%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM541+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Thu Sep 24 01:40:56 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 50
% Syntax : Number of formulae : 203 ( 17 unt; 35 def)
% Number of atoms : 769 ( 89 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 952 ( 386 ~; 392 |; 108 &)
% ( 45 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 40 ( 38 usr; 32 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 189 ( 180 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
<=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,szszuzczcdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [W0,W1,W2] :
( ( aElementOf0(W2,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W2)
& sdtlseqdt0(W0,W1) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,definition,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> isFinite0(slbdtrb0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
( aElementOf0(xn,szNzAzT0)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,conjecture,
( ( ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) )
=> ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) )
& ( ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
=> ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
~ ( ( ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) )
=> ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) )
& ( ( aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
=> ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f62,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f63,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f66,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f67,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
( ! [W0] :
( aElementOf0(sK0_skl(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f68]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f77,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [W0] :
( ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) ) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f81,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ aElementOf0(W2,W0)
& aElementOf0(W2,W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [W0] :
( ( ! [W1] :
( ( ~ aElementOf0(sK1_skl(W1,W0),W0)
& aElementOf0(sK1_skl(W1,W0),W1) )
| ~ aSet0(W1)
| aSubsetOf0(W1,W0) )
& ! [W1] :
( ( ! [W2] :
( aElementOf0(W2,W0)
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| ~ aSubsetOf0(W1,W0) ) )
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f82]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f96,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f97,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ( ( ! [W3] :
( ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f97]) ).
fof(f99,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( ( sK2_skl(W2,W1,W0) = W1
| aElementOf0(sK2_skl(W2,W1,W0),W0) )
& aElement0(sK2_skl(W2,W1,W0)) )
| aElementOf0(sK2_skl(W2,W1,W0),W2) )
& ( ( sK2_skl(W2,W1,W0) != W1
& ~ aElementOf0(sK2_skl(W2,W1,W0),W0) )
| ~ aElement0(sK2_skl(W2,W1,W0))
| ~ aElementOf0(sK2_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W3,sK2_skl(W2,W1,W0))],[f98]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aElement0(sK2_skl(X2,X1,X0))
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f106,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) != X1
| ~ aElement0(sK2_skl(X2,X1,X0))
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f132,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f133,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f134,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f135,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f136,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f144,plain,
! [W0] :
( W0 != szszuzczcdt0(W0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f145,plain,
! [X0] :
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f152,plain,
! [W0,W1] :
( ( sdtlseqdt0(W0,W1)
<=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f153,plain,
! [W0,W1] :
( ( ( ~ sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1))
| sdtlseqdt0(W0,W1) )
& ( sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1))
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f152]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f156,plain,
! [W0] :
( sdtlseqdt0(W0,szszuzczcdt0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f157,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f160,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f161,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [W0,W1,W2] :
( sdtlseqdt0(W0,W2)
| ~ sdtlseqdt0(W1,W2)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f163,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [W0,W1] :
( sdtlseqdt0(szszuzczcdt0(W1),W0)
| sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f165,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f208,plain,
! [W0] :
( ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) ) )
& aSet0(W1) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f209,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ( ( ! [W2] :
( ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| aElementOf0(W2,W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ! [W1] :
( ( ! [W2] :
( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(miniscoping,[status(thm)],[f209]) ).
fof(f211,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtlseqdt0(szszuzczcdt0(sK8_skl(W1,W0)),W0)
& aElementOf0(sK8_skl(W1,W0),szNzAzT0) )
| aElementOf0(sK8_skl(W1,W0),W1) )
& ( ~ sdtlseqdt0(szszuzczcdt0(sK8_skl(W1,W0)),W0)
| ~ aElementOf0(sK8_skl(W1,W0),szNzAzT0)
| ~ aElementOf0(sK8_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slbdtrb0(W0) )
& ! [W1] :
( ( ! [W2] :
( ~ sdtlseqdt0(szszuzczcdt0(W2),W0)
| ~ aElementOf0(W2,szNzAzT0)
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtlseqdt0(szszuzczcdt0(W2),W0)
& aElementOf0(W2,szNzAzT0) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slbdtrb0(W0) ) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W2,sK8_skl(W1,W0))],[f210]) ).
fof(f212,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f213,plain,
! [X0,X1,X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f214,plain,
! [X0,X1,X2] :
( sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f215,plain,
! [X0,X1,X2] :
( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1)
| X1 != slbdtrb0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f219,plain,
! [W0] :
( isFinite0(slbdtrb0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f220,plain,
! [X0] :
( isFinite0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f221,plain,
slbdtrb0(sz00) = slcrc0,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f222,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f223,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f224,plain,
( ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) )
| ( xm != xn
& ~ aElementOf0(xm,slbdtrb0(xn))
& ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f225,definition,
( sP1_prd
<=> ( xm != xn
& ~ aElementOf0(xm,slbdtrb0(xn))
& ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f226,plain,
( ( ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
& ( xm = xn
| ( aElementOf0(xm,slbdtrb0(xn))
& sdtlseqdt0(szszuzczcdt0(xm),xn) ) ) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f224,f225]) ).
fof(f227,plain,
( xm = xn
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f229,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f237,plain,
( ( xm = xn
| aElementOf0(xm,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| sP1_prd )
& ( ( xm != xn
& ~ aElementOf0(xm,slbdtrb0(xn))
& ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
& aElementOf0(xm,slbdtrb0(szszuzczcdt0(xn)))
& sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f225]) ).
fof(f238,plain,
( sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f242,plain,
( xm != xn
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f244,definition,
( sQ0_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f247,definition,
( sQ1_spl
<=> sdtlseqdt0(szszuzczcdt0(xm),xn) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ1_spl
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
( sQ2_spl
<=> xm = xn ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ2_spl
| xm = xn ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f227,f244,f247,f250]) ).
fof(f258,definition,
( sQ4_spl
<=> sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ4_spl
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn)) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f229,f244,f258]) ).
fof(f266,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f238,f244,f258]) ).
fof(f268,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f240,f244,f247]) ).
fof(f270,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f242,f244,f250]) ).
fof(f273,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f71]) ).
fof(f289,plain,
! [X0] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f212]) ).
fof(f290,plain,
! [X0,X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f213]) ).
fof(f291,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f214]) ).
fof(f292,plain,
! [X0,X1] :
( ~ sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f215]) ).
fof(f296,plain,
( ~ aSet0(slcrc0)
| slcrc0 = slcrc0 ),
inference(resolution,[status(thm)],[f72,f273]) ).
fof(f297,definition,
( sQ6_spl
<=> slcrc0 = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f300,definition,
( sQ7_spl
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f296,f297,f300]) ).
fof(f307,plain,
xm != szszuzczcdt0(xm),
inference(resolution,[status(thm)],[f145,f222]) ).
fof(f314,definition,
( sQ10_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ10_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f318,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f132]) ).
fof(f319,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( ~ isFinite0(szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f77,f133]) ).
fof(f322,definition,
( sQ11_spl
<=> isFinite0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f321,f314,f322]) ).
fof(f328,definition,
( sQ12_spl
<=> aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ12_spl
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ13_spl
<=> aElementOf0(xn,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ13_spl
| ~ aElementOf0(xn,szNzAzT0) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f346,definition,
( sQ16_spl
<=> aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ16_spl
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f353,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f223]) ).
fof(f354,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f355,plain,
( sQ12_spl
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f330,f136]) ).
fof(f356,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f222]) ).
fof(f357,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f389,plain,
( sQ16_spl
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[f348,f136]) ).
fof(f390,plain,
( sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f389,f331,f346]) ).
fof(f396,plain,
( aSet0(slcrc0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f221,f289]) ).
fof(f397,definition,
( sQ20_spl
<=> aElementOf0(sz00,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ20_spl
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,plain,
( sQ7_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f396,f397,f300]) ).
fof(f401,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f134]) ).
fof(f402,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f416,plain,
( sQ1_spl
| sdtlseqdt0(xn,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[f165,f249]) ).
fof(f419,definition,
( sQ23_spl
<=> aElementOf0(xm,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( sQ23_spl
| ~ aElementOf0(xm,szNzAzT0) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,definition,
( sQ24_spl
<=> sdtlseqdt0(xn,xm) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( ~ sQ24_spl
| sdtlseqdt0(xn,xm) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( sQ1_spl
| sQ24_spl
| ~ sQ23_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f416,f331,f419,f422,f247]) ).
fof(f434,definition,
( sQ25_spl
<=> sdtlseqdt0(xm,szszuzczcdt0(xm)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ25_spl
| sdtlseqdt0(xm,szszuzczcdt0(xm)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( sQ25_spl
| ~ sdtlseqdt0(xm,szszuzczcdt0(xm)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ26_spl
<=> xm = szszuzczcdt0(xm) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ26_spl
| xm = szszuzczcdt0(xm) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f441,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f421,f222]) ).
fof(f442,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f443,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f307]) ).
fof(f444,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f448,plain,
( sQ4_spl
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(resolution,[status(thm)],[f260,f165]) ).
fof(f449,plain,
! [X0] :
( sQ4_spl
| ~ sdtlseqdt0(X0,szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolution,[status(thm)],[f260,f163]) ).
fof(f451,definition,
( sQ27_spl
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ27_spl
| ~ sdtlseqdt0(xm,xn) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f455,definition,
( sQ28_spl
<=> sdtlseqdt0(szszuzczcdt0(xn),xm) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ28_spl
| sdtlseqdt0(szszuzczcdt0(xn),xm) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( sQ4_spl
| sQ28_spl
| ~ sQ23_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f448,f346,f419,f455,f258]) ).
fof(f459,definition,
! [X0] :
( sQ29_spl
<=> ( ~ sdtlseqdt0(X0,szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f460,plain,
! [X0] :
( ~ sQ29_spl
| ~ sdtlseqdt0(X0,szszuzczcdt0(xn))
| ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( sQ4_spl
| ~ sQ16_spl
| sQ29_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f449,f328,f459,f346,f258]) ).
fof(f468,plain,
! [X0,X1] :
( ~ aSet0(X1)
| aSubsetOf0(X1,szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(sK1_skl(X1,szNzAzT0),slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f290,f87]) ).
fof(f470,definition,
! [X0,X1] :
( sQ31_spl
<=> ( ~ aSet0(X1)
| aSubsetOf0(X1,szNzAzT0)
| ~ aElementOf0(sK1_skl(X1,szNzAzT0),slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ10_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f468,f470,f314]) ).
fof(f479,plain,
( sQ27_spl
| ~ sdtlseqdt0(szszuzczcdt0(xm),szszuzczcdt0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f453,f155]) ).
fof(f484,plain,
( sQ27_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f479,f419,f331,f258,f451]) ).
fof(f499,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(X2,X1,X0),X0)
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f63]) ).
fof(f501,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(szNzAzT0,X1,X0),slbdtrb0(X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(sK2_skl(szNzAzT0,X1,X0),X0)
| ~ aSet0(szNzAzT0)
| szNzAzT0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f499,f290]) ).
fof(f503,definition,
! [X0,X1,X2] :
( sQ35_spl
<=> ( ~ aElementOf0(sK2_skl(szNzAzT0,X1,X0),slbdtrb0(X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(sK2_skl(szNzAzT0,X1,X0),X0)
| szNzAzT0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ10_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f501,f503,f314]) ).
fof(f507,plain,
( sQ25_spl
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f436,f157]) ).
fof(f510,plain,
( sQ25_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f507,f419,f434]) ).
fof(f523,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slcrc0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f221,f292]) ).
fof(f526,definition,
! [X0] :
( sQ38_spl
<=> ( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slcrc0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ38_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f523,f397,f526]) ).
fof(f531,plain,
( isFinite0(slcrc0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f221,f220]) ).
fof(f532,definition,
( sQ39_spl
<=> isFinite0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ39_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f531,f397,f532]) ).
fof(f536,plain,
( ~ sQ24_spl
| xm = xn
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f423,f161]) ).
fof(f537,plain,
( ~ sQ24_spl
| sQ2_spl
| ~ sQ27_spl
| ~ sQ13_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f536,f419,f331,f451,f250,f422]) ).
fof(f542,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) != X1
| ~ aElementOf0(sK2_skl(X2,X1,X0),X2)
| ~ aSet0(X2)
| X2 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f63]) ).
fof(f545,plain,
! [X0,X1,X2] :
( ~ aElementOf0(sK2_skl(szNzAzT0,X1,X0),slbdtrb0(X2))
| ~ aElementOf0(X2,szNzAzT0)
| sK2_skl(szNzAzT0,X1,X0) != X1
| ~ aSet0(szNzAzT0)
| szNzAzT0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f542,f290]) ).
fof(f548,definition,
! [X0,X1,X2] :
( sQ40_spl
<=> ( ~ aElementOf0(sK2_skl(szNzAzT0,X1,X0),slbdtrb0(X2))
| ~ aElementOf0(X2,szNzAzT0)
| sK2_skl(szNzAzT0,X1,X0) != X1
| szNzAzT0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( ~ sQ10_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f545,f548,f314]) ).
fof(f564,plain,
( ~ sQ25_spl
| szszuzczcdt0(xm) = xm
| ~ sdtlseqdt0(szszuzczcdt0(xm),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolution,[status(thm)],[f435,f161]) ).
fof(f565,definition,
( sQ41_spl
<=> sdtlseqdt0(szszuzczcdt0(xm),xm) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ41_spl
| ~ sdtlseqdt0(szszuzczcdt0(xm),xm) ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,plain,
( ~ sQ25_spl
| sQ26_spl
| ~ sQ41_spl
| ~ sQ23_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f564,f328,f419,f565,f437,f434]) ).
fof(f601,plain,
( sQ41_spl
| ~ aElementOf0(xm,slbdtrb0(xm))
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f567,f291]) ).
fof(f602,plain,
( sQ41_spl
| sdtlseqdt0(xm,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f567,f165]) ).
fof(f603,plain,
! [X0] :
( sQ41_spl
| ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolution,[status(thm)],[f567,f163]) ).
fof(f604,plain,
( sQ41_spl
| ~ sdtlseqdt0(szszuzczcdt0(szszuzczcdt0(xm)),szszuzczcdt0(xm))
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xm),szNzAzT0) ),
inference(resolution,[status(thm)],[f567,f155]) ).
fof(f605,definition,
( sQ46_spl
<=> aElementOf0(xm,slbdtrb0(xm)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ41_spl
| ~ sQ46_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f601,f419,f605,f565]) ).
fof(f609,definition,
( sQ47_spl
<=> sdtlseqdt0(xm,xm) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f610,plain,
( ~ sQ47_spl
| sdtlseqdt0(xm,xm) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,plain,
( sQ41_spl
| sQ47_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f602,f419,f609,f565]) ).
fof(f613,definition,
! [X0] :
( sQ48_spl
<=> ( ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(szszuzczcdt0(xm),X0)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( sQ41_spl
| ~ sQ23_spl
| sQ48_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f603,f328,f613,f419,f565]) ).
fof(f617,definition,
( sQ49_spl
<=> sdtlseqdt0(szszuzczcdt0(szszuzczcdt0(xm)),szszuzczcdt0(xm)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f620,plain,
( sQ41_spl
| ~ sQ49_spl
| ~ sQ23_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f604,f328,f419,f617,f565]) ).
fof(f621,plain,
( ~ sQ47_spl
| xm = xm
| ~ sdtlseqdt0(xm,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[f610,f161]) ).
fof(f622,definition,
( sQ50_spl
<=> xm = xm ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( sQ50_spl
| ~ sQ47_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f621,f419,f609,f622]) ).
fof(f642,plain,
( ~ sQ29_spl
| ~ aElementOf0(xn,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(xm),xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[f460,f157]) ).
fof(f658,plain,
( ~ sQ29_spl
| ~ sQ1_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f642,f331,f247,f459]) ).
fof(f675,plain,
( ~ sQ28_spl
| ~ sQ2_spl
| sdtlseqdt0(szszuzczcdt0(xm),xm) ),
inference(backward_demodulation,[status(thm)],[f251,f456]) ).
fof(f682,plain,
( ~ sQ28_spl
| ~ sQ2_spl
| sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f567]) ).
fof(f683,plain,
( ~ sQ28_spl
| ~ sQ2_spl
| sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f682]) ).
fof(f684,plain,
$false,
inference(sat_refutation,[status(thm)],[f253,f261,f266,f268,f270,f303,f319,f325,f354,f357,f390,f400,f402,f425,f442,f444,f458,f462,f473,f484,f506,f510,f529,f535,f537,f551,f568,f608,f612,f616,f620,f625,f658,f683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM541+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:39:11 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.068423 seconds
% 0.11/0.44 % CPU time: 0.291634 seconds
% 0.11/0.44 % Total memory used: 109.559 MB
% 0.11/0.44 % Net memory used: 109.192 MB
%------------------------------------------------------------------------------