%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 01:40:54 PM UTC 2026
% Result : Theorem 0.03s 0.40s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 56
% Syntax : Number of formulae : 252 ( 16 unt; 50 def)
% Number of atoms : 1185 ( 163 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 1485 ( 552 ~; 603 |; 232 &)
% ( 79 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 54 ( 52 usr; 45 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 300 ( 278 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
( aSet0(xS)
& aElement0(xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
~ aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
( ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ( ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
=> aElementOf0(W0,xS) ) ) ) )
& ( ( ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f28,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,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))],[f34]) ).
fof(f36,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0] :
( aElementOf0(sK0_skl(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f42,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f48,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)],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f62,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(f63,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)],[f62]) ).
fof(f64,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)],[f63]) ).
fof(f65,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))],[f64]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( aElement0(X3)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f74,plain,
! [X0,X1,X2] :
( sK2_skl(X2,X1,X0) = X1
| 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(cnf_transformation,[status(thm)],[f65]) ).
fof(f75,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(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)],[f16]) ).
fof(f76,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f77,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> sP0_prd(W3,W1,W0) )
& aSet0(W2) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f75,f76]) ).
fof(f78,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ~ sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ( ( ! [W3] :
( ( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ~ sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP0_prd(sK3_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK3_skl(W2,W1,W0),W2) )
& ( ~ sP0_prd(sK3_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK3_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtmndt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ~ sP0_prd(W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP0_prd(W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtmndt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f79]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X3,X1,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X3,X1,X0)
| aElementOf0(X3,X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f88,plain,
aElement0(xx),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f89,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f90,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f91,plain,
( ( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) )
| ( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f92,definition,
( sP1_prd
<=> ( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f93,plain,
( ( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) )
| sP1_prd ),
inference(formula_renaming,[status(thm)],[f91,f92]) ).
fof(f94,plain,
( ( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,sdtpldt0(xS,xx))
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ( ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) ) )
& aSet0(sdtpldt0(xS,xx)) )
| sP1_prd ),
inference(NNF_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
( ( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,sdtpldt0(xS,xx))
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) )
& aSet0(sdtpldt0(xS,xx)) )
| sP1_prd ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f96,plain,
( ( ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
& ~ aElementOf0(sK4_skl,xS)
& aElementOf0(sK4_skl,sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,sdtpldt0(xS,xx))
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) )
& aSet0(sdtpldt0(xS,xx)) )
| sP1_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(W0,sK4_skl)],[f95]) ).
fof(f97,plain,
( aSet0(sdtpldt0(xS,xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f99,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f101,plain,
! [X0] :
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f107,plain,
( aElementOf0(sK4_skl,sdtmndt0(sdtpldt0(xS,xx),xx))
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f108,plain,
( ~ aElementOf0(sK4_skl,xS)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f110,plain,
! [W0,W1,W3] :
( ( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| sP0_prd(W3,W1,W0) )
& ( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ sP0_prd(W3,W1,W0) ) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f111,plain,
( ! [W0,W1,W3] :
( W3 = W1
| ~ aElementOf0(W3,W0)
| ~ aElement0(W3)
| sP0_prd(W3,W1,W0) )
& ! [W0,W1,W3] :
( ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) )
| ~ sP0_prd(W3,W1,W0) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f113,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f115,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ aElementOf0(X0,X2)
| ~ aElement0(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f116,definition,
! [W0] :
( sP2_prd(W0)
<=> ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f117,plain,
( sP1_prd
<=> ( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> sP2_prd(W0) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( aElementOf0(W0,sdtpldt0(xS,xx))
<=> ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) ) )
& aSet0(sdtpldt0(xS,xx)) ) ),
inference(formula_renaming,[status(thm)],[f92,f116]) ).
fof(f118,plain,
( ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElementOf0(W0,xS) )
| ? [W0] :
( ( sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ( ~ sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ? [W0] :
( ( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) ) )
| ~ aSet0(sdtpldt0(xS,xx))
| sP1_prd )
& ( ( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ( ~ sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ( sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) ) )
& aSet0(sdtpldt0(xS,xx)) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
( ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElementOf0(W0,xS) )
| ? [W0] :
( ( sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ( ~ sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ? [W0] :
( ( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) ) )
| ~ aSet0(sdtpldt0(xS,xx))
| sP1_prd )
& ( ( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ? [W0] :
( ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(W0,xS) )
& ! [W0] :
( ~ sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) )
& aSet0(sdtpldt0(xS,xx)) )
| ~ sP1_prd ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f120,plain,
( ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ! [W0] :
( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElementOf0(W0,xS) )
| ( ( sP2_prd(sK7_skl)
| aElementOf0(sK7_skl,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ( ~ sP2_prd(sK7_skl)
| ~ aElementOf0(sK7_skl,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ( ( ( ( sK6_skl = xx
| aElementOf0(sK6_skl,xS) )
& aElement0(sK6_skl) )
| aElementOf0(sK6_skl,sdtpldt0(xS,xx)) )
& ( ( sK6_skl != xx
& ~ aElementOf0(sK6_skl,xS) )
| ~ aElement0(sK6_skl)
| ~ aElementOf0(sK6_skl,sdtpldt0(xS,xx)) ) )
| ~ aSet0(sdtpldt0(xS,xx))
| sP1_prd )
& ( ( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
& ~ aElementOf0(sK5_skl,sdtmndt0(sdtpldt0(xS,xx),xx))
& aElementOf0(sK5_skl,xS)
& ! [W0] :
( ~ sP2_prd(W0)
| aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& ! [W0] :
( sP2_prd(W0)
| ~ aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,xS) )
| ~ aElement0(W0)
| aElementOf0(W0,sdtpldt0(xS,xx)) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,xS) )
& aElement0(W0) )
| ~ aElementOf0(W0,sdtpldt0(xS,xx)) )
& aSet0(sdtpldt0(xS,xx)) )
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(W0,sK5_skl),skolemize(W0,sK6_skl),skolemize(W0,sK7_skl)],[f119]) ).
fof(f121,plain,
( aSet0(sdtpldt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0] :
( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f125,plain,
! [X0] :
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f128,plain,
! [X0] :
( ~ sP2_prd(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f129,plain,
( aElementOf0(sK5_skl,xS)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f130,plain,
( ~ aElementOf0(sK5_skl,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f140,plain,
! [W0] :
( ( W0 = xx
| ~ aElementOf0(W0,sdtpldt0(xS,xx))
| ~ aElement0(W0)
| sP2_prd(W0) )
& ( ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) )
| ~ sP2_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f141,plain,
( ! [W0] :
( W0 = xx
| ~ aElementOf0(W0,sdtpldt0(xS,xx))
| ~ aElement0(W0)
| sP2_prd(W0) )
& ! [W0] :
( ( W0 != xx
& aElementOf0(W0,sdtpldt0(xS,xx))
& aElement0(W0) )
| ~ sP2_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f140]) ).
fof(f143,plain,
! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f144,plain,
! [X0] :
( X0 != xx
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f145,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,definition,
( sQ0_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f149,definition,
( sQ1_spl
<=> aSet0(sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f146,f149]) ).
fof(f153,definition,
! [X0] :
( sQ2_spl
<=> ( aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f154,plain,
! [X0] :
( ~ sQ2_spl
| aElement0(X0)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f98,f146,f153]) ).
fof(f157,definition,
! [X0] :
( sQ3_spl
<=> ( X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ3_spl
| X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f99,f146,f157]) ).
fof(f165,definition,
! [X0] :
( sQ5_spl
<=> ( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f166,plain,
! [X0] :
( ~ sQ5_spl
| X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f101,f146,f165]) ).
fof(f189,definition,
( sQ11_spl
<=> aElementOf0(sK4_skl,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ11_spl
| aElementOf0(sK4_skl,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f107,f146,f189]) ).
fof(f193,definition,
( sQ12_spl
<=> aElementOf0(sK4_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ12_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f108,f146,f193]) ).
fof(f201,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f121,f146,f149]) ).
fof(f202,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f122,f146,f153]) ).
fof(f203,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f123,f146,f157]) ).
fof(f205,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f125,f146,f165]) ).
fof(f211,definition,
! [X0] :
( sQ15_spl
<=> ( ~ sP2_prd(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0] :
( ~ sQ15_spl
| ~ sP2_prd(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f128,f146,f211]) ).
fof(f215,definition,
( sQ16_spl
<=> aElementOf0(sK5_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ16_spl
| aElementOf0(sK5_skl,xS) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f146,f215]) ).
fof(f219,definition,
( sQ17_spl
<=> aElementOf0(sK5_skl,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ17_spl
| ~ aElementOf0(sK5_skl,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( ~ sQ17_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f130,f146,f219]) ).
fof(f256,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f257,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f260,plain,
! [X0,X1,X2] :
( aElement0(X2)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f261,plain,
! [X0,X1,X2] :
( X2 = X1
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f262,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElement0(X2)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f263,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f70]) ).
fof(f264,plain,
! [X0,X1] :
( aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f263]) ).
fof(f266,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f82]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1,X0)
| aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f268,plain,
! [X0,X1] : ~ sP0_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f114]) ).
fof(f269,plain,
~ sP2_prd(xx),
inference(destructive_equality_resolution,[status(thm)],[f144]) ).
fof(f270,plain,
( ~ sQ5_spl
| ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(xS,xx)) ),
inference(destructive_equality_resolution,[status(thm)],[f166]) ).
fof(f274,definition,
! [X0] :
( sQ26_spl
<=> ( ~ sP2_prd(X0)
| aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ16_spl
| aElement0(sK5_skl)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f216,f29]) ).
fof(f279,definition,
( sQ27_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ27_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ28_spl
<=> aElement0(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( ~ sQ16_spl
| sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f278,f279,f282,f215]) ).
fof(f286,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f89]) ).
fof(f287,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f289,plain,
! [X0] :
( ~ sQ2_spl
| X0 = xx
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| sP2_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f145,f154]) ).
fof(f295,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(resolution,[status(thm)],[f43,f39]) ).
fof(f296,definition,
( sQ29_spl
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ29_spl
| ~ aSet0(slcrc0) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ30_spl
<=> isCountable0(slcrc0) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f295,f296,f299]) ).
fof(f303,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f256]) ).
fof(f304,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f305,plain,
( ~ aSet0(slcrc0)
| slcrc0 = slcrc0 ),
inference(resolution,[status(thm)],[f38,f257]) ).
fof(f307,plain,
! [X0] :
( aElement0(sK0_skl(X0))
| ~ aSet0(X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(resolution,[status(thm)],[f38,f29]) ).
fof(f308,definition,
( sQ31_spl
<=> slcrc0 = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ29_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f305,f308,f296]) ).
fof(f319,plain,
! [X0] :
( aElement0(sK0_skl(X0))
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(duplicate_literals_removal,[status(thm)],[f307]) ).
fof(f325,definition,
( sQ34_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f339,plain,
! [X0] :
( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f257]) ).
fof(f345,definition,
! [X0] :
( sQ36_spl
<=> ( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ29_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f339,f345,f296]) ).
fof(f359,plain,
( ~ sQ5_spl
| aElementOf0(xx,sdtpldt0(xS,xx)) ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f88]) ).
fof(f361,plain,
( ~ sQ5_spl
| aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f359,f29]) ).
fof(f362,plain,
( ~ sQ5_spl
| sQ34_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f361,f149,f325,f165]) ).
fof(f367,plain,
( ~ sQ2_spl
| ~ aElement0(xx)
| ~ aSet0(xS)
| xx = xx
| sP2_prd(xx) ),
inference(resolution,[status(thm)],[f289,f264]) ).
fof(f368,definition,
( sQ38_spl
<=> sP2_prd(xx) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( ~ sQ38_spl
| sP2_prd(xx) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,definition,
( sQ39_spl
<=> xx = xx ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ27_spl
| sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f367,f368,f371,f279,f325,f153]) ).
fof(f387,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f269]) ).
fof(f388,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f411,definition,
( sQ45_spl
<=> aElementOf0(xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( ~ sQ45_spl
| aElementOf0(xx,xS) ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f438,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| aElement0(X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f260,f264]) ).
fof(f441,definition,
! [X0] :
( sQ47_spl
<=> ( ~ aSet0(X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f442,plain,
! [X0] :
( ~ sQ47_spl
| ~ aSet0(X0)
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
! [X1] :
( sQ48_spl
<=> ( ~ aElement0(X1)
| aElement0(X1)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ48_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f438,f441,f444]) ).
fof(f448,plain,
! [X0] :
( ~ sQ47_spl
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f442]) ).
fof(f456,plain,
( ~ sQ47_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f256,f448]) ).
fof(f460,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f456]) ).
fof(f496,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f29]) ).
fof(f497,plain,
! [X0] :
( ~ sQ2_spl
| aElement0(X0)
| ~ aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f496,f154]) ).
fof(f498,plain,
! [X0] :
( ~ sQ3_spl
| X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f496,f158]) ).
fof(f500,definition,
! [X0] :
( sQ50_spl
<=> ( aElement0(X0)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f501,plain,
! [X0] :
( ~ sQ50_spl
| aElement0(X0)
| ~ aElementOf0(X0,xS) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,plain,
( ~ sQ2_spl
| sQ50_spl
| ~ sQ34_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f497,f279,f325,f500,f153]) ).
fof(f504,definition,
! [X0] :
( sQ51_spl
<=> ( X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( ~ sQ3_spl
| sQ51_spl
| ~ sQ34_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f498,f279,f325,f504,f157]) ).
fof(f523,plain,
( ~ sQ50_spl
| ~ aSet0(xS)
| xS = slcrc0
| aElement0(sK0_skl(xS)) ),
inference(resolution,[status(thm)],[f501,f38]) ).
fof(f526,definition,
( sQ54_spl
<=> aElement0(sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f529,definition,
( sQ55_spl
<=> xS = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( ~ sQ55_spl
| xS = slcrc0 ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,plain,
( ~ sQ50_spl
| ~ sQ27_spl
| sQ55_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f523,f526,f529,f279,f500]) ).
fof(f536,plain,
! [X0] :
( ~ sQ2_spl
| ~ aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| X0 = xx
| sP2_prd(X0) ),
inference(resolution,[status(thm)],[f289,f496]) ).
fof(f540,definition,
! [X0] :
( sQ56_spl
<=> ( ~ aElementOf0(X0,xS)
| X0 = xx
| sP2_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f541,plain,
! [X0] :
( ~ sQ56_spl
| ~ aElementOf0(X0,xS)
| X0 = xx
| sP2_prd(X0) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ27_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f536,f540,f279,f325,f153]) ).
fof(f546,plain,
( ~ sQ56_spl
| ~ aSet0(xS)
| xS = slcrc0
| sK0_skl(xS) = xx
| sP2_prd(sK0_skl(xS)) ),
inference(resolution,[status(thm)],[f541,f38]) ).
fof(f547,plain,
( ~ sQ16_spl
| ~ sQ56_spl
| sK5_skl = xx
| sP2_prd(sK5_skl) ),
inference(resolution,[status(thm)],[f541,f216]) ).
fof(f550,definition,
( sQ57_spl
<=> sP2_prd(sK0_skl(xS)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f553,definition,
( sQ58_spl
<=> sK0_skl(xS) = xx ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( ~ sQ58_spl
| sK0_skl(xS) = xx ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f556,plain,
( ~ sQ56_spl
| ~ sQ27_spl
| sQ55_spl
| sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f546,f550,f553,f529,f279,f540]) ).
fof(f557,definition,
( sQ59_spl
<=> sP2_prd(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f560,definition,
( sQ60_spl
<=> sK5_skl = xx ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ60_spl
| sK5_skl = xx ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,plain,
( ~ sQ16_spl
| ~ sQ56_spl
| sQ60_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f547,f557,f560,f540,f215]) ).
fof(f581,plain,
! [X0] :
( ~ sQ55_spl
| ~ aElementOf0(X0,xS) ),
inference(backward_demodulation,[status(thm)],[f530,f257]) ).
fof(f589,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f90]) ).
fof(f590,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f607,plain,
( ~ sQ60_spl
| ~ aElementOf0(sK5_skl,xS) ),
inference(backward_demodulation,[status(thm)],[f561,f90]) ).
fof(f624,plain,
( ~ sQ58_spl
| aElement0(xx)
| ~ aSet0(xS)
| xS = slcrc0 ),
inference(paramodulation,[status(thm)],[f554,f319]) ).
fof(f625,plain,
( ~ sQ58_spl
| sQ34_spl
| ~ sQ27_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f624,f529,f279,f325,f553]) ).
fof(f635,plain,
( ~ sQ16_spl
| ~ sQ55_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f216,f581]) ).
fof(f636,plain,
( ~ sQ16_spl
| ~ sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f635]) ).
fof(f651,plain,
! [X0,X1] :
( ~ sQ50_spl
| sK2_skl(xS,X0,X1) = X0
| aElementOf0(sK2_skl(xS,X0,X1),X1)
| ~ aSet0(xS)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(xS,X0,X1)) ),
inference(resolution,[status(thm)],[f501,f74]) ).
fof(f652,definition,
! [X0,X1] :
( sQ64_spl
<=> ( sK2_skl(xS,X0,X1) = X0
| aElementOf0(sK2_skl(xS,X0,X1),X1)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| aElement0(sK2_skl(xS,X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( ~ sQ50_spl
| ~ sQ27_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f651,f652,f279,f500]) ).
fof(f658,plain,
! [X0] :
( ~ sQ15_spl
| sP0_prd(X0,xx,sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx))
| ~ sP2_prd(X0) ),
inference(resolution,[status(thm)],[f212,f266]) ).
fof(f664,definition,
! [X0] :
( sQ66_spl
<=> ( sP0_prd(X0,xx,sdtpldt0(xS,xx))
| ~ sP2_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f665,plain,
! [X0] :
( ~ sQ66_spl
| sP0_prd(X0,xx,sdtpldt0(xS,xx))
| ~ sP2_prd(X0) ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f667,plain,
( ~ sQ15_spl
| ~ sQ34_spl
| ~ sQ1_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f658,f664,f149,f325,f211]) ).
fof(f669,plain,
! [X0,X1] :
( ~ sQ56_spl
| sK2_skl(xS,X0,X1) = X0
| aElementOf0(sK2_skl(xS,X0,X1),X1)
| ~ aSet0(xS)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sK2_skl(xS,X0,X1) = xx
| sP2_prd(sK2_skl(xS,X0,X1)) ),
inference(resolution,[status(thm)],[f541,f74]) ).
fof(f670,definition,
! [X0,X1] :
( sQ67_spl
<=> ( sK2_skl(xS,X0,X1) = X0
| aElementOf0(sK2_skl(xS,X0,X1),X1)
| xS = sdtpldt0(X1,X0)
| ~ aElement0(X0)
| ~ aSet0(X1)
| sK2_skl(xS,X0,X1) = xx
| sP2_prd(sK2_skl(xS,X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ56_spl
| ~ sQ27_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f669,f670,f279,f540]) ).
fof(f686,definition,
( sQ69_spl
<=> sK4_skl = xx ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f687,plain,
( ~ sQ69_spl
| sK4_skl = xx ),
inference(component_clause,[status(thm)],[f686]) ).
fof(f719,plain,
! [X0,X1] :
( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| ~ aSet0(slcrc0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f257,f74]) ).
fof(f720,definition,
! [X0,X1] :
( sQ72_spl
<=> ( sK2_skl(slcrc0,X1,X0) = X1
| aElementOf0(sK2_skl(slcrc0,X1,X0),X0)
| slcrc0 = sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( ~ sQ29_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f719,f720,f296]) ).
fof(f791,plain,
! [X0] :
( aElement0(X0)
| ~ aElement0(xx)
| ~ aSet0(xS)
| ~ sP2_prd(X0) ),
inference(resolution,[status(thm)],[f143,f260]) ).
fof(f792,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,xS)
| ~ aElement0(xx)
| ~ aSet0(xS)
| ~ sP2_prd(X0) ),
inference(resolution,[status(thm)],[f143,f261]) ).
fof(f795,plain,
( ~ sQ34_spl
| ~ sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f791,f274,f279,f325]) ).
fof(f796,definition,
! [X0] :
( sQ76_spl
<=> ( X0 = xx
| aElementOf0(X0,xS)
| ~ sP2_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f799,plain,
( ~ sQ34_spl
| ~ sQ27_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f792,f796,f279,f325]) ).
fof(f826,plain,
( ~ sQ11_spl
| sP0_prd(sK4_skl,xx,sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f190,f266]) ).
fof(f828,definition,
( sQ79_spl
<=> sP0_prd(sK4_skl,xx,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ79_spl
| sP0_prd(sK4_skl,xx,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,plain,
( ~ sQ11_spl
| sQ79_spl
| ~ sQ34_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f826,f149,f325,f828,f189]) ).
fof(f836,plain,
( ~ sQ79_spl
| aElementOf0(sK4_skl,sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f829,f113]) ).
fof(f840,plain,
( ~ sQ79_spl
| sK4_skl = xx
| aElementOf0(sK4_skl,xS)
| ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f836,f261]) ).
fof(f843,plain,
( ~ sQ79_spl
| sQ69_spl
| sQ12_spl
| ~ sQ34_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f840,f279,f325,f193,f686,f828]) ).
fof(f853,plain,
( ~ sQ79_spl
| ~ sQ69_spl
| sP0_prd(sK4_skl,xx,sdtpldt0(xS,sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f687,f829]) ).
fof(f872,plain,
( ~ sQ79_spl
| ~ sQ69_spl
| sP0_prd(sK4_skl,sK4_skl,sdtpldt0(xS,sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f687,f853]) ).
fof(f873,plain,
( ~ sQ79_spl
| ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f872,f268]) ).
fof(f874,plain,
( ~ sQ79_spl
| ~ sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f873]) ).
fof(f937,plain,
! [X0] :
( ~ sQ56_spl
| sK1_skl(xS,X0) = xx
| sP2_prd(sK1_skl(xS,X0))
| ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f541]) ).
fof(f938,plain,
! [X0] :
( ~ sQ50_spl
| aElement0(sK1_skl(xS,X0))
| ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f52,f501]) ).
fof(f945,definition,
! [X0] :
( sQ82_spl
<=> ( sK1_skl(xS,X0) = xx
| sP2_prd(sK1_skl(xS,X0))
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f948,plain,
( ~ sQ56_spl
| ~ sQ27_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f937,f945,f279,f540]) ).
fof(f949,definition,
! [X0] :
( sQ83_spl
<=> ( aElement0(sK1_skl(xS,X0))
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( ~ sQ50_spl
| ~ sQ27_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f938,f949,f279,f500]) ).
fof(f1015,plain,
( sQ17_spl
| ~ sP0_prd(sK5_skl,xx,sdtpldt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtpldt0(xS,xx)) ),
inference(resolution,[status(thm)],[f221,f267]) ).
fof(f1016,definition,
( sQ86_spl
<=> sP0_prd(sK5_skl,xx,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1018,plain,
( sQ86_spl
| ~ sP0_prd(sK5_skl,xx,sdtpldt0(xS,xx)) ),
inference(component_clause,[status(thm)],[f1016]) ).
fof(f1019,plain,
( sQ17_spl
| ~ sQ86_spl
| ~ sQ34_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1015,f149,f325,f1016,f219]) ).
fof(f1020,plain,
( ~ sQ66_spl
| sQ86_spl
| ~ sP2_prd(sK5_skl) ),
inference(resolution,[status(thm)],[f1018,f665]) ).
fof(f1021,plain,
( sQ86_spl
| sK5_skl = xx
| ~ aElementOf0(sK5_skl,sdtpldt0(xS,xx))
| ~ aElement0(sK5_skl) ),
inference(resolution,[status(thm)],[f1018,f115]) ).
fof(f1022,plain,
( ~ sQ66_spl
| sQ86_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f1020,f557,f1016,f664]) ).
fof(f1023,definition,
( sQ87_spl
<=> aElementOf0(sK5_skl,sdtpldt0(xS,xx)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( sQ86_spl
| sQ60_spl
| ~ sQ87_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1021,f282,f1023,f560,f1016]) ).
fof(f1027,plain,
( ~ sQ60_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f607,f215,f560]) ).
fof(f1028,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f156,f160,f168,f192,f196,f201,f202,f203,f205,f214,f218,f222,f285,f287,f302,f304,f311,f348,f362,f386,f388,f447,f460,f503,f507,f532,f543,f556,f563,f590,f625,f636,f655,f667,f673,f723,f795,f799,f831,f843,f874,f948,f952,f1019,f1022,f1026,f1027]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM537+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:38:35 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 0.03/0.40 % Refutation found
% 0.03/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.42 % Elapsed time: 0.058265 seconds
% 0.03/0.42 % CPU time: 0.204386 seconds
% 0.03/0.42 % Total memory used: 79.896 MB
% 0.03/0.42 % Net memory used: 79.741 MB
%------------------------------------------------------------------------------