%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG112+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:05:01 PM UTC 2026
% Result : Theorem 0.14s 0.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 90 ( 13 unt; 13 def)
% Number of atoms : 511 ( 141 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 620 ( 199 ~; 191 |; 202 &)
% ( 21 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 10 con; 0-2 aty)
% Number of variables : 206 ( 135 !; 71 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/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)) ) ) )
=> ? [W1] :
( ! [W2] :
( ( W2 != sz00
& ( aElementOf0(W2,xI)
| ? [W3,W4] :
( sdtpldt0(W3,W4) = W2
& aElementOf0(W4,slsdtgt0(xb))
& aElementOf0(W3,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) )
& W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,conjecture,
? [W0] :
( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) )
& W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
~ ? [W0] :
( ! [W1] :
( ( W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) )
& W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f221,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(f222,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)],[f221]) ).
fof(f223,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)],[f222]) ).
fof(f224,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))],[f223]) ).
fof(f239,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f253,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(f254,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)],[f253]) ).
fof(f255,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)],[f254]) ).
fof(f262,plain,
aElementOf0(sK34_skl,slsdtgt0(xa)),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f263,plain,
aElementOf0(sK35_skl,slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f264,plain,
sdtpldt0(sK34_skl,sK35_skl) = sK31_skl,
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f265,plain,
aElementOf0(sK31_skl,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f266,plain,
sK31_skl != sz00,
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f267,plain,
! [W0] :
( ? [W1] :
( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
| W2 = sz00
| ( ~ aElementOf0(W2,xI)
& ! [W3,W4] :
( sdtpldt0(W3,W4) != W2
| ~ aElementOf0(W4,slsdtgt0(xb))
| ~ aElementOf0(W3,slsdtgt0(xa)) ) ) )
& W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f268,definition,
! [W0] :
( sP4_prd(W0)
<=> ( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f269,plain,
! [W0] :
( ? [W1] :
( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
| W2 = sz00
| ( ~ aElementOf0(W2,xI)
& ! [W3,W4] :
( sdtpldt0(W3,W4) != W2
| ~ aElementOf0(W4,slsdtgt0(xb))
| ~ aElementOf0(W3,slsdtgt0(xa)) ) ) )
& W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
| sP4_prd(W0) ),
inference(formula_renaming,[status(thm)],[f267,f268]) ).
fof(f270,plain,
( ? [W1] :
( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1))
| W2 = sz00
| ( ~ aElementOf0(W2,xI)
& ! [W3,W4] :
( sdtpldt0(W3,W4) != W2
| ~ aElementOf0(W4,slsdtgt0(xb))
| ~ aElementOf0(W3,slsdtgt0(xa)) ) ) )
& W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
| ! [W0] : sP4_prd(W0) ),
inference(miniscoping,[status(thm)],[f269]) ).
fof(f271,plain,
( ( ! [W2] :
( ~ iLess0(sbrdtbr0(W2),sbrdtbr0(sK36_skl))
| W2 = sz00
| ( ~ aElementOf0(W2,xI)
& ! [W3,W4] :
( sdtpldt0(W3,W4) != W2
| ~ aElementOf0(W4,slsdtgt0(xb))
| ~ aElementOf0(W3,slsdtgt0(xa)) ) ) )
& sK36_skl != sz00
& aElementOf0(sK36_skl,xI)
& sdtpldt0(sK37_skl,sK38_skl) = sK36_skl
& aElementOf0(sK38_skl,slsdtgt0(xb))
& aElementOf0(sK37_skl,slsdtgt0(xa)) )
| ! [W0] : sP4_prd(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36_skl,sK37_skl,sK38_skl]),skolemize(W1,sK36_skl),skolemize(W2,sK37_skl),skolemize(W3,sK38_skl)],[f270]) ).
fof(f275,plain,
! [X0] :
( aElementOf0(sK36_skl,xI)
| sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f276,plain,
! [X0] :
( sK36_skl != sz00
| sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f278,plain,
! [X0,X1] :
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK36_skl))
| X1 = sz00
| ~ aElementOf0(X1,xI)
| sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f279,plain,
! [W0] :
( ? [W1] :
( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
& W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
| W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f280,definition,
! [W0] :
( sP5_prd(W0)
<=> ( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f281,plain,
! [W0] :
( ? [W1] :
( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
& W1 != sz00
& aElementOf0(W1,xI)
& ? [W2,W3] :
( sdtpldt0(W2,W3) = W1
& aElementOf0(W3,slsdtgt0(xb))
& aElementOf0(W2,slsdtgt0(xa)) ) )
| sP5_prd(W0) ),
inference(formula_renaming,[status(thm)],[f279,f280]) ).
fof(f282,plain,
! [W0] :
( ( iLess0(sbrdtbr0(sK39_skl(W0)),sbrdtbr0(W0))
& sK39_skl(W0) != sz00
& aElementOf0(sK39_skl(W0),xI)
& sdtpldt0(sK40_skl(W0),sK41_skl(W0)) = sK39_skl(W0)
& aElementOf0(sK41_skl(W0),slsdtgt0(xb))
& aElementOf0(sK40_skl(W0),slsdtgt0(xa)) )
| sP5_prd(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl]),skolemize(W1,sK39_skl(W0)),skolemize(W2,sK40_skl(W0)),skolemize(W3,sK41_skl(W0))],[f281]) ).
fof(f286,plain,
! [X0] :
( aElementOf0(sK39_skl(X0),xI)
| sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f287,plain,
! [X0] :
( sK39_skl(X0) != sz00
| sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f288,plain,
! [X0] :
( iLess0(sbrdtbr0(sK39_skl(X0)),sbrdtbr0(X0))
| sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f317,plain,
! [W0] :
( ( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
| sP4_prd(W0) )
& ( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
| ~ sP4_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f318,plain,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
| sP4_prd(W0) )
& ! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
| ~ sP4_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f317]) ).
fof(f319,plain,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ( sdtpldt0(sK43_skl(W0),sK44_skl(W0)) = W0
& aElementOf0(sK44_skl(W0),slsdtgt0(xb))
& aElementOf0(sK43_skl(W0),slsdtgt0(xa)) ) ) )
| sP4_prd(W0) )
& ! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
| ~ sP4_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl]),skolemize(W1,sK43_skl(W0)),skolemize(W2,sK44_skl(W0))],[f318]) ).
fof(f321,plain,
! [X0] :
( X0 = sz00
| ~ aElementOf0(X0,xI)
| ~ sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f319]) ).
fof(f326,plain,
! [W0] :
( ( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
| sP5_prd(W0) )
& ( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
| ~ sP5_prd(W0) ) ),
inference(NNF_transformation,[status(thm)],[f280]) ).
fof(f327,plain,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ? [W1,W2] :
( sdtpldt0(W1,W2) = W0
& aElementOf0(W2,slsdtgt0(xb))
& aElementOf0(W1,slsdtgt0(xa)) ) ) )
| sP5_prd(W0) )
& ! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
| ~ sP5_prd(W0) ) ),
inference(miniscoping,[status(thm)],[f326]) ).
fof(f328,plain,
( ! [W0] :
( ( W0 != sz00
& ( aElementOf0(W0,xI)
| ( sdtpldt0(sK45_skl(W0),sK46_skl(W0)) = W0
& aElementOf0(sK46_skl(W0),slsdtgt0(xb))
& aElementOf0(sK45_skl(W0),slsdtgt0(xa)) ) ) )
| sP5_prd(W0) )
& ! [W0] :
( W0 = sz00
| ( ~ aElementOf0(W0,xI)
& ! [W1,W2] :
( sdtpldt0(W1,W2) != W0
| ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
| ~ sP5_prd(W0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(W1,sK45_skl(W0)),skolemize(W2,sK46_skl(W0))],[f327]) ).
fof(f330,plain,
! [X0] :
( X0 = sz00
| ~ aElementOf0(X0,xI)
| ~ sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f351,definition,
! [X0] :
( sQ2_spl
<=> sP4_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f352,plain,
! [X0] :
( ~ sQ2_spl
| sP4_prd(X0) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f366,definition,
( sQ6_spl
<=> aElementOf0(sK36_skl,xI) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( ~ sQ6_spl
| aElementOf0(sK36_skl,xI) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f275,f351,f366]) ).
fof(f370,definition,
( sQ7_spl
<=> sK36_skl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( ~ sQ7_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f276,f351,f370]) ).
fof(f378,definition,
! [X1] :
( sQ9_spl
<=> ( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK36_skl))
| X1 = sz00
| ~ aElementOf0(X1,xI) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f379,plain,
! [X0] :
( ~ sQ9_spl
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK36_skl))
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( sQ9_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f278,f351,f378]) ).
fof(f400,plain,
aElementOf0(sK31_skl,xI),
inference(forward_demodulation,[status(thm)],[f239,f265]) ).
fof(f407,plain,
! [X0] :
( ~ sQ2_spl
| X0 = sz00
| ~ aElementOf0(X0,xI) ),
inference(backward_subsumption_resolution,[status(thm)],[f321,f352]) ).
fof(f442,plain,
( ~ sQ2_spl
| sK31_skl = sz00 ),
inference(resolution,[status(thm)],[f407,f400]) ).
fof(f445,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f266]) ).
fof(f446,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ6_spl
| sK36_skl = sz00
| ~ sP5_prd(sK36_skl) ),
inference(resolution,[status(thm)],[f330,f367]) ).
fof(f452,definition,
( sQ17_spl
<=> sP5_prd(sK36_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( sQ17_spl
| ~ sP5_prd(sK36_skl) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ6_spl
| sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f448,f452,f370,f366]) ).
fof(f459,definition,
( sQ19_spl
<=> sK31_skl = sz00 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ19_spl
| sK31_skl = sz00 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f464,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f266]) ).
fof(f465,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f464]) ).
fof(f469,definition,
( sQ20_spl
<=> aElementOf0(sK34_skl,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( sQ20_spl
| ~ aElementOf0(sK34_skl,slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,definition,
( sQ21_spl
<=> aElementOf0(sK35_skl,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ21_spl
| ~ aElementOf0(sK35_skl,slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,definition,
( sQ22_spl
<=> sdtpldt0(sK34_skl,sK35_skl) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ22_spl
| sdtpldt0(sK34_skl,sK35_skl) = sz00 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f479,plain,
( ~ sQ22_spl
| sK31_skl = sz00 ),
inference(forward_demodulation,[status(thm)],[f264,f476]) ).
fof(f480,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f266]) ).
fof(f481,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f263]) ).
fof(f483,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f484,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f262]) ).
fof(f485,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f488,plain,
( ~ sQ9_spl
| sP5_prd(sK36_skl)
| sK39_skl(sK36_skl) = sz00
| ~ aElementOf0(sK39_skl(sK36_skl),xI) ),
inference(resolution,[status(thm)],[f379,f288]) ).
fof(f489,definition,
( sQ23_spl
<=> aElementOf0(sK39_skl(sK36_skl),xI) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( sQ23_spl
| ~ aElementOf0(sK39_skl(sK36_skl),xI) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,definition,
( sQ24_spl
<=> sK39_skl(sK36_skl) = sz00 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ24_spl
| sK39_skl(sK36_skl) = sz00 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( ~ sQ9_spl
| sQ17_spl
| sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f488,f489,f492,f452,f378]) ).
fof(f497,plain,
( ~ sQ24_spl
| sP5_prd(sK36_skl) ),
inference(resolution,[status(thm)],[f493,f287]) ).
fof(f502,plain,
( ~ sQ24_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f454]) ).
fof(f503,plain,
( ~ sQ24_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f504,plain,
( sQ23_spl
| sP5_prd(sK36_skl) ),
inference(resolution,[status(thm)],[f491,f286]) ).
fof(f505,plain,
( sQ23_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f454]) ).
fof(f506,plain,
( sQ23_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
$false,
inference(sat_refutation,[status(thm)],[f369,f373,f381,f446,f455,f465,f481,f483,f485,f495,f503,f506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG112+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 04:20:35 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.44 % Drodi V4.1.1
% 0.14/0.58 % Refutation found
% 0.14/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.62 % Elapsed time: 0.187139 seconds
% 0.14/0.62 % CPU time: 1.027410 seconds
% 0.14/0.62 % Total memory used: 121.144 MB
% 0.14/0.62 % Net memory used: 120.247 MB
%------------------------------------------------------------------------------