%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM535+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 : n009.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 32.43s 12.37s
% Output : CNFRefutation 32.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 193 ( 23 unt; 6 def)
% Number of atoms : 908 ( 142 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 990 ( 391 ~; 450 |; 118 &)
% ( 22 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 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 : 360 ( 0 sgn 347 !; 13 ?; 144 :)
% 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,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
& aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] :
( X0 = slcrc0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f29,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f13]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f33]) ).
fof(f37,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(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(flattening,[],[f37]) ).
fof(f39,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(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(flattening,[],[f39]) ).
fof(f41,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0] :
( ( slcrc0 != X0
| ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) )
& ( ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0)
| X0 = slcrc0 ) ),
inference(nnf_transformation,[],[f28]) ).
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,[],[f29]) ).
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,[],[f27]) ).
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,[],[f32]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f34]) ).
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(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,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(cnf_transformation,[],[f41]) ).
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_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,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_90,plain,
( aSubsetOf0(xS,xS)
| ~ aSet0(xS) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_105,plain,
( ( xS = xS )
| ~ aSet0(xS)
| ~ aSubsetOf0(xS,xS) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_612,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_613,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_612]) ).
tcf(c_646,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_647,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_646]) ).
tcf(c_4649,definition,
iPr_def_10 = sdtmndt0(xS,xx),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4650,definition,
iPr_def_11 = sdtpldt0(iPr_def_10,xx),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4651,negated_conjecture,
( ~ aSubsetOf0(iPr_def_11,xS)
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_88,c_4649,c_4650]) ).
tcf(c_4652,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_4655,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X0,X2)
| ~ aElementOf0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5269,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_87,c_49]) ).
tcf(c_5270,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_5269,c_86]) ).
tcf(c_5350,plain,
( sP0(iPr_def_11,iPr_def_10,xx)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_4650,c_613]) ).
tcf(c_5357,plain,
( sP0(iPr_def_11,iPr_def_10,xx)
| ~ aSet0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5350,c_5270]) ).
tcf(c_5438,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK4(X0),X1)
| ( X0 = slcrc0 )
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_57]) ).
tcf(c_5555,plain,
( sP2(iPr_def_10,xS,xx)
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_4649,c_647]) ).
tcf(c_5563,plain,
sP2(iPr_def_10,xS,xx),
inference(forward_subsumption_resolution,[status(thm)],[c_5555,c_86,c_5270]) ).
tcf(c_5597,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK4(X0),X1)
| ( X0 = slcrc0 )
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5438,c_56,c_5438]) ).
tcf(c_5712,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_5833,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,X1)
| ~ aElementOf0(xx,xS)
| ( X1 != xS )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_4656]) ).
tcf(c_5836,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_5896,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElement0(xx)
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_4655]) ).
tcf(c_6130,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X1)
| ~ aElementOf0(xx,X2)
| ( X1 != X2 )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_4656]) ).
tcf(c_6746,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_4652]) ).
tcf(c_28122,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_87,c_49]) ).
tcf(c_28123,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[c_28122,c_86]) ).
tcf(c_43855,plain,
! [X0: $i] :
( aElementOf0(sK5(xS,iPr_def_11),X0)
| ~ aElementOf0(xx,xS)
| ( X0 != xS )
| ( sK5(xS,iPr_def_11) != xx ) ),
inference(instantiation,[status(thm)],[c_5833]) ).
tcf(c_43856,plain,
( aElementOf0(sK5(xS,iPr_def_11),xS)
| ~ aElementOf0(xx,xS)
| ( xS != xS )
| ( sK5(xS,iPr_def_11) != xx ) ),
inference(instantiation,[status(thm)],[c_43855]) ).
tcf(c_103214,plain,
! [X0: $i] :
( aElementOf0(sK5(iPr_def_11,xS),iPr_def_11)
| ~ aElementOf0(xx,X0)
| ( iPr_def_11 != X0 )
| ( sK5(iPr_def_11,xS) != xx ) ),
inference(instantiation,[status(thm)],[c_6130]) ).
tcf(c_115475,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_103214]) ).
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,[],[f38,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,[],[f40,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(f88,plain,
! [X2,X0,X1] :
( aElementOf0(sK6(X0,X1,X2),X0)
| sK6(X0,X1,X2) = X2
| aElementOf0(sK6(X0,X1,X2),X1)
| ~ aSet0(X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
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]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2)
| aElementOf0(sK6(X0,X1,X2),X1)
| aElementOf0(sK6(X0,X1,X2),X0)
| ( sK6(X0,X1,X2) = X2 )
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f88]) ).
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_5371,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aSet0(iPr_def_10)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_5357,c_71]) ).
tcf(c_5372,plain,
( aElementOf0(xx,iPr_def_11)
| ~ aSet0(iPr_def_10)
| ~ aElement0(xx) ),
inference(superposition,[status(thm)],[c_5357,c_70]) ).
tcf(c_5373,plain,
( aSet0(iPr_def_11)
| ~ aSet0(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5357,c_68]) ).
tcf(c_5376,plain,
( aElementOf0(xx,iPr_def_11)
| ~ aSet0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5372,c_5270]) ).
tcf(c_5474,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aSet0(iPr_def_10)
| ~ aElement0(X0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5357,c_69]) ).
tcf(c_5575,plain,
! [X0: $i] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5563,c_83]) ).
tcf(c_5576,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5563,c_82]) ).
tcf(c_5578,plain,
aSet0(iPr_def_10),
inference(superposition,[status(thm)],[c_5563,c_80]) ).
tcf(c_5584,plain,
aSet0(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_5373,c_5578]) ).
tcf(c_5585,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5371,c_5578]) ).
tcf(c_5586,plain,
sP0(iPr_def_11,iPr_def_10,xx),
inference(backward_subsumption_resolution,[status(thm)],[c_5357,c_5578]) ).
tcf(c_5724,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtmndt0(X1,X2))
| ( X0 = X2 )
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_647,c_81]) ).
tcf(c_5725,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_5563,c_81]) ).
tcf(c_5747,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_5586,c_72]) ).
tcf(c_5748,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElement0(X0)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5586,c_69]) ).
tcf(c_5846,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_5575]) ).
tcf(c_5848,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),xS)
| ( X0 = slcrc0 )
| ~ aSet0(iPr_def_10)
| ~ aSubsetOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5597,c_5575]) ).
tcf(c_5856,plain,
! [X0: $i] :
( aElementOf0(sK4(X0),xS)
| ( X0 = slcrc0 )
| ~ aSubsetOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5848,c_5578]) ).
tcf(c_6001,plain,
! [X0: $i,X1: $i] :
( sP0(slcrc0,X0,X1)
| aElementOf0(sK6(slcrc0,X0,X1),X0)
| ( sK6(slcrc0,X0,X1) = X1 )
| ~ aSet0(slcrc0) ),
inference(superposition,[status(thm)],[c_67,c_52]) ).
tcf(c_6013,plain,
! [X0: $i,X1: $i] :
( sP0(slcrc0,X0,X1)
| aElementOf0(sK6(slcrc0,X0,X1),X0)
| ( sK6(slcrc0,X0,X1) = X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6001,c_51]) ).
tcf(c_6148,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_11)
| ~ aElementOf0(X0,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_5748,c_5474,c_5578,c_5576]) ).
tcf(c_6265,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_5747]) ).
tcf(c_6293,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_6265,c_5584]) ).
tcf(c_6628,plain,
! [X0: $i,X1: $i] :
( aElementOf0(sK4(X0),X1)
| ( X0 = slcrc0 )
| ~ aSet0(X1)
| ~ aSubsetOf0(xS,X1)
| ~ aSubsetOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_5856,c_57]) ).
tcf(c_17983,plain,
! [X0: $i] :
( sP0(slcrc0,slcrc0,X0)
| ( sK6(slcrc0,slcrc0,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_6013,c_52]) ).
tcf(c_18297,plain,
! [X0: $i] :
( aElementOf0(X0,slcrc0)
| ( sK6(slcrc0,slcrc0,X0) = X0 )
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_17983,c_70]) ).
tcf(c_18299,plain,
! [X0: $i] :
( ( sK6(slcrc0,slcrc0,X0) = X0 )
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18297,c_52]) ).
tcf(c_19526,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_6293,c_5575]) ).
tcf(c_29099,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtmndt0(X1,X2))
| ( X0 = X2 )
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_647,c_81]) ).
tcf(c_33035,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_19526,c_54]) ).
tcf(c_33037,plain,
( aSubsetOf0(iPr_def_11,xS)
| ( sK5(xS,iPr_def_11) = xx ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33035,c_5584,c_86]) ).
tcf(c_33064,plain,
( ( sK5(xS,iPr_def_11) = xx )
| ~ aSubsetOf0(xS,iPr_def_11) ),
inference(superposition,[status(thm)],[c_33037,c_4651]) ).
tcf(c_43730,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_5846]) ).
tcf(c_43732,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElementOf0(sK7(xS,iPr_def_10,X0),xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43730,c_86]) ).
tcf(c_43876,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElement0(sK7(xS,iPr_def_10,X0))
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_43732,c_49]) ).
tcf(c_43878,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| aElement0(sK7(xS,iPr_def_10,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43876,c_86]) ).
tcf(c_43947,plain,
! [X0: $i] :
( sP2(xS,iPr_def_10,X0)
| ( sK6(slcrc0,slcrc0,sK7(xS,iPr_def_10,X0)) = sK7(xS,iPr_def_10,X0) ) ),
inference(superposition,[status(thm)],[c_43878,c_18299]) ).
tcf(c_47048,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ( sK6(slcrc0,slcrc0,sK7(xS,iPr_def_10,X1)) = sK7(xS,iPr_def_10,X1) )
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_43947,c_82]) ).
tcf(c_47778,plain,
! [X0: $i] :
( aElement0(sK4(X0))
| ( X0 = slcrc0 )
| ~ aSet0(iPr_def_11)
| ~ aSubsetOf0(xS,iPr_def_11)
| ~ aSubsetOf0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_6628,c_5585]) ).
tcf(c_47814,plain,
! [X0: $i] :
( aElement0(sK4(X0))
| ( X0 = slcrc0 )
| ~ aSubsetOf0(xS,iPr_def_11)
| ~ aSubsetOf0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47778,c_5584]) ).
tcf(c_48087,plain,
~ aSubsetOf0(xS,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_47814,c_86,c_87,c_90,c_105,c_4651,c_5584,c_5836,c_33064,c_43856]) ).
tcf(c_60816,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtmndt0(X1,X2))
| ( X0 = X2 )
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_29099,c_49,c_5724]) ).
tcf(c_60828,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aSet0(xS)
| ~ aElement0(xx)
| ~ aElementOf0(X0,xS) ),
inference(superposition,[status(thm)],[c_4649,c_60816]) ).
tcf(c_60847,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60828,c_86,c_28123]) ).
tcf(c_61249,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(global_subsumption_just,[status(thm)],[c_47048,c_5270,c_5576,c_5896,c_60847]) ).
tcf(c_61256,plain,
! [X0: $i] :
( aElementOf0(X0,iPr_def_10)
| ( X0 = xx )
| ~ aElementOf0(X0,xS) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5725,c_61249]) ).
tcf(c_61504,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_61256]) ).
tcf(c_61610,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_61504,c_86]) ).
tcf(c_65140,plain,
! [X0: $i] :
( aSubsetOf0(xS,X0)
| aElementOf0(sK5(X0,xS),iPr_def_11)
| ( sK5(X0,xS) = xx )
| ~ aSet0(X0) ),
inference(superposition,[status(thm)],[c_61610,c_6148]) ).
tcf(c_121088,plain,
( aSubsetOf0(xS,iPr_def_11)
| ( sK5(iPr_def_11,xS) = xx )
| ~ aSet0(iPr_def_11)
| ~ aSet0(xS) ),
inference(superposition,[status(thm)],[c_65140,c_54]) ).
tcf(c_121100,plain,
sK5(iPr_def_11,xS) = xx,
inference(forward_subsumption_resolution,[status(thm)],[c_121088,c_48087,c_5584,c_86]) ).
tcf(c_121168,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_121100,c_115475,c_48087,c_6746,c_5712,c_5578,c_5584,c_5376,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM535+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n009.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 04:29:34 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 32.43/12.37 % SZS status Started for theBenchmark.p
% 32.43/12.37 % SZS status Theorem for theBenchmark.p
% 32.43/12.37
% 32.43/12.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.43/12.37
% 32.43/12.37 % ------ iProver source info
% 32.43/12.37
% 32.43/12.37 % git: date: 2026-07-19 20:42:38 +0200
% 32.43/12.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.43/12.37 % git: non_committed_changes: false
% 32.43/12.37
% 32.43/12.37 % ------ Parsing...
% 32.43/12.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.43/12.37
% 32.43/12.37 % ------ 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 %
% 32.43/12.37
% 32.43/12.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 32.43/12.37
% 32.43/12.37 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.43/12.37 % ------ Proving...
% 32.43/12.37 % ------ Problem Properties
% 32.43/12.37
% 32.43/12.37 %
% 32.43/12.37 % clauses 38
% 32.43/12.37 % conjectures 1
% 32.43/12.37 % EPR 21
% 32.43/12.37 % Horn 28
% 32.43/12.37 % unary 6
% 32.43/12.37 % binary 5
% 32.43/12.37 % lits 117
% 32.43/12.37 % lits eq 12
% 32.43/12.37 % fd_pure 0
% 32.43/12.37 % fd_pseudo 0
% 32.43/12.37 % fd_cond 1
% 32.43/12.37 % fd_pseudo_cond 5
% 32.43/12.37 % AC symbols 0
% 32.43/12.37
% 32.43/12.37 % ------ Schedule dynamic 5 is on
% 32.43/12.37
% 32.43/12.37 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.43/12.37
% 32.43/12.37
% 32.43/12.37 % ------
% 32.43/12.37 % Current options:
% 32.43/12.37 % ------
% 32.43/12.37
% 32.43/12.37
% 32.43/12.37 %
% 32.43/12.37
% 32.43/12.37 % ------ Proving...
% 32.43/12.37 %
% 32.43/12.37
% 32.43/12.37 % SZS status Theorem for theBenchmark.p
% 32.43/12.37
% 32.43/12.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.43/12.38
% 32.43/12.38
%------------------------------------------------------------------------------