101,c_5802,c_6116,c_6267,c_6266,c_6854,c_7091,c_8349]) ).
tcf(c_17798,plain,
( aElementOf0(sK4(xS),xS)
| ( sK4(xS) = xx ) ),
inference(superposition,[status(thm)],[c_17770,c_5518]) ).
tcf(c_17939,plain,
aElementOf0(sK4(xS),xS),
inference(global_subsumption_just,[status(thm)],[c_17798,c_86,c_51,c_87,c_90,c_101,c_5802,c_6116,c_6267,c_6266,c_7091]) ).
tcf(c_17943,plain,
! [X0: $i] :
( aElementOf0(sK4(xS),X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(xS,X0) ),
inference(superposition,[status(thm)],[c_17939,c_57]) ).
tcf(c_24872,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_16275,c_54]) ).
tcf(c_24874,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24872,c_5527,c_86]) ).
tcf(c_24897,plain,
( ( xS = iPr_def_11 )
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(xS)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(superposition,[status(thm)],[c_24874,c_107]) ).
tcf(c_24900,plain,
( ( xS = iPr_def_11 )
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24897,c_86]) ).
tcf(c_33315,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(slcrc0,sK6(slcrc0,X1,X0)) = slcrc0 )
| ~ aSet0(slcrc0)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_8710,c_52]) ).
tcf(c_33362,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(slcrc0,sK6(slcrc0,X1,X0)) = slcrc0 )
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33315,c_51]) ).
tcf(c_33996,plain,
! [X0: $i,X1: $i] :
( sP2(iPr_def_11,iPr_def_11,X1)
| ( sdtmndt0(slcrc0,sK6(slcrc0,X0,sK7(iPr_def_11,iPr_def_11,X1))) = slcrc0 ) ),
inference(superposition,[status(thm)],[c_6523,c_33362]) ).
tcf(c_34812,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(slcrc0,sK6(slcrc0,X1,sK7(iPr_def_11,iPr_def_11,X0))) = slcrc0 )
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_33996,c_84]) ).
tcf(c_35557,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,sK6(slcrc0,X0,sK7(iPr_def_11,iPr_def_11,sK4(xS)))) = slcrc0 )
| ~ aSet0(iPr_def_11)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(superposition,[status(thm)],[c_17943,c_34812]) ).
tcf(c_35584,plain,
! [X0: $i] :
( ( sdtmndt0(slcrc0,sK6(slcrc0,X0,sK7(iPr_def_11,iPr_def_11,sK4(xS)))) = slcrc0 )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35557,c_5527]) ).
tcf(c_38270,plain,
~ aSubsetOf0(xS,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_35584,c_86,c_87,c_4620,c_5527,c_6501,c_6710,c_6711,c_8596,c_11989,c_24900,c_29246]) ).
tcf(c_43207,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElementOf0(sK7(xS,iPr_def_10,X0),xS)
| ~ aSet0(xS) ),
inference(equality_factoring,[status(thm)],[c_5781]) ).
tcf(c_43209,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElementOf0(sK7(xS,iPr_def_10,X0),xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43207,c_86]) ).
tcf(c_43421,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElement0(sK7(xS,iPr_def_10,X0))
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_43209,c_49]) ).
tcf(c_43423,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElement0(sK7(xS,iPr_def_10,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43421,c_86]) ).
tcf(c_43548,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| ( sdtmndt0(slcrc0,sK7(xS,iPr_def_10,X0)) = slcrc0 ) ),
inference(superposition,[status(thm)],[c_43423,c_8101]) ).
tcf(c_43604,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ( sdtmndt0(slcrc0,sK7(xS,iPr_def_10,X1)) = slcrc0 )
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_43548,c_82]) ).
tcf(c_43941,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(global_subsumption_just,[status(thm)],[c_43604,c_86,c_28599]) ).
tcf(c_43948,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,xS) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5676,c_43941]) ).
tcf(c_45055,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ( sK5(X0,xS) = xx )
| ~ aSet0(xS)
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_55,c_43948]) ).
tcf(c_45143,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_10)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45055,c_86]) ).
tcf(c_49749,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_11)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_45143,c_5560]) ).
tcf(c_82189,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_49749,c_54]) ).
tcf(c_82206,plain,
sK5(iPr_def_11,xS) = xx,
inference(forward_subsumption_resolution,[status(thm)],[c_82189,c_38270,c_5527,c_86]) ).
tcf(c_82276,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_82206,c_39615,c_38270,c_6711,c_5772,c_5521,c_5527,c_5319,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM534+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 04:32:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 28.80/4.72 % SZS status Started for theBenchmark.p
% 28.80/4.72 % SZS status Theorem for theBenchmark.p
% 28.80/4.72
% 28.80/4.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 28.80/4.72
% 28.80/4.72 % ------ iProver source info
% 28.80/4.72
% 28.80/4.72 % git: date: 2026-07-19 20:42:38 +0200
% 28.80/4.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 28.80/4.72 % git: non_committed_changes: false
% 28.80/4.72
% 28.80/4.72 % ------ Parsing...
% 28.80/4.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 28.80/4.72
% 28.80/4.72 % ------ Preprocessing... sup_sim: 0 sf_s rm: 4 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 %
% 28.80/4.72
% 28.80/4.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 28.80/4.72
% 28.80/4.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 28.80/4.72 % ------ Proving...
% 28.80/4.72 % ------ Problem Properties
% 28.80/4.72
% 28.80/4.72 %
% 28.80/4.72 % clauses 38
% 28.80/4.72 % conjectures 1
% 28.80/4.72 % EPR 21
% 28.80/4.72 % Horn 28
% 28.80/4.72 % unary 7
% 28.80/4.72 % binary 4
% 28.80/4.72 % lits 116
% 28.80/4.72 % lits eq 13
% 28.80/4.72 % fd_pure 0
% 28.80/4.72 % fd_pseudo 0
% 28.80/4.72 % fd_cond 1
% 28.80/4.72 % fd_pseudo_cond 5
% 28.80/4.72 % AC symbols 0
% 28.80/4.72
% 28.80/4.72 % ------ Schedule dynamic 5 is on
% 28.80/4.72
% 28.80/4.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 28.80/4.72
% 28.80/4.72
% 28.80/4.72 % ------
% 28.80/4.72 % Current options:
% 28.80/4.72 % ------
% 28.80/4.72
% 28.80/4.72
% 28.80/4.72 %
% 28.80/4.72
% 28.80/4.72 % ------ Proving...
% 28.80/4.72 %
% 28.80/4.72
% 28.80/4.72 % SZS status Theorem for theBenchmark.p
% 28.80/4.72
% 28.80/4.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.80/4.73
% 28.80/4.73
%------------------------------------------------------------------------------