%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG118+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 02:05:02 PM UTC 2026
% Result : Theorem 0.22s 0.65s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 98 ( 17 unt; 13 def)
% Number of atoms : 471 ( 116 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 546 ( 173 ~; 177 |; 167 &)
% ( 21 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 14 con; 0-2 aty)
% Number of variables : 157 ( 106 !; 51 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [W0,W1] :
( ( W1 != sz00
& aElement0(W1)
& aElement0(W0) )
=> ? [W2,W3] :
( ( W3 != sz00
=> iLess0(sbrdtbr0(W3),sbrdtbr0(W1)) )
& W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xb))
<=> ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) ) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xa))
<=> ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,conjecture,
? [W0,W1] :
( ( iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
| W1 = sz00 )
& xb = sdtpldt0(sdtasdt0(W0,xu),W1)
& aElement0(W1)
& aElement0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
~ ? [W0,W1] :
( ( iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
| W1 = sz00 )
& xb = sdtpldt0(sdtasdt0(W0,xu),W1)
& aElement0(W1)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f55,plain,
aElement0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f95,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f96,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f158,plain,
! [W0,W1] :
( ? [W2,W3] :
( ( iLess0(sbrdtbr0(W3),sbrdtbr0(W1))
| W3 = sz00 )
& W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f159,plain,
! [W0,W1] :
( ? [W3] :
( ( iLess0(sbrdtbr0(W3),sbrdtbr0(W1))
| W3 = sz00 )
& ? [W2] :
( W0 = sdtpldt0(sdtasdt0(W2,W1),W3)
& aElement0(W3)
& aElement0(W2) ) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f158]) ).
fof(f160,plain,
! [W0,W1] :
( ( ( iLess0(sbrdtbr0(sK13_skl(W1,W0)),sbrdtbr0(W1))
| sK13_skl(W1,W0) = sz00 )
& W0 = sdtpldt0(sdtasdt0(sK14_skl(W1,W0),W1),sK13_skl(W1,W0))
& aElement0(sK13_skl(W1,W0))
& aElement0(sK14_skl(W1,W0)) )
| W1 = sz00
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(W3,sK13_skl(W1,W0)),skolemize(W2,sK14_skl(W1,W0))],[f159]) ).
fof(f161,plain,
! [X0,X1] :
( aElement0(sK14_skl(X1,X0))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( aElement0(sK13_skl(X1,X0))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f163,plain,
! [X0,X1] :
( X0 = sdtpldt0(sdtasdt0(sK14_skl(X1,X0),X1),sK13_skl(X1,X0))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f164,plain,
! [X0,X1] :
( iLess0(sbrdtbr0(sK13_skl(X1,X0)),sbrdtbr0(X1))
| sK13_skl(X1,X0) = sz00
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f204,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f205,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f225,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( aElementOf0(W0,xI)
<=> ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f226,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) ) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) ) )
& ! [W0] :
( ( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) ) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(NNF_transformation,[status(thm)],[f225]) ).
fof(f227,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ! [W0] :
( ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(miniscoping,[status(thm)],[f226]) ).
fof(f228,plain,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [W0] :
( ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) )
| aElementOf0(W0,xI) )
& ! [W0] :
( ( sdtpldt0(sK25_skl(W0),sK26_skl(W0)) = W0
& aElementOf0(sK26_skl(W0),slsdtgt0(xb))
& aElementOf0(sK25_skl(W0),slsdtgt0(xa)) )
| ~ aElementOf0(W0,xI) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ( sdtasdt0(xb,sK24_skl(W0)) = W0
& aElement0(sK24_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ( sdtasdt0(xa,sK23_skl(W0)) = W0
& aElement0(sK23_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(W1,sK23_skl(W0)),skolemize(W1,sK24_skl(W0)),skolemize(W1,sK25_skl(W0)),skolemize(W2,sK26_skl(W0))],[f227]) ).
fof(f229,plain,
aSet0(xI),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f244,plain,
( aElementOf0(xb,slsdtgt0(xb))
& sdtasdt0(xb,sK30_skl) = xb
& aElement0(sK30_skl)
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,sK29_skl) = sz00
& aElement0(sK29_skl)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,sK28_skl) = xa
& aElement0(sK28_skl)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,sK27_skl) = sz00
& aElement0(sK27_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl,sK28_skl,sK29_skl,sK30_skl]),skolemize(W0,sK27_skl),skolemize(W0,sK28_skl),skolemize(W0,sK29_skl),skolemize(W0,sK30_skl)],[f43]) ).
fof(f253,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f257,plain,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) ) )
& ! [W1] :
( ( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f258,plain,
? [W0] :
( W0 != sz00
& aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ? [W2] :
( sdtasdt0(xb,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ? [W2] :
( sdtasdt0(xa,W2) = W1
& aElement0(W2) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ),
inference(miniscoping,[status(thm)],[f257]) ).
fof(f259,plain,
( sK31_skl != sz00
& aElementOf0(sK31_skl,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& sdtpldt0(sK34_skl,sK35_skl) = sK31_skl
& aElementOf0(sK35_skl,slsdtgt0(xb))
& aElementOf0(sK34_skl,slsdtgt0(xa))
& ! [W1] :
( ! [W2] :
( sdtasdt0(xb,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ( sdtasdt0(xb,sK33_skl(W1)) = W1
& aElement0(sK33_skl(W1)) )
| ~ aElementOf0(W1,slsdtgt0(xb)) )
& ! [W1] :
( ! [W2] :
( sdtasdt0(xa,W2) != W1
| ~ aElement0(W2) )
| aElementOf0(W1,slsdtgt0(xa)) )
& ! [W1] :
( ( sdtasdt0(xa,sK32_skl(W1)) = W1
& aElement0(sK32_skl(W1)) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl,sK32_skl,sK33_skl,sK34_skl,sK35_skl]),skolemize(W0,sK31_skl),skolemize(W2,sK32_skl(W1)),skolemize(W2,sK33_skl(W1)),skolemize(W1,sK34_skl),skolemize(W2,sK35_skl)],[f258]) ).
fof(f263,plain,
! [X0] :
( aElement0(sK33_skl(X0))
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f271,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xu
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f272,plain,
( ! [W0] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
& xu != sz00
& aElementOf0(xu,xI)
& sdtpldt0(sK36_skl,sK37_skl) = xu
& aElementOf0(sK37_skl,slsdtgt0(xb))
& aElementOf0(sK36_skl,slsdtgt0(xa)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36_skl,sK37_skl]),skolemize(W0,sK36_skl),skolemize(W1,sK37_skl)],[f271]) ).
fof(f276,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f277,plain,
xu != sz00,
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f297,plain,
! [W0,W1] :
( ( ~ iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
& W1 != sz00 )
| xb != sdtpldt0(sdtasdt0(W0,xu),W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f298,plain,
! [W1] :
( ( ~ iLess0(sbrdtbr0(W1),sbrdtbr0(xu))
& W1 != sz00 )
| ! [W0] :
( xb != sdtpldt0(sdtasdt0(W0,xu),W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(miniscoping,[status(thm)],[f297]) ).
fof(f299,plain,
! [X0,X1] :
( X1 != sz00
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f405,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(sz00)
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f299]) ).
fof(f407,plain,
! [X0] :
( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
| ~ aElement0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f405,f55]) ).
fof(f413,definition,
( sQ12_spl
<=> aElement0(sz00) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( sQ12_spl
| ~ aElement0(sz00) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f425,definition,
( sQ15_spl
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f428,definition,
( sQ16_spl
<=> xu = sz00 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ16_spl
| xu = sz00 ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f432,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f429,f277]) ).
fof(f433,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f432]) ).
fof(f497,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f96,f276]) ).
fof(f500,definition,
( sQ32_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ32_spl
| ~ aSet0(xI) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,plain,
( sQ15_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f497,f500,f425]) ).
fof(f512,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f229]) ).
fof(f513,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f531,plain,
aElement0(sK33_skl(sz00)),
inference(resolution,[status(thm)],[f263,f253]) ).
fof(f533,definition,
( sQ37_spl
<=> aElementOf0(sz00,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ37_spl
| ~ aElementOf0(sz00,slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,definition,
( sQ38_spl
<=> aElement0(xb) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( sQ38_spl
| ~ aElement0(xb) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f548,plain,
( sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f205]) ).
fof(f549,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f253]) ).
fof(f551,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f577,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f55]) ).
fof(f578,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f580,definition,
( sQ43_spl
<=> aElement0(sK33_skl(sz00)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ43_spl
| ~ aElement0(sK33_skl(sz00)) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f587,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f531]) ).
fof(f588,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f723,plain,
( ~ iLess0(sbrdtbr0(sK13_skl(xu,xb)),sbrdtbr0(xu))
| ~ aElement0(sK13_skl(xu,xb))
| ~ aElement0(sK14_skl(xu,xb))
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f163,f300]) ).
fof(f724,definition,
( sQ63_spl
<=> aElement0(sK14_skl(xu,xb)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f726,plain,
( sQ63_spl
| ~ aElement0(sK14_skl(xu,xb)) ),
inference(component_clause,[status(thm)],[f724]) ).
fof(f727,definition,
( sQ64_spl
<=> aElement0(sK13_skl(xu,xb)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f729,plain,
( sQ64_spl
| ~ aElement0(sK13_skl(xu,xb)) ),
inference(component_clause,[status(thm)],[f727]) ).
fof(f730,definition,
( sQ65_spl
<=> iLess0(sbrdtbr0(sK13_skl(xu,xb)),sbrdtbr0(xu)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f732,plain,
( sQ65_spl
| ~ iLess0(sbrdtbr0(sK13_skl(xu,xb)),sbrdtbr0(xu)) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f733,plain,
( ~ sQ65_spl
| ~ sQ64_spl
| ~ sQ63_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f723,f536,f425,f428,f724,f727,f730]) ).
fof(f737,definition,
( sQ66_spl
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( sQ66_spl
| ~ aElement0(xa) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f748,plain,
( sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f204]) ).
fof(f749,plain,
sQ66_spl,
inference(contradiction_clause,[status(thm)],[f748]) ).
fof(f759,plain,
( sQ64_spl
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f729,f162]) ).
fof(f760,plain,
( sQ64_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f759,f536,f425,f428,f727]) ).
fof(f761,plain,
( sQ63_spl
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f726,f161]) ).
fof(f762,plain,
( sQ63_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f761,f536,f425,f428,f724]) ).
fof(f763,plain,
( sQ65_spl
| sK13_skl(xu,xb) = sz00
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f732,f164]) ).
fof(f764,definition,
( sQ70_spl
<=> sK13_skl(xu,xb) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( ~ sQ70_spl
| sK13_skl(xu,xb) = sz00 ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( sQ65_spl
| sQ70_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f763,f536,f425,f428,f764,f730]) ).
fof(f771,plain,
( ~ sQ70_spl
| xb = sdtpldt0(sdtasdt0(sK14_skl(xu,xb),xu),sz00)
| xu = sz00
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(paramodulation,[status(thm)],[f765,f163]) ).
fof(f778,definition,
( sQ72_spl
<=> xb = sdtpldt0(sdtasdt0(sK14_skl(xu,xb),xu),sz00) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f779,plain,
( ~ sQ72_spl
| xb = sdtpldt0(sdtasdt0(sK14_skl(xu,xb),xu),sz00) ),
inference(component_clause,[status(thm)],[f778]) ).
fof(f781,plain,
( ~ sQ70_spl
| sQ72_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f771,f536,f425,f428,f778,f764]) ).
fof(f789,plain,
( ~ sQ72_spl
| ~ aElement0(sK14_skl(xu,xb)) ),
inference(resolution,[status(thm)],[f779,f407]) ).
fof(f800,plain,
( ~ sQ72_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f789,f724,f778]) ).
fof(f838,plain,
$false,
inference(sat_refutation,[status(thm)],[f433,f503,f513,f549,f551,f578,f588,f733,f749,f760,f762,f767,f781,f800]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG118+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % Computer : n008.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.48 % CPULimit : 300
% 0.17/0.48 % WCLimit : 300
% 0.17/0.48 % DateTime : Mon Sep 21 04:21:25 UTC 2026
% 0.17/0.48 % CPUTime :
% 0.17/0.50 % Drodi V4.1.1
% 0.22/0.65 % Refutation found
% 0.22/0.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.71 % Elapsed time: 0.213065 seconds
% 0.22/0.71 % CPU time: 1.156611 seconds
% 0.22/0.71 % Total memory used: 121.006 MB
% 0.22/0.71 % Net memory used: 120.085 MB
%------------------------------------------------------------------------------