%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM554+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 17.53s 2.89s
% Output : CNFRefutation 14.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 45
% Syntax : Number of formulae : 182 ( 24 unt; 30 def)
% Number of atoms : 733 ( 103 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 913 ( 362 ~; 389 |; 102 &)
% ( 44 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 26 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 209 ( 201 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
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(f22,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f57,definition,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,conjecture,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
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(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(f102,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
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(f119,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)],[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(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(f152,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f153,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f189,plain,
! [W0] :
( ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f190,plain,
! [W0] :
( ( ( ~ isFinite0(W0)
| aElementOf0(sbrdtbr0(W0),szNzAzT0) )
& ( isFinite0(W0)
| ~ aElementOf0(sbrdtbr0(W0),szNzAzT0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0] :
( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
! [X0] :
( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
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(f254,plain,
! [W0,W1] :
( ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f255,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ( ( ! [W3] :
( ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| aElementOf0(W3,W2) )
& ( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f255]) ).
fof(f257,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( sbrdtbr0(sK10_skl(W2,W1,W0)) = W1
& aSubsetOf0(sK10_skl(W2,W1,W0),W0) )
| aElementOf0(sK10_skl(W2,W1,W0),W2) )
& ( sbrdtbr0(sK10_skl(W2,W1,W0)) != W1
| ~ aSubsetOf0(sK10_skl(W2,W1,W0),W0)
| ~ aElementOf0(sK10_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = slbdtsldtrb0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( sbrdtbr0(W3) != W1
| ~ aSubsetOf0(W3,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != slbdtsldtrb0(W0,W1) ) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f256]) ).
fof(f259,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f261,plain,
! [X0,X1,X2,X3] :
( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f271,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f272,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f277,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f278,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f279,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f281,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f283,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f284,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f286,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f287,plain,
~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f288,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(f289,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)],[f288]) ).
fof(f291,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f300,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f117]) ).
fof(f302,plain,
! [X0,X1,X2] :
( X2 = X1
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f119]) ).
fof(f310,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f132]) ).
fof(f311,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(f327,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X0)
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f259]) ).
fof(f329,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aElementOf0(X1,slbdtsldtrb0(X0,sbrdtbr0(X1)))
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f261]) ).
fof(f331,plain,
( aSubsetOf0(xQ,xS)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f327,f278]) ).
fof(f332,definition,
( sQ0_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ0_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ1_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ1_spl
| ~ aElementOf0(xk,szNzAzT0) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,definition,
( sQ2_spl
<=> aSubsetOf0(xQ,xS) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ2_spl
| aSubsetOf0(xQ,xS) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f331,f332,f335,f338]) ).
fof(f347,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f271]) ).
fof(f348,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f272]) ).
fof(f350,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f362,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f80,f277]) ).
fof(f367,definition,
( sQ6_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ6_spl
| ~ aSet0(xQ) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,definition,
( sQ7_spl
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f374,definition,
( sQ8_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f362,f332,f374]) ).
fof(f399,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f279]) ).
fof(f400,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f448,plain,
! [X0] :
( ~ sQ2_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f102,f339]) ).
fof(f451,definition,
! [X0] :
( sQ20_spl
<=> ( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f452,plain,
! [X0] :
( ~ sQ20_spl
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( ~ sQ2_spl
| sQ20_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f448,f332,f451,f338]) ).
fof(f457,plain,
( ~ sQ20_spl
| aElementOf0(xy,xS) ),
inference(resolution,[status(thm)],[f452,f283]) ).
fof(f465,plain,
( ~ sQ20_spl
| aElement0(xy)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f457,f80]) ).
fof(f466,plain,
( ~ sQ20_spl
| sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f465,f332,f370,f451]) ).
fof(f671,definition,
( sQ46_spl
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1424,plain,
( aSet0(xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f286,f300]) ).
fof(f1425,definition,
( sQ101_spl
<=> aSet0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1427,plain,
( sQ101_spl
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f1425]) ).
fof(f1428,definition,
( sQ102_spl
<=> aSet0(xP) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1431,plain,
( sQ102_spl
| ~ sQ8_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f1424,f1425,f374,f1428]) ).
fof(f1432,plain,
( sQ101_spl
| ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f1427,f310]) ).
fof(f1433,plain,
( sQ101_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1432,f367,f370,f1425]) ).
fof(f1445,definition,
( sQ105_spl
<=> aElementOf0(xx,sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1446,plain,
( ~ sQ105_spl
| aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f1445]) ).
fof(f1743,plain,
( isFinite0(xQ)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f281,f191]) ).
fof(f1745,plain,
( sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1743,f367,f335,f671]) ).
fof(f1802,plain,
( ~ sQ105_spl
| sP0_prd(xx,xy,xQ)
| ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f311,f1446]) ).
fof(f1810,definition,
( sQ139_spl
<=> sP0_prd(xx,xy,xQ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1811,plain,
( ~ sQ139_spl
| sP0_prd(xx,xy,xQ) ),
inference(component_clause,[status(thm)],[f1810]) ).
fof(f1813,plain,
( ~ sQ105_spl
| sQ139_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1802,f367,f370,f1810,f1445]) ).
fof(f1871,plain,
( ~ sQ139_spl
| aElementOf0(xx,xQ) ),
inference(resolution,[status(thm)],[f1811,f291]) ).
fof(f1872,plain,
( ~ sQ139_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1871,f284]) ).
fof(f1873,plain,
~ sQ139_spl,
inference(contradiction_clause,[status(thm)],[f1872]) ).
fof(f2246,definition,
( sQ196_spl
<=> aElementOf0(xy,xQ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2248,plain,
( sQ196_spl
| ~ aElementOf0(xy,xQ) ),
inference(component_clause,[status(thm)],[f2246]) ).
fof(f2255,plain,
( sQ196_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2248,f283]) ).
fof(f2256,plain,
sQ196_spl,
inference(contradiction_clause,[status(thm)],[f2255]) ).
fof(f2490,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f286,f302]) ).
fof(f2498,definition,
! [X0] :
( sQ226_spl
<=> ( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2499,plain,
! [X0] :
( ~ sQ226_spl
| X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f2498]) ).
fof(f2501,plain,
( sQ226_spl
| ~ sQ8_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f2490,f1425,f374,f2498]) ).
fof(f2884,definition,
( sQ264_spl
<=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2885,plain,
( ~ sQ264_spl
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP) ),
inference(component_clause,[status(thm)],[f2884]) ).
fof(f2888,plain,
( sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f286,f198]) ).
fof(f2889,definition,
( sQ265_spl
<=> isFinite0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2891,plain,
( sQ265_spl
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f2889]) ).
fof(f2892,plain,
( sQ264_spl
| sQ105_spl
| ~ sQ8_spl
| ~ sQ265_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f2888,f1425,f2889,f374,f1445,f2884]) ).
fof(f2935,plain,
! [X0] :
( ~ sQ226_spl
| sP0_prd(X0,xy,xQ)
| ~ aElement0(xy)
| ~ aSet0(xQ)
| X0 = xx
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f2499,f311]) ).
fof(f2949,definition,
! [X0] :
( sQ275_spl
<=> ( sP0_prd(X0,xy,xQ)
| X0 = xx
| ~ aElementOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2950,plain,
! [X0] :
( ~ sQ275_spl
| sP0_prd(X0,xy,xQ)
| X0 = xx
| ~ aElementOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f2949]) ).
fof(f2952,plain,
( ~ sQ226_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f2935,f2949,f367,f370,f2498]) ).
fof(f2971,plain,
( ~ sQ264_spl
| sbrdtbr0(xP) = sbrdtbr0(xQ)
| ~ aElementOf0(xy,xQ)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f2885,f200]) ).
fof(f2983,plain,
( ~ sQ264_spl
| aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,xy)),szNzAzT0) ),
inference(paramodulation,[status(thm)],[f2885,f153]) ).
fof(f2989,definition,
( sQ278_spl
<=> sbrdtbr0(xP) = sbrdtbr0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2990,plain,
( ~ sQ278_spl
| sbrdtbr0(xP) = sbrdtbr0(xQ) ),
inference(component_clause,[status(thm)],[f2989]) ).
fof(f2992,plain,
( ~ sQ264_spl
| sQ278_spl
| ~ sQ196_spl
| ~ sQ46_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2971,f367,f671,f2246,f2989,f2884]) ).
fof(f2997,definition,
( sQ280_spl
<=> aElementOf0(sbrdtbr0(sdtmndt0(xQ,xy)),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2999,plain,
( sQ280_spl
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,xy)),szNzAzT0) ),
inference(component_clause,[status(thm)],[f2997]) ).
fof(f3040,definition,
( sQ291_spl
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3043,plain,
( ~ sQ264_spl
| sQ291_spl
| ~ sQ280_spl ),
inference(split_clause,[status(thm)],[f2983,f2997,f3040,f2884]) ).
fof(f3065,plain,
( ~ sQ278_spl
| sbrdtbr0(xP) = xk ),
inference(forward_demodulation,[status(thm)],[f281,f2990]) ).
fof(f3078,plain,
! [X0] :
( ~ sQ278_spl
| ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f3065,f329]) ).
fof(f3098,definition,
! [X0] :
( sQ299_spl
<=> ( ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f3099,plain,
! [X0] :
( ~ sQ299_spl
| ~ aSubsetOf0(xP,X0)
| aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f3098]) ).
fof(f3101,plain,
( ~ sQ278_spl
| ~ sQ291_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f3078,f3098,f3040,f2989]) ).
fof(f3142,plain,
( sQ280_spl
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[f2999,f192]) ).
fof(f3143,plain,
( sQ280_spl
| ~ sQ265_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f3142,f1425,f2889,f2997]) ).
fof(f3192,plain,
( sQ265_spl
| ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[f148,f2891]) ).
fof(f3196,plain,
( sQ265_spl
| ~ sQ46_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3192,f370,f367,f671,f2889]) ).
fof(f3912,plain,
! [X0] :
( ~ sQ275_spl
| aElementOf0(X0,xQ)
| X0 = xx
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f2950,f291]) ).
fof(f4175,plain,
! [X0] :
( ~ sQ275_spl
| ~ aSet0(xP)
| aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ)
| sK1_skl(xP,X0) = xx ),
inference(resolution,[status(thm)],[f3912,f103]) ).
fof(f4208,definition,
! [X0] :
( sQ375_spl
<=> ( aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ)
| sK1_skl(xP,X0) = xx ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f4209,plain,
! [X0] :
( ~ sQ375_spl
| aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ)
| sK1_skl(xP,X0) = xx ),
inference(component_clause,[status(thm)],[f4208]) ).
fof(f4211,plain,
( ~ sQ275_spl
| ~ sQ102_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4175,f4208,f1428,f2949]) ).
fof(f5329,plain,
( ~ sQ299_spl
| ~ aSubsetOf0(xP,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f3099,f287]) ).
fof(f5333,definition,
( sQ466_spl
<=> aSubsetOf0(xP,xS) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f5336,plain,
( ~ sQ299_spl
| ~ sQ466_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5329,f332,f5333,f3098]) ).
fof(f6394,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ375_spl
| aElementOf0(sK1_skl(xP,X0),xS)
| aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| sK1_skl(xP,X0) = xx ),
inference(resolution,[status(thm)],[f4209,f452]) ).
fof(f6556,plain,
( ~ sQ20_spl
| ~ sQ375_spl
| aSubsetOf0(xP,xS)
| ~ aSet0(xS)
| sK1_skl(xP,xS) = xx
| ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f104,f6394]) ).
fof(f6564,definition,
( sQ591_spl
<=> sK1_skl(xP,xS) = xx ),
introduced(definition,[new_symbols(definition,[sQ591_spl])],[split_symbol_definition]) ).
fof(f6565,plain,
( ~ sQ591_spl
| sK1_skl(xP,xS) = xx ),
inference(component_clause,[status(thm)],[f6564]) ).
fof(f6567,plain,
( ~ sQ20_spl
| ~ sQ375_spl
| sQ591_spl
| ~ sQ102_spl
| sQ466_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f6556,f332,f5333,f1428,f6564,f4208,f451]) ).
fof(f6695,plain,
( ~ sQ591_spl
| ~ aElementOf0(xx,xS)
| ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS) ),
inference(paramodulation,[status(thm)],[f6565,f104]) ).
fof(f6697,definition,
( sQ605_spl
<=> aElementOf0(xx,xS) ),
introduced(definition,[new_symbols(definition,[sQ605_spl])],[split_symbol_definition]) ).
fof(f6699,plain,
( sQ605_spl
| ~ aElementOf0(xx,xS) ),
inference(component_clause,[status(thm)],[f6697]) ).
fof(f6703,plain,
( ~ sQ591_spl
| ~ sQ605_spl
| ~ sQ102_spl
| sQ466_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f6695,f332,f5333,f1428,f6697,f6564]) ).
fof(f6705,plain,
( sQ605_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6699,f277]) ).
fof(f6706,plain,
sQ605_spl,
inference(contradiction_clause,[status(thm)],[f6705]) ).
fof(f6707,plain,
$false,
inference(sat_refutation,[status(thm)],[f341,f348,f350,f377,f400,f454,f466,f1431,f1433,f1745,f1813,f1873,f2256,f2501,f2892,f2952,f2992,f3043,f3101,f3143,f3196,f4211,f5336,f6567,f6703,f6706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM554+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n026.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 02:42:23 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.57 % Drodi V4.1.1
% 17.53/2.89 % Refutation found
% 17.53/2.89 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.53/2.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.53/2.94 % Elapsed time: 2.364051 seconds
% 14.53/2.94 % CPU time: 18.539724 seconds
% 14.53/2.94 % Total memory used: 249.371 MB
% 14.53/2.94 % Net memory used: 232.531 MB
%------------------------------------------------------------------------------