%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM542+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 02:25:56 PM UTC 2026
% Result : Theorem 63.74s 14.93s
% Output : CNFRefutation 63.74s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f294ERROR: Could not build tree for root c_68770ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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(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(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f26,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f28,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> X0 != szszuzczcdt0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f32,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTrans) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f53,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
<=> ( X0 = X1
| aElementOf0(X0,slbdtrb0(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegSucc) ).
fof(f54,axiom,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1964) ).
fof(f55,conjecture,
( sdtlseqdt0(xm,xn)
<=> aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
<=> aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f64,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f70,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f78,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(f79,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,[],[f78]) ).
fof(f82,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f93,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f26]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(ennf_transformation,[],[f27]) ).
fof(f97,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| X0 != szszuzczcdt0(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f109]) ).
fof(f128,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
<=> ( X0 = X1
| aElementOf0(X0,slbdtrb0(X1)) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f131,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
<=> ( X0 = X1
| aElementOf0(X0,slbdtrb0(X1)) ) ) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
( sdtlseqdt0(xm,xn)
<~> aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f143,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,[],[f70]) ).
fof(f144,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,[],[f143]) ).
fof(f145,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,[],[f144]) ).
fof(f146,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))],[f145]) ).
fof(f147,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,[],[f134]) ).
fof(f148,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,[],[f147]) ).
fof(f159,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(sK8(X0)) = X0
& aElementOf0(sK8(X0),szNzAzT0) )
| X0 = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f97]) ).
fof(f160,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( ( ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f172,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f173,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(flattening,[],[f172]) ).
fof(f174,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(rectify,[],[f173]) ).
fof(f175,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK12(X0,X1),X1)
| ( sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
& aElementOf0(sK12(X0,X1),szNzAzT0) ) )
& ( ~ aElementOf0(sK12(X0,X1),X1)
| ~ sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
| ~ aElementOf0(sK12(X0,X1),szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f174]) ).
fof(f176,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( ( ~ aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| X0 = X1
| aElementOf0(X0,slbdtrb0(X1)) )
& ( ( X0 != X1
& ~ aElementOf0(X0,slbdtrb0(X1)) )
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1))) ) ) ),
inference(nnf_transformation,[],[f131]) ).
fof(f177,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( ( ~ aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| X0 = X1
| aElementOf0(X0,slbdtrb0(X1)) )
& ( ( X0 != X1
& ~ aElementOf0(X0,slbdtrb0(X1)) )
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1))) ) ) ),
inference(flattening,[],[f176]) ).
fof(f178,plain,
( ( sdtlseqdt0(xm,xn)
| aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) )
& ( ~ sdtlseqdt0(xm,xn)
| ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f179,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f186,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f188,plain,
! [X0,X1] :
( ~ aSet0(X0)
| aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1)
| sdtpldt0(X1,X0) != X2
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f205,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f218,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f82]) ).
fof(f225,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f227,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sz00 != szszuzczcdt0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f228,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f229,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f95]) ).
fof(f230,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK8(X0)) = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f231,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sK8(X0),szNzAzT0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f159]) ).
fof(f232,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != X0 ),
inference(cnf_transformation,[],[f98]) ).
fof(f236,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f160]) ).
fof(f237,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f239,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f106]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f241,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f261,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X3,X1)
| sdtlseqdt0(szszuzczcdt0(X3),X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f262,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,szNzAzT0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f263,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f264,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f175]) ).
fof(f270,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| X0 = X1
| aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f177]) ).
fof(f272,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1))
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1))) ),
inference(cnf_transformation,[],[f177]) ).
fof(f273,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f54]) ).
fof(f274,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f54]) ).
fof(f275,plain,
( sdtlseqdt0(xm,xn)
| aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f276,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f280,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sP0(sdtpldt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f194]) ).
fof(f289,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(X0)) ),
inference(equality_resolution,[],[f264]) ).
fof(f290,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,slbdtrb0(X0)) ),
inference(equality_resolution,[],[f263]) ).
fof(f291,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| aElementOf0(X3,szNzAzT0) ),
inference(equality_resolution,[],[f262]) ).
fof(f292,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| sdtlseqdt0(szszuzczcdt0(X3),X0) ),
inference(equality_resolution,[],[f261]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aElementOf0(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(X0,X1)
| aElementOf0(sK5(X1,X0),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f280]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sP1(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtmndt0(X1,X0),X0) = X1 )
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_94,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f225]) ).
tcf(c_97,plain,
! [X0: $i] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_98,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00 ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(X1) ) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_100,plain,
! [X0: $i] :
( aElementOf0(sK8(X0),szNzAzT0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( szszuzczcdt0(sK8(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_102,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != X0 ) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_107,plain,
! [X0: $i] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X2,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_134,plain,
! [X0: $i] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_141,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(X1))
| ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1))) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_143,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f274]) ).
tcf(c_144,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f273]) ).
tcf(c_145,negated_conjecture,
( ~ sdtlseqdt0(xm,xn)
| ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_146,negated_conjecture,
( sdtlseqdt0(xm,xn)
| aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_140,c_136,c_140]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_1742,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_75,c_236]) ).
tcf(c_1743,plain,
! [X0: $i,X1: $i] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_1742]) ).
tcf(c_10644,plain,
( aSet0(slbdtrb0(xm))
| ~ aElementOf0(xm,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_10645,plain,
( aSet0(slbdtrb0(xn))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_10649,plain,
( sdtlseqdt0(xn,szszuzczcdt0(xn))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_10654,plain,
! [X0: $i] :
( sdtlseqdt0(xm,X0)
| sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_10682,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_10683,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_10685,plain,
( ~ aElementOf0(xm,szNzAzT0)
| ( szszuzczcdt0(xm) != sz00 ) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_10686,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ( szszuzczcdt0(xn) != sz00 ) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_10693,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ( szszuzczcdt0(xn) != xn ) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_11286,plain,
( ( szszuzczcdt0(xm) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(xm))) = szszuzczcdt0(xm) )
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_11288,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0)
| ( szszuzczcdt0(xm) = sz00 )
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_11343,plain,
( ( szszuzczcdt0(xn) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(xn))) = szszuzczcdt0(xn) )
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_11345,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0)
| ( szszuzczcdt0(xn) = sz00 )
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_11760,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(X0))) = szszuzczcdt0(X0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_101]) ).
tcf(c_12150,plain,
( ( szszuzczcdt0(xn) = xn )
| ~ aElementOf0(xn,szNzAzT0)
| ~ sdtlseqdt0(xn,szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_12545,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_10654]) ).
tcf(c_12645,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(xn),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xn,slbdtrb0(X0)) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_13062,plain,
! [X0: $i] :
( ( X0 = xm )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(xm) ) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_13142,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(xn) ) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_17291,plain,
( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),slbdtrb0(xm))
| ~ aSet0(slbdtrb0(xn))
| ~ aSet0(slbdtrb0(xm)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_17292,plain,
( aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
| ~ aSet0(slbdtrb0(xn))
| ~ aSet0(slbdtrb0(xm))
| ~ aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),slbdtrb0(xn)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_18040,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(X0))) = szszuzczcdt0(X0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_101]) ).
tcf(c_21059,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_21060,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_21621,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xn,slbdtrb0(xn)) ),
inference(instantiation,[status(thm)],[c_12645]) ).
tcf(c_21663,plain,
( ( sK8(szszuzczcdt0(xm)) = xm )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0)
| ( szszuzczcdt0(sK8(szszuzczcdt0(xm))) != szszuzczcdt0(xm) ) ),
inference(instantiation,[status(thm)],[c_13062]) ).
tcf(c_21732,plain,
( ( sK8(szszuzczcdt0(xn)) = xn )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0)
| ( szszuzczcdt0(sK8(szszuzczcdt0(xn))) != szszuzczcdt0(xn) ) ),
inference(instantiation,[status(thm)],[c_13142]) ).
tcf(c_22054,plain,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(sK8(szszuzczcdt0(X0))) = szszuzczcdt0(X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_18040,c_98,c_11760]) ).
tcf(c_22055,plain,
! [X0: $i] :
( ( szszuzczcdt0(sK8(szszuzczcdt0(X0))) = szszuzczcdt0(X0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(renaming,[status(thm)],[c_22054]) ).
tcf(c_22078,plain,
szszuzczcdt0(sK8(szszuzczcdt0(xm))) = szszuzczcdt0(xm),
inference(superposition,[status(thm)],[c_143,c_22055]) ).
tcf(c_22079,plain,
szszuzczcdt0(sK8(szszuzczcdt0(xn))) = szszuzczcdt0(xn),
inference(superposition,[status(thm)],[c_144,c_22055]) ).
tcf(c_22512,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_22078,c_141]) ).
tcf(c_22825,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),slbdtrb0(szszuzczcdt0(xn)))
| ~ aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_22079,c_141]) ).
tcf(c_26996,plain,
! [X0: $i] :
( aElement0(szszuzczcdt0(X0))
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_49]) ).
tcf(c_27001,plain,
! [X0: $i] :
( aElement0(szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26996,c_94]) ).
tcf(c_27022,plain,
aElement0(szszuzczcdt0(xm)),
inference(superposition,[status(thm)],[c_143,c_27001]) ).
tcf(c_27460,plain,
! [X0: $i] :
( ( sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(X0)),szszuzczcdt0(X0)) = szNzAzT0 )
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_88]) ).
tcf(c_27472,plain,
! [X0: $i] :
( ( sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(X0)),szszuzczcdt0(X0)) = szNzAzT0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27460,c_94]) ).
tcf(c_27635,plain,
sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(xm)),szszuzczcdt0(xm)) = szNzAzT0,
inference(superposition,[status(thm)],[c_143,c_27472]) ).
tcf(c_39974,plain,
( aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),slbdtrb0(xm)) ),
inference(instantiation,[status(thm)],[c_21060]) ).
tcf(c_39975,plain,
( sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(xn),slbdtrb0(xm))),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),slbdtrb0(xm)) ),
inference(instantiation,[status(thm)],[c_21059]) ).
tcf(c_40022,plain,
( aElementOf0(szszuzczcdt0(sK5(slbdtrb0(xn),slbdtrb0(xm))),szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_40192,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ sdtlseqdt0(X1,xn)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_44647,plain,
aSet0(slbdtrb0(xn)),
inference(superposition,[status(thm)],[c_144,c_134]) ).
tcf(c_44669,plain,
! [X0: $i] :
( aElement0(szszuzczcdt0(X0))
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_49]) ).
tcf(c_44674,plain,
! [X0: $i] :
( aElement0(szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44669,c_94]) ).
tcf(c_44695,plain,
aElement0(szszuzczcdt0(xm)),
inference(superposition,[status(thm)],[c_143,c_44674]) ).
tcf(c_44696,plain,
aElement0(szszuzczcdt0(xn)),
inference(superposition,[status(thm)],[c_144,c_44674]) ).
tcf(c_45195,plain,
! [X0: $i] :
( ( sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(X0)),szszuzczcdt0(X0)) = szNzAzT0 )
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_88]) ).
tcf(c_45207,plain,
! [X0: $i] :
( ( sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(X0)),szszuzczcdt0(X0)) = szNzAzT0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45195,c_94]) ).
tcf(c_45483,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| aElementOf0(X0,slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_111,c_135]) ).
tcf(c_47026,plain,
sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(xm)),szszuzczcdt0(xm)) = szNzAzT0,
inference(superposition,[status(thm)],[c_143,c_45207]) ).
tcf(c_47027,plain,
sdtpldt0(sdtmndt0(szNzAzT0,szszuzczcdt0(xn)),szszuzczcdt0(xn)) = szNzAzT0,
inference(superposition,[status(thm)],[c_144,c_45207]) ).
tcf(c_53735,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_40192]) ).
tcf(c_62217,plain,
( sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(xn),slbdtrb0(xm))),xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(xn),slbdtrb0(xm))),xm)
| ~ aElementOf0(szszuzczcdt0(sK5(slbdtrb0(xn),slbdtrb0(xm))),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_53735]) ).
tcf(c_68769,plain,
( aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),slbdtrb0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(sK5(slbdtrb0(xn),slbdtrb0(xm)),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK5(slbdtrb0(xn),slbdtrb0(xm))),xn) ),
inference(instantiation,[status(thm)],[c_135]) ).
fof(f133,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(f134,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(f135,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP1(X1,X0) ),
inference(definition_folding,[],[f79,f134,f133]) ).
fof(f149,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,[],[f133]) ).
fof(f150,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,[],[f149]) ).
fof(f151,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,[],[f150]) ).
fof(f152,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))],[f151]) ).
fof(f198,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| X2 != X4
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f281,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f198]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,X0)
| ~ aElement0(X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f281]) ).
tcf(c_27221,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_1743,c_72]) ).
tcf(c_27918,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElement0(szszuzczcdt0(xm))
| ~ aSet0(sdtmndt0(szNzAzT0,szszuzczcdt0(xm))) ),
inference(superposition,[status(thm)],[c_27635,c_27221]) ).
tcf(c_27922,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aSet0(sdtmndt0(szNzAzT0,szszuzczcdt0(xm))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27918,c_27022]) ).
tcf(c_28516,plain,
aElementOf0(szszuzczcdt0(xm),szNzAzT0),
inference(global_subsumption_just,[status(thm)],[c_27922,c_143,c_10682]) ).
tcf(c_28524,plain,
( ( szszuzczcdt0(xm) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(xm))) = szszuzczcdt0(xm) ) ),
inference(superposition,[status(thm)],[c_28516,c_101]) ).
tcf(c_30078,plain,
szszuzczcdt0(sK8(szszuzczcdt0(xm))) = szszuzczcdt0(xm),
inference(global_subsumption_just,[status(thm)],[c_28524,c_143,c_10682,c_10685,c_11286]) ).
tcf(c_30084,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(sK8(szszuzczcdt0(xm)))) ),
inference(superposition,[status(thm)],[c_30078,c_216]) ).
tcf(c_30096,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_30078,c_141]) ).
tcf(c_30789,plain,
aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(szszuzczcdt0(xm))),
inference(global_subsumption_just,[status(thm)],[c_30096,c_143,c_10682,c_10685,c_11288,c_22512]) ).
tcf(c_30796,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(superposition,[status(thm)],[c_30789,c_136]) ).
tcf(c_30797,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(xm))
| ( sK8(szszuzczcdt0(xm)) = xm )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_30789,c_142]) ).
tcf(c_30798,plain,
aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[c_30796,c_28516]) ).
tcf(c_30801,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(xm))
| ( sK8(szszuzczcdt0(xm)) = xm )
| ~ aElementOf0(xm,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30797,c_30798]) ).
tcf(c_30802,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(xm))
| ( sK8(szszuzczcdt0(xm)) = xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30801,c_143]) ).
tcf(c_30810,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(X0,slbdtrb0(sK8(szszuzczcdt0(xm)))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_30084,c_30798]) ).
tcf(c_32058,plain,
sK8(szszuzczcdt0(xm)) = xm,
inference(global_subsumption_just,[status(thm)],[c_30802,c_143,c_10682,c_10685,c_11288,c_11286,c_21663]) ).
tcf(c_32090,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(light_normalisation,[status(thm)],[c_30810,c_32058]) ).
tcf(c_32103,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(xm))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(superposition,[status(thm)],[c_32090,c_137]) ).
tcf(c_32104,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(superposition,[status(thm)],[c_32090,c_136]) ).
tcf(c_32107,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32104,c_28516]) ).
tcf(c_32108,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(xm))
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32103,c_28516]) ).
tcf(c_32795,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(superposition,[status(thm)],[c_32108,c_105]) ).
tcf(c_32798,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32795,c_143]) ).
tcf(c_33061,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(global_subsumption_just,[status(thm)],[c_32798,c_32107,c_32798]) ).
tcf(c_44965,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtpldt0(X1,X0))
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(superposition,[status(thm)],[c_1743,c_72]) ).
tcf(c_47060,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElement0(szszuzczcdt0(xm))
| ~ aSet0(sdtmndt0(szNzAzT0,szszuzczcdt0(xm))) ),
inference(superposition,[status(thm)],[c_47026,c_44965]) ).
tcf(c_47064,plain,
( aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aSet0(sdtmndt0(szNzAzT0,szszuzczcdt0(xm))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47060,c_44695]) ).
tcf(c_47171,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElement0(szszuzczcdt0(xn))
| ~ aSet0(sdtmndt0(szNzAzT0,szszuzczcdt0(xn))) ),
inference(superposition,[status(thm)],[c_47027,c_44965]) ).
tcf(c_47175,plain,
( aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aSet0(sdtmndt0(szNzAzT0,szszuzczcdt0(xn))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47171,c_44696]) ).
tcf(c_47246,plain,
aElementOf0(szszuzczcdt0(xm),szNzAzT0),
inference(global_subsumption_just,[status(thm)],[c_47064,c_143,c_10682]) ).
tcf(c_47254,plain,
( ( szszuzczcdt0(xm) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(xm))) = szszuzczcdt0(xm) ) ),
inference(superposition,[status(thm)],[c_47246,c_101]) ).
tcf(c_47341,plain,
szszuzczcdt0(sK8(szszuzczcdt0(xm))) = szszuzczcdt0(xm),
inference(global_subsumption_just,[status(thm)],[c_47254,c_143,c_10682,c_10685,c_11286]) ).
tcf(c_47347,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(sK8(szszuzczcdt0(xm)))) ),
inference(superposition,[status(thm)],[c_47341,c_216]) ).
tcf(c_47358,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_47341,c_141]) ).
tcf(c_47371,plain,
aElementOf0(szszuzczcdt0(xn),szNzAzT0),
inference(global_subsumption_just,[status(thm)],[c_47175,c_144,c_10683]) ).
tcf(c_47379,plain,
( ( szszuzczcdt0(xn) = sz00 )
| ( szszuzczcdt0(sK8(szszuzczcdt0(xn))) = szszuzczcdt0(xn) ) ),
inference(superposition,[status(thm)],[c_47371,c_101]) ).
tcf(c_47470,plain,
szszuzczcdt0(sK8(szszuzczcdt0(xn))) = szszuzczcdt0(xn),
inference(global_subsumption_just,[status(thm)],[c_47379,c_144,c_10683,c_10686,c_11343]) ).
tcf(c_47481,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(xn),X0)
| sdtlseqdt0(X0,sK8(szszuzczcdt0(xn)))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_47470,c_111]) ).
tcf(c_47487,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),slbdtrb0(szszuzczcdt0(xn)))
| ~ aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_47470,c_141]) ).
tcf(c_47999,plain,
aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(szszuzczcdt0(xm))),
inference(global_subsumption_just,[status(thm)],[c_47358,c_143,c_10682,c_10685,c_11288,c_22512]) ).
tcf(c_48006,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(superposition,[status(thm)],[c_47999,c_136]) ).
tcf(c_48007,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(xm))
| ( sK8(szszuzczcdt0(xm)) = xm )
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_47999,c_142]) ).
tcf(c_48008,plain,
aElementOf0(sK8(szszuzczcdt0(xm)),szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[c_48006,c_47246]) ).
tcf(c_48011,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(xm))
| ( sK8(szszuzczcdt0(xm)) = xm )
| ~ aElementOf0(xm,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48007,c_48008]) ).
tcf(c_48012,plain,
( aElementOf0(sK8(szszuzczcdt0(xm)),slbdtrb0(xm))
| ( sK8(szszuzczcdt0(xm)) = xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48011,c_143]) ).
tcf(c_48020,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(X0,slbdtrb0(sK8(szszuzczcdt0(xm)))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_47347,c_48008]) ).
tcf(c_48157,plain,
aElementOf0(sK8(szszuzczcdt0(xn)),slbdtrb0(szszuzczcdt0(xn))),
inference(global_subsumption_just,[status(thm)],[c_47487,c_144,c_10683,c_10686,c_11345,c_22825]) ).
tcf(c_48164,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_48157,c_136]) ).
tcf(c_48165,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),slbdtrb0(xn))
| ( sK8(szszuzczcdt0(xn)) = xn )
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0) ),
inference(superposition,[status(thm)],[c_48157,c_142]) ).
tcf(c_48166,plain,
aElementOf0(sK8(szszuzczcdt0(xn)),szNzAzT0),
inference(forward_subsumption_resolution,[status(thm)],[c_48164,c_47371]) ).
tcf(c_48169,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),slbdtrb0(xn))
| ( sK8(szszuzczcdt0(xn)) = xn )
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48165,c_48166]) ).
tcf(c_48170,plain,
( aElementOf0(sK8(szszuzczcdt0(xn)),slbdtrb0(xn))
| ( sK8(szszuzczcdt0(xn)) = xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48169,c_144]) ).
tcf(c_48174,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(xn),X0)
| sdtlseqdt0(X0,sK8(szszuzczcdt0(xn)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_47481,c_48166]) ).
tcf(c_48686,plain,
sK8(szszuzczcdt0(xm)) = xm,
inference(global_subsumption_just,[status(thm)],[c_48012,c_143,c_10682,c_10685,c_11288,c_11286,c_21663]) ).
tcf(c_48785,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(xm)))
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(light_normalisation,[status(thm)],[c_48020,c_48686]) ).
tcf(c_48798,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(xm))
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(superposition,[status(thm)],[c_48785,c_137]) ).
tcf(c_48803,plain,
! [X0: $i] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(xm))
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48798,c_47246]) ).
tcf(c_48901,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(superposition,[status(thm)],[c_48803,c_105]) ).
tcf(c_48904,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48901,c_143]) ).
tcf(c_48946,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(global_subsumption_just,[status(thm)],[c_48904,c_33061]) ).
tcf(c_49022,plain,
sK8(szszuzczcdt0(xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_48170,c_144,c_10683,c_10686,c_11345,c_11343,c_21732]) ).
tcf(c_49631,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xn)
| sdtlseqdt0(szszuzczcdt0(xn),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(light_normalisation,[status(thm)],[c_48174,c_49022]) ).
tcf(c_51938,plain,
! [X0: $i] :
( sdtlseqdt0(xm,X0)
| sdtlseqdt0(X0,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_45483,c_48946]) ).
tcf(c_51954,plain,
! [X0: $i] :
( sdtlseqdt0(xm,X0)
| sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51938,c_143]) ).
tcf(c_52101,plain,
( sdtlseqdt0(xm,szszuzczcdt0(xn))
| sdtlseqdt0(szszuzczcdt0(xn),xm) ),
inference(superposition,[status(thm)],[c_47371,c_51954]) ).
tcf(c_52166,plain,
( sdtlseqdt0(xm,szszuzczcdt0(xn))
| aElementOf0(xn,slbdtrb0(xm))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_52101,c_135]) ).
tcf(c_52167,plain,
( sdtlseqdt0(xm,szszuzczcdt0(xn))
| aElementOf0(xn,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52166,c_144,c_143]) ).
tcf(c_52174,plain,
( aElementOf0(xn,slbdtrb0(xm))
| ( szszuzczcdt0(xn) = xm )
| ~ aElementOf0(xm,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(superposition,[status(thm)],[c_52167,c_109]) ).
tcf(c_52175,plain,
( aElementOf0(xn,slbdtrb0(xm))
| ( szszuzczcdt0(xn) = xm )
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52174,c_143,c_47371]) ).
tcf(c_52340,plain,
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,slbdtrb0(xm))
| ( szszuzczcdt0(xn) = xm )
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_49631,c_52175]) ).
tcf(c_52342,plain,
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,slbdtrb0(xm))
| ( szszuzczcdt0(xn) = xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52340,c_143]) ).
tcf(c_52769,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ( szszuzczcdt0(xn) = xm )
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_52342,c_137]) ).
tcf(c_52774,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ( szszuzczcdt0(xn) = xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52769,c_143]) ).
tcf(c_52789,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm) ),
inference(global_subsumption_just,[status(thm)],[c_52774,c_144,c_143,c_12545]) ).
tcf(c_52794,plain,
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,slbdtrb0(xm))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[status(thm)],[c_52789,c_135]) ).
tcf(c_52796,plain,
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,slbdtrb0(xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52794,c_144,c_143]) ).
tcf(c_52802,plain,
! [X0: $i] :
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(slbdtrb0(xm),X0) ),
inference(superposition,[status(thm)],[c_52796,c_59]) ).
tcf(c_54723,plain,
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,slbdtrb0(xn))
| ~ aSet0(slbdtrb0(xn)) ),
inference(superposition,[status(thm)],[c_146,c_52802]) ).
tcf(c_54725,plain,
( sdtlseqdt0(xm,xn)
| aElementOf0(xn,slbdtrb0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54723,c_44647]) ).
tcf(c_68770,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_68769,c_62217,c_54725,c_40022,c_39974,c_39975,c_21621,c_17292,c_17291,c_12150,c_10693,c_10683,c_10649,c_10645,c_10644,c_145,c_143,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM542+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.40 % Computer : n015.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.11/5.40 % CPULimit : 300
% 0.15/5.40 % WCLimit : 300
% 0.15/5.40 % DateTime : Thu Sep 24 04:35:16 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 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
% 0.15/5.45
% 0.15/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.45
% 0.15/5.45 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 63.74/14.93 % SZS status Started for theBenchmark.p
% 63.74/14.93 % SZS status Theorem for theBenchmark.p
% 63.74/14.93
% 63.74/14.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 63.74/14.93
% 63.74/14.93 % ------ iProver source info
% 63.74/14.93
% 63.74/14.93 % git: date: 2026-07-19 20:42:38 +0200
% 63.74/14.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 63.74/14.93 % git: non_committed_changes: false
% 63.74/14.93
% 63.74/14.93 % ------ Parsing...
% 63.74/14.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 63.74/14.93
% 63.74/14.93 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 63.74/14.93
% 63.74/14.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 63.74/14.93
% 63.74/14.93 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 63.74/14.93 % ------ Proving...
% 63.74/14.93 % ------ Problem Properties
% 63.74/14.93
% 63.74/14.93 %
% 63.74/14.93 % clauses 96
% 63.74/14.93 % conjectures 2
% 63.74/14.93 % EPR 31
% 63.74/14.93 % Horn 68
% 63.74/14.93 % unary 11
% 63.74/14.93 % binary 17
% 63.74/14.93 % lits 320
% 63.74/14.93 % lits eq 46
% 63.74/14.93 % fd_pure 0
% 63.74/14.93 % fd_pseudo 0
% 63.74/14.93 % fd_cond 8
% 63.74/14.93 % fd_pseudo_cond 15
% 63.74/14.93 % AC symbols 0
% 63.74/14.93
% 63.74/14.93 % ------ Input Options Time Limit: Unbounded
% 63.74/14.93
% 63.74/14.93
% 63.74/14.93 % ------
% 63.74/14.93 % Current options:
% 63.74/14.93 % ------
% 63.74/14.93
% 63.74/14.93
% 63.74/14.93 %
% 63.74/14.93
% 63.74/14.93 % ------ Proving...
% 63.74/14.93 %
% 63.74/14.93
% 63.74/14.93 % SZS status Theorem for theBenchmark.p
% 63.74/14.93
% 63.74/14.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 63.74/14.94
% 63.74/14.94
%------------------------------------------------------------------------------