%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM554+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 01:40:58 PM UTC 2026
% Result : Theorem 28.47s 4.20s
% Output : CNFRefutation 28.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 58
% Syntax : Number of formulae : 262 ( 38 unt; 38 def)
% Number of atoms : 1052 ( 154 equ)
% Maximal formula atoms : 43 ( 4 avg)
% Number of connectives : 1265 ( 475 ~; 467 |; 232 &)
% ( 52 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 34 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 12 con; 0-3 aty)
% Number of variables : 278 ( 259 !; 19 ?)
% 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(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(f12,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [W0,W1] :
( ( aSet0(W1)
& aElement0(W0) )
=> ( ~ aElementOf0(W0,W1)
=> sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtpldt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( aElementOf0(W1,W0)
& isFinite0(W0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ),
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(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
( ~ ( ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xT)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) ) )
& aSet0(xP)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,conjecture,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
~ ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
| ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f79,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f80,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f84,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f86,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))],[f85]) ).
fof(f87,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f97,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(f98,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)],[f97]) ).
fof(f99,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)],[f98]) ).
fof(f100,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))],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f107,plain,
! [W0] :
( aSubsetOf0(W0,W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f108,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f113,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(f114,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)],[f113]) ).
fof(f115,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)],[f114]) ).
fof(f116,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))],[f115]) ).
fof(f117,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,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)],[f116]) ).
fof(f126,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(f127,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f128,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)],[f126,f127]) ).
fof(f129,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)],[f128]) ).
fof(f130,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)],[f129]) ).
fof(f131,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))],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,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)],[f131]) ).
fof(f137,plain,
! [W0] :
( ! [W1] :
( sdtpldt0(sdtmndt0(W0,W1),W1) = W0
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f138,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [W0,W1] :
( sdtmndt0(sdtpldt0(W1,W0),W0) = W1
| aElementOf0(W0,W1)
| ~ aSet0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f140,plain,
! [X0,X1] :
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f145,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtpldt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f146,plain,
! [X0,X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtmndt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f148,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f193,plain,
! [W0] :
( ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f194,plain,
! [W0] :
( ( ( W0 != slcrc0
| sbrdtbr0(W0) = sz00 )
& ( W0 = slcrc0
| sbrdtbr0(W0) != sz00 ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f193]) ).
fof(f196,plain,
! [X0] :
( X0 != slcrc0
| sbrdtbr0(X0) = sz00
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f197,plain,
! [W0] :
( ! [W1] :
( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0))
| aElementOf0(W1,W0)
| ~ aElement0(W1) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f198,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
! [W0] :
( ! [W1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0)
| ~ aElementOf0(W1,W0)
| ~ isFinite0(W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f200,plain,
! [X0,X1] :
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f236,plain,
! [W0] :
( isFinite0(slbdtrb0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f237,plain,
! [X0] :
( isFinite0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f271,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f272,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f273,plain,
aSet0(xT),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f274,plain,
xk != sz00,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f275,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ? [W1] :
( ~ aElementOf0(W1,xT)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f276,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ? [W1] :
( ~ aElementOf0(W1,xT)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ? [W1] :
( ~ aElementOf0(W1,xS)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(miniscoping,[status(thm)],[f275]) ).
fof(f277,plain,
( slbdtsldtrb0(xS,xk) != slcrc0
& aElementOf0(sK14_skl,slbdtsldtrb0(xS,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sK13_skl(W0),xS)
& aElementOf0(sK13_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xT)
& ( ( ~ aElementOf0(sK12_skl(W0),xT)
& aElementOf0(sK12_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,xT)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,xS)
& ( ( ~ aElementOf0(sK11_skl(W0),xS)
& aElementOf0(sK11_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,xS)
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(W1,sK11_skl(W0)),skolemize(W1,sK12_skl(W0)),skolemize(W1,sK13_skl(W0)),skolemize(W0,sK14_skl)],[f276]) ).
fof(f279,plain,
! [X0] :
( aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f290,plain,
! [X0] :
( sbrdtbr0(X0) = xk
| ~ aElementOf0(X0,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f294,plain,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f303,plain,
aElementOf0(sK14_skl,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f305,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f306,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f308,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f309,plain,
aSubsetOf0(xQ,xS),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f310,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f313,plain,
isFinite0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f316,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f317,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f319,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( ( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xQ,xy)) )
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) )
| ~ aElementOf0(W0,xP) ) )
& aSet0(xP)
& ! [W0] :
( ( W0 = xy
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& ( ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xQ,xy)) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(NNF_transformation,[status(thm)],[f70]) ).
fof(f320,plain,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( ( W0 != xx
& ~ aElementOf0(W0,sdtmndt0(xQ,xy)) )
| ~ aElement0(W0)
| aElementOf0(W0,xP) )
& ! [W0] :
( ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) )
| ~ aElementOf0(W0,xP) )
& aSet0(xP)
& ! [W0] :
( W0 = xy
| ~ aElementOf0(W0,xQ)
| ~ aElement0(W0)
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& ! [W0] :
( ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) )
| ~ aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aSet0(sdtmndt0(xQ,xy)) ),
inference(miniscoping,[status(thm)],[f319]) ).
fof(f321,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f324,plain,
! [X0] :
( X0 != xy
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f326,plain,
aSet0(xP),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f328,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f330,plain,
! [X0] :
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f331,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f332,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( sbrdtbr0(xP) != xk
| ( ~ aSubsetOf0(xP,xS)
& ? [W0] :
( ~ aElementOf0(W0,xS)
& aElementOf0(W0,xP) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f72]) ).
fof(f333,plain,
( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
& ( sbrdtbr0(xP) != xk
| ( ~ aSubsetOf0(xP,xS)
& ~ aElementOf0(sK15_skl,xS)
& aElementOf0(sK15_skl,xP) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(W0,sK15_skl)],[f332]) ).
fof(f334,plain,
( sbrdtbr0(xP) != xk
| aElementOf0(sK15_skl,xP) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f335,plain,
( sbrdtbr0(xP) != xk
| ~ aElementOf0(sK15_skl,xS) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f337,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f338,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)],[f127]) ).
fof(f339,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)],[f338]) ).
fof(f341,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f344,definition,
( sQ0_spl
<=> aElementOf0(sK15_skl,xP) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( ~ sQ0_spl
| aElementOf0(sK15_skl,xP) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ1_spl
<=> sbrdtbr0(xP) = xk ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f334,f344,f347]) ).
fof(f351,definition,
( sQ2_spl
<=> aElementOf0(sK15_skl,xS) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ2_spl
| ~ aElementOf0(sK15_skl,xS) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f335,f351,f347]) ).
fof(f359,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f87]) ).
fof(f362,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f117]) ).
fof(f365,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElement0(X2)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f120]) ).
fof(f368,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f132]) ).
fof(f369,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f133]) ).
fof(f371,plain,
( sbrdtbr0(slcrc0) = sz00
| ~ aSet0(slcrc0) ),
inference(destructive_equality_resolution,[status(thm)],[f196]) ).
fof(f386,plain,
~ aElementOf0(xy,sdtmndt0(xQ,xy)),
inference(destructive_equality_resolution,[status(thm)],[f324]) ).
fof(f387,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(destructive_equality_resolution,[status(thm)],[f330]) ).
fof(f395,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f80,f305]) ).
fof(f398,definition,
( sQ4_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( sQ4_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,definition,
( sQ5_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( ~ sQ5_spl
| aElement0(xx) ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f404,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f395,f398,f401]) ).
fof(f418,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f272]) ).
fof(f419,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f455,definition,
( sQ17_spl
<=> aSet0(xP) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ17_spl
| ~ aSet0(xP) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f477,definition,
( sQ20_spl
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( sQ20_spl
| ~ isFinite0(xQ) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f512,definition,
( sQ30_spl
<=> isFinite0(xP) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f313]) ).
fof(f528,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f559,plain,
( aSet0(xQ)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f309,f101]) ).
fof(f571,definition,
( sQ39_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( sQ39_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f559,f398,f571]) ).
fof(f593,plain,
( aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f316,f80]) ).
fof(f594,plain,
! [X0] :
( aElementOf0(xy,X0)
| ~ aSubsetOf0(xQ,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f316,f102]) ).
fof(f595,definition,
( sQ40_spl
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f593,f571,f595]) ).
fof(f617,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f457,f326]) ).
fof(f618,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f729,definition,
( sQ58_spl
<=> isFinite0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( sQ58_spl
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f879,definition,
( sQ66_spl
<=> aSet0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f881,plain,
( sQ66_spl
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f879]) ).
fof(f913,plain,
( ~ aSet0(xQ)
| aElementOf0(xy,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f594,f108]) ).
fof(f918,definition,
( sQ72_spl
<=> aElementOf0(xy,xQ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f921,plain,
( sQ72_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f913,f571,f918]) ).
fof(f945,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(X3,X0)
| ~ aSubsetOf0(sdtpldt0(X1,X2),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f102,f365]) ).
fof(f960,plain,
sbrdtbr0(slcrc0) = sz00,
inference(forward_subsumption_resolution,[status(thm)],[f371,f359]) ).
fof(f984,definition,
( sQ80_spl
<=> isFinite0(slbdtrb0(xk)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f986,plain,
( sQ80_spl
| ~ isFinite0(slbdtrb0(xk)) ),
inference(component_clause,[status(thm)],[f984]) ).
fof(f990,plain,
isFinite0(slbdtrb0(xk)),
inference(resolution,[status(thm)],[f237,f271]) ).
fof(f998,plain,
aSet0(sK14_skl),
inference(resolution,[status(thm)],[f303,f279]) ).
fof(f1110,plain,
( sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f881,f321]) ).
fof(f1111,plain,
sQ66_spl,
inference(contradiction_clause,[status(thm)],[f1110]) ).
fof(f1302,plain,
( ~ sQ5_spl
| aElementOf0(xx,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f402]) ).
fof(f1304,plain,
! [X0] :
( ~ sQ5_spl
| aElementOf0(xx,X0)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f1302,f102]) ).
fof(f1442,plain,
( ~ sQ5_spl
| ~ aSet0(xP)
| aElementOf0(xx,xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f1304,f108]) ).
fof(f1443,definition,
( sQ148_spl
<=> aElementOf0(xx,xP) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1446,plain,
( ~ sQ5_spl
| sQ148_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1442,f455,f1443,f401]) ).
fof(f1935,plain,
( sQ58_spl
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[f731,f148]) ).
fof(f1936,plain,
( sQ58_spl
| ~ sQ20_spl
| ~ sQ39_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f1935,f595,f571,f477,f729]) ).
fof(f1971,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(paramodulation,[status(thm)],[f331,f146]) ).
fof(f1973,plain,
( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(paramodulation,[status(thm)],[f331,f140]) ).
fof(f1976,plain,
( sQ30_spl
| ~ sQ58_spl
| ~ sQ66_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1971,f401,f879,f729,f512]) ).
fof(f1978,definition,
( sQ200_spl
<=> aElementOf0(xx,sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f1979,plain,
( ~ sQ200_spl
| aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f1978]) ).
fof(f1981,definition,
( sQ201_spl
<=> sdtmndt0(xP,xx) = sdtmndt0(xQ,xy) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f1982,plain,
( ~ sQ201_spl
| sdtmndt0(xP,xx) = sdtmndt0(xQ,xy) ),
inference(component_clause,[status(thm)],[f1981]) ).
fof(f1984,plain,
( sQ201_spl
| sQ200_spl
| ~ sQ66_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1973,f401,f879,f1978,f1981]) ).
fof(f1991,plain,
( ~ sQ200_spl
| sP0_prd(xx,xy,xQ)
| ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f1979,f369]) ).
fof(f1994,definition,
( sQ203_spl
<=> sP0_prd(xx,xy,xQ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f1995,plain,
( ~ sQ203_spl
| sP0_prd(xx,xy,xQ) ),
inference(component_clause,[status(thm)],[f1994]) ).
fof(f1997,plain,
( ~ sQ200_spl
| sQ203_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1991,f571,f595,f1994,f1978]) ).
fof(f2000,plain,
( ~ sQ203_spl
| aElementOf0(xx,xQ) ),
inference(resolution,[status(thm)],[f1995,f341]) ).
fof(f2002,plain,
( ~ sQ203_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2000,f317]) ).
fof(f2003,plain,
~ sQ203_spl,
inference(contradiction_clause,[status(thm)],[f2002]) ).
fof(f2271,definition,
( sQ228_spl
<=> aSet0(xT) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2273,plain,
( sQ228_spl
| ~ aSet0(xT) ),
inference(component_clause,[status(thm)],[f2271]) ).
fof(f2289,plain,
( sQ228_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2273,f273]) ).
fof(f2290,plain,
sQ228_spl,
inference(contradiction_clause,[status(thm)],[f2289]) ).
fof(f2809,plain,
( ~ sQ201_spl
| ~ aElementOf0(xy,sdtmndt0(xP,xx)) ),
inference(backward_demodulation,[status(thm)],[f1982,f386]) ).
fof(f2818,plain,
( ~ sQ201_spl
| isFinite0(sdtmndt0(xP,xx))
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(paramodulation,[status(thm)],[f1982,f148]) ).
fof(f2820,plain,
( ~ sQ201_spl
| sdtpldt0(sdtmndt0(xP,xx),xy) = xQ
| ~ aElementOf0(xy,xQ)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f1982,f138]) ).
fof(f2823,plain,
( ~ sQ201_spl
| aSet0(sdtmndt0(xP,xx))
| ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f1982,f368]) ).
fof(f2824,definition,
( sQ295_spl
<=> isFinite0(sdtmndt0(xP,xx)) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f2827,plain,
( ~ sQ201_spl
| sQ295_spl
| ~ sQ20_spl
| ~ sQ39_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f2818,f595,f571,f477,f2824,f1981]) ).
fof(f2832,definition,
( sQ297_spl
<=> sdtpldt0(sdtmndt0(xP,xx),xy) = xQ ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2833,plain,
( ~ sQ297_spl
| sdtpldt0(sdtmndt0(xP,xx),xy) = xQ ),
inference(component_clause,[status(thm)],[f2832]) ).
fof(f2835,plain,
( ~ sQ201_spl
| sQ297_spl
| ~ sQ72_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2820,f571,f918,f2832,f1981]) ).
fof(f2844,definition,
( sQ300_spl
<=> aSet0(sdtmndt0(xP,xx)) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f2847,plain,
( ~ sQ201_spl
| sQ300_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2823,f571,f595,f2844,f1981]) ).
fof(f2885,definition,
( sQ303_spl
<=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f2886,plain,
( ~ sQ303_spl
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xQ) ),
inference(component_clause,[status(thm)],[f2885]) ).
fof(f2889,plain,
( ~ sQ303_spl
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = xk ),
inference(forward_demodulation,[status(thm)],[f310,f2886]) ).
fof(f2977,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f986,f990]) ).
fof(f2978,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f2977]) ).
fof(f3064,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(X3,X0)
| ~ aSubsetOf0(sdtpldt0(X1,X2),X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f945,f80]) ).
fof(f3065,plain,
! [X0,X1,X2] :
( ~ aSet0(sdtpldt0(X0,X1))
| ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[f3064,f108]) ).
fof(f3066,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElement0(X1)
| ~ aSet0(X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aSet0(sdtpldt0(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f3065]) ).
fof(f3067,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X0,X1)
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(X0,sdtpldt0(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3066,f362]) ).
fof(f3390,definition,
( sQ374_spl
<=> aSubsetOf0(sK14_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f3392,plain,
( sQ374_spl
| ~ aSubsetOf0(sK14_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f3390]) ).
fof(f3766,plain,
( sQ374_spl
| ~ aSet0(sK14_skl) ),
inference(resolution,[status(thm)],[f3392,f108]) ).
fof(f3767,plain,
( sQ374_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3766,f998]) ).
fof(f3768,plain,
sQ374_spl,
inference(contradiction_clause,[status(thm)],[f3767]) ).
fof(f5322,plain,
! [X0] :
( ~ sQ297_spl
| ~ aElementOf0(X0,sdtmndt0(xP,xx))
| ~ aElement0(xy)
| ~ aSet0(sdtmndt0(xP,xx))
| aElementOf0(X0,xQ) ),
inference(paramodulation,[status(thm)],[f2833,f3067]) ).
fof(f5324,plain,
( ~ sQ297_spl
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx)))
| aElementOf0(xy,sdtmndt0(xP,xx))
| ~ aElement0(xy)
| ~ isFinite0(sdtmndt0(xP,xx))
| ~ aSet0(sdtmndt0(xP,xx)) ),
inference(paramodulation,[status(thm)],[f2833,f198]) ).
fof(f5332,definition,
! [X0] :
( sQ623_spl
<=> ( ~ aElementOf0(X0,sdtmndt0(xP,xx))
| aElementOf0(X0,xQ) ) ),
introduced(definition,[new_symbols(definition,[sQ623_spl])],[split_symbol_definition]) ).
fof(f5333,plain,
! [X0] :
( ~ sQ623_spl
| ~ aElementOf0(X0,sdtmndt0(xP,xx))
| aElementOf0(X0,xQ) ),
inference(component_clause,[status(thm)],[f5332]) ).
fof(f5335,plain,
( ~ sQ297_spl
| ~ sQ40_spl
| ~ sQ300_spl
| sQ623_spl ),
inference(split_clause,[status(thm)],[f5322,f5332,f2844,f595,f2832]) ).
fof(f5340,definition,
( sQ625_spl
<=> aElementOf0(xy,sdtmndt0(xP,xx)) ),
introduced(definition,[new_symbols(definition,[sQ625_spl])],[split_symbol_definition]) ).
fof(f5341,plain,
( ~ sQ625_spl
| aElementOf0(xy,sdtmndt0(xP,xx)) ),
inference(component_clause,[status(thm)],[f5340]) ).
fof(f5343,plain,
( ~ sQ297_spl
| sQ303_spl
| sQ625_spl
| ~ sQ40_spl
| ~ sQ295_spl
| ~ sQ300_spl ),
inference(split_clause,[status(thm)],[f5324,f2844,f2824,f595,f5340,f2885,f2832]) ).
fof(f5357,plain,
( ~ sQ625_spl
| ~ sQ201_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5341,f2809]) ).
fof(f5358,plain,
( ~ sQ625_spl
| ~ sQ201_spl ),
inference(contradiction_clause,[status(thm)],[f5357]) ).
fof(f5359,plain,
( ~ sQ303_spl
| xk = sbrdtbr0(xP)
| ~ aElementOf0(xx,xP)
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(paramodulation,[status(thm)],[f2889,f200]) ).
fof(f5380,plain,
( ~ sQ303_spl
| sQ1_spl
| ~ sQ148_spl
| ~ sQ30_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5359,f455,f512,f1443,f347,f2885]) ).
fof(f5487,definition,
( sQ642_spl
<=> aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f5488,plain,
( ~ sQ642_spl
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(component_clause,[status(thm)],[f5487]) ).
fof(f7856,plain,
( ~ sQ642_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5488,f337]) ).
fof(f7857,plain,
~ sQ642_spl,
inference(contradiction_clause,[status(thm)],[f7856]) ).
fof(f8127,definition,
! [X0] :
( sQ892_spl
<=> ~ aElementOf0(X0,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ892_spl])],[split_symbol_definition]) ).
fof(f8128,plain,
! [X0] :
( ~ sQ892_spl
| ~ aElementOf0(X0,szNzAzT0) ),
inference(component_clause,[status(thm)],[f8127]) ).
fof(f8185,plain,
( ~ sQ892_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f271,f8128]) ).
fof(f8196,plain,
~ sQ892_spl,
inference(contradiction_clause,[status(thm)],[f8185]) ).
fof(f8880,definition,
( sQ980_spl
<=> aElementOf0(sK14_skl,slbdtsldtrb0(xT,xk)) ),
introduced(definition,[new_symbols(definition,[sQ980_spl])],[split_symbol_definition]) ).
fof(f8882,plain,
( sQ980_spl
| ~ aElementOf0(sK14_skl,slbdtsldtrb0(xT,xk)) ),
inference(component_clause,[status(thm)],[f8880]) ).
fof(f8896,definition,
( sQ984_spl
<=> aElementOf0(slcrc0,slbdtsldtrb0(xT,xk)) ),
introduced(definition,[new_symbols(definition,[sQ984_spl])],[split_symbol_definition]) ).
fof(f8897,plain,
( ~ sQ984_spl
| aElementOf0(slcrc0,slbdtsldtrb0(xT,xk)) ),
inference(component_clause,[status(thm)],[f8896]) ).
fof(f9112,plain,
( ~ sQ984_spl
| sbrdtbr0(slcrc0) = xk ),
inference(resolution,[status(thm)],[f8897,f290]) ).
fof(f9120,plain,
( ~ sQ984_spl
| sz00 = xk ),
inference(forward_demodulation,[status(thm)],[f960,f9112]) ).
fof(f9121,plain,
( ~ sQ984_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9120,f274]) ).
fof(f9122,plain,
~ sQ984_spl,
inference(contradiction_clause,[status(thm)],[f9121]) ).
fof(f9170,plain,
aElementOf0(sK14_skl,slbdtsldtrb0(xT,xk)),
inference(resolution,[status(thm)],[f294,f303]) ).
fof(f9203,plain,
( sQ980_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9170,f8882]) ).
fof(f9204,plain,
sQ980_spl,
inference(contradiction_clause,[status(thm)],[f9203]) ).
fof(f9899,definition,
( sQ1107_spl
<=> xx = xy ),
introduced(definition,[new_symbols(definition,[sQ1107_spl])],[split_symbol_definition]) ).
fof(f9900,plain,
( ~ sQ1107_spl
| xx = xy ),
inference(component_clause,[status(thm)],[f9899]) ).
fof(f10107,plain,
! [X0] :
( ~ sQ201_spl
| X0 = xx
| aElementOf0(X0,sdtmndt0(xP,xx))
| ~ aElementOf0(X0,xP) ),
inference(forward_demodulation,[status(thm)],[f1982,f328]) ).
fof(f10112,plain,
! [X0] :
( ~ sQ623_spl
| ~ sQ201_spl
| aElementOf0(X0,xQ)
| X0 = xx
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f10107,f5333]) ).
fof(f10565,plain,
( ~ sQ1107_spl
| ~ aElementOf0(xy,xQ) ),
inference(backward_demodulation,[status(thm)],[f9900,f317]) ).
fof(f10574,plain,
( ~ sQ1107_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10565,f316]) ).
fof(f10575,plain,
~ sQ1107_spl,
inference(contradiction_clause,[status(thm)],[f10574]) ).
fof(f13206,plain,
( ~ sQ0_spl
| ~ sQ623_spl
| ~ sQ201_spl
| aElementOf0(sK15_skl,xQ)
| sK15_skl = xx ),
inference(resolution,[status(thm)],[f10112,f345]) ).
fof(f13262,definition,
( sQ1459_spl
<=> sK15_skl = xx ),
introduced(definition,[new_symbols(definition,[sQ1459_spl])],[split_symbol_definition]) ).
fof(f13263,plain,
( ~ sQ1459_spl
| sK15_skl = xx ),
inference(component_clause,[status(thm)],[f13262]) ).
fof(f13265,definition,
( sQ1460_spl
<=> aElementOf0(sK15_skl,xQ) ),
introduced(definition,[new_symbols(definition,[sQ1460_spl])],[split_symbol_definition]) ).
fof(f13266,plain,
( ~ sQ1460_spl
| aElementOf0(sK15_skl,xQ) ),
inference(component_clause,[status(thm)],[f13265]) ).
fof(f13268,plain,
( ~ sQ0_spl
| ~ sQ623_spl
| ~ sQ201_spl
| sQ1460_spl
| sQ1459_spl ),
inference(split_clause,[status(thm)],[f13206,f13262,f13265,f1981,f5332,f344]) ).
fof(f13351,plain,
( ~ sQ1459_spl
| aElementOf0(sK15_skl,xS) ),
inference(backward_demodulation,[status(thm)],[f13263,f305]) ).
fof(f13361,plain,
( ~ sQ1459_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13351,f353]) ).
fof(f13362,plain,
( ~ sQ1459_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f13361]) ).
fof(f13424,plain,
( ~ sQ1460_spl
| aElementOf0(sK15_skl,xS) ),
inference(resolution,[status(thm)],[f13266,f308]) ).
fof(f13427,plain,
( ~ sQ1460_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13424,f353]) ).
fof(f13428,plain,
( ~ sQ1460_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f13427]) ).
fof(f13429,plain,
$false,
inference(sat_refutation,[status(thm)],[f350,f354,f404,f419,f528,f574,f598,f618,f921,f1111,f1446,f1936,f1976,f1984,f1997,f2003,f2290,f2827,f2835,f2847,f2978,f3768,f5335,f5343,f5358,f5380,f7857,f8196,f9122,f9204,f10575,f13268,f13362,f13428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM554+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:39:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 28.47/4.20 % Refutation found
% 28.47/4.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 28.47/4.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 28.47/4.27 % Elapsed time: 3.890980 seconds
% 28.47/4.27 % CPU time: 30.335826 seconds
% 28.47/4.27 % Total memory used: 245.472 MB
% 28.47/4.27 % Net memory used: 231.856 MB
%------------------------------------------------------------------------------