%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG126+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 : 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 02:05:04 PM UTC 2026
% Result : Theorem 0.15s 0.88s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 83 ( 14 unt; 11 def)
% Number of atoms : 481 ( 111 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 592 ( 194 ~; 188 |; 166 &)
% ( 31 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-5 aty)
% Number of functors : 28 ( 28 usr; 9 con; 0-4 aty)
% Number of variables : 238 ( 177 !; 61 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,definition,
! [W0,W1] :
( ( aSet0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/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/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)) ) ) )
=> ~ 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/sandbox/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
? [W0] :
( sdtasdt0(xu,W0) = xc
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
( ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
=> ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xc
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1] :
( sdtasdt0(xa,W1) = W0
& aElement0(W1) ) )
=> ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1] :
( sdtasdt0(xb,W1) = W0
& aElement0(W1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = xc
& aElementOf0(W1,slsdtgt0(xb))
& aElementOf0(W0,slsdtgt0(xa)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f71,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f72,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f93,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f94,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f101,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f102,definition,
! [W0,W1,W3,W4,W5] :
( sP1_prd(W5,W4,W3,W1,W0)
<=> ( sdtpldt0(W4,W5) = W3
& aElementOf0(W5,W1)
& aElementOf0(W4,W0) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f103,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0) )
& aSet0(W2) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(formula_renaming,[status(thm)],[f101,f102]) ).
fof(f104,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ( ( ! [W3] :
( ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( ? [W4,W5] : sP1_prd(W5,W4,W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( sP1_prd(sK6_skl(W2,W1,W0),sK5_skl(W2,W1,W0),sK4_skl(W2,W1,W0),W1,W0)
| aElementOf0(sK4_skl(W2,W1,W0),W2) )
& ( ! [W4,W5] : ~ sP1_prd(W5,W4,sK4_skl(W2,W1,W0),W1,W0)
| ~ aElementOf0(sK4_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt1(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ! [W4,W5] : ~ sP1_prd(W5,W4,W3,W1,W0)
| aElementOf0(W3,W2) )
& ! [W3] :
( sP1_prd(sK3_skl(W3,W2,W1,W0),sK2_skl(W3,W2,W1,W0),W3,W1,W0)
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt1(W0,W1) ) )
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(W4,sK2_skl(W3,W2,W1,W0)),skolemize(W5,sK3_skl(W3,W2,W1,W0)),skolemize(W3,sK4_skl(W2,W1,W0)),skolemize(W4,sK5_skl(W2,W1,W0)),skolemize(W5,sK6_skl(W2,W1,W0))],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtpldt1(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f189,plain,
! [W0] :
( ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f190,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f190]) ).
fof(f192,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtasdt0(W0,sK19_skl(W1,W0)) = sK18_skl(W1,W0)
& aElement0(sK19_skl(W1,W0)) )
| aElementOf0(sK18_skl(W1,W0),W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != sK18_skl(W1,W0)
| ~ aElement0(W3) )
| ~ aElementOf0(sK18_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtasdt0(W0,sK17_skl(W2,W1,W0)) = W2
& aElement0(sK17_skl(W2,W1,W0)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(W3,sK17_skl(W2,W1,W0)),skolemize(W2,sK18_skl(W1,W0)),skolemize(W3,sK19_skl(W1,W0))],[f191]) ).
fof(f193,plain,
! [X0,X1] :
( aSet0(X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f202,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f203,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f223,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(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) )
& ( ? [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)],[f223]) ).
fof(f225,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)],[f224]) ).
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) )
& ! [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))],[f225]) ).
fof(f229,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f241,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f269,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(f270,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)],[f269]) ).
fof(f274,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f287,plain,
( sdtasdt0(xu,sK40_skl) = xc
& aElement0(sK40_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40_skl]),skolemize(W0,sK40_skl)],[f47]) ).
fof(f288,plain,
aElement0(sK40_skl),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
sdtasdt0(xu,sK40_skl) = xc,
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f290,plain,
( ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W0,W1] :
( sdtpldt0(W0,W1) != xc
| ~ aElementOf0(W1,slsdtgt0(xb))
| ~ aElementOf0(W0,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) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f291,plain,
( ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W0,W1] :
( sdtpldt0(W0,W1) != xc
| ~ aElementOf0(W1,slsdtgt0(xb))
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& ! [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)) ) ) ),
inference(NNF_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
( ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W0,W1] :
( sdtpldt0(W0,W1) != xc
| ~ aElementOf0(W1,slsdtgt0(xb))
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& ! [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)) ) ),
inference(miniscoping,[status(thm)],[f291]) ).
fof(f293,plain,
( ~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W0,W1] :
( sdtpldt0(W0,W1) != xc
| ~ aElementOf0(W1,slsdtgt0(xb))
| ~ aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xb,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ( sdtasdt0(xb,sK42_skl(W0)) = W0
& aElement0(sK42_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xb)) )
& ! [W0] :
( ! [W1] :
( sdtasdt0(xa,W1) != W0
| ~ aElement0(W1) )
| aElementOf0(W0,slsdtgt0(xa)) )
& ! [W0] :
( ( sdtasdt0(xa,sK41_skl(W0)) = W0
& aElement0(sK41_skl(W0)) )
| ~ aElementOf0(W0,slsdtgt0(xa)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(W1,sK41_skl(W0)),skolemize(W1,sK42_skl(W0))],[f292]) ).
fof(f301,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f346,plain,
! [X0,X1] :
( aSet0(sdtpldt1(X0,X1))
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f107]) ).
fof(f354,plain,
! [X0] :
( aSet0(slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f193]) ).
fof(f371,plain,
~ aElementOf0(xc,xI),
inference(backward_demodulation,[status(thm)],[f241,f301]) ).
fof(f373,plain,
( aSet0(xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(paramodulation,[status(thm)],[f241,f346]) ).
fof(f384,definition,
( sQ5_spl
<=> aSet0(slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ5_spl
| ~ aSet0(slsdtgt0(xa)) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
( sQ6_spl
<=> aSet0(slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ6_spl
| ~ aSet0(slsdtgt0(xb)) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ7_spl
<=> aSet0(xI) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f373,f384,f387,f390]) ).
fof(f396,plain,
( sQ5_spl
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f354,f386]) ).
fof(f397,plain,
( sQ6_spl
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f354,f389]) ).
fof(f398,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f202]) ).
fof(f399,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f397,f203]) ).
fof(f401,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f1084,definition,
( sQ134_spl
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1381,plain,
( sdtasdt0(sK40_skl,xu) = xc
| ~ aElement0(xu)
| ~ aElement0(sK40_skl) ),
inference(paramodulation,[status(thm)],[f289,f72]) ).
fof(f1387,definition,
( sQ189_spl
<=> aElement0(sK40_skl) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
( sQ189_spl
| ~ aElement0(sK40_skl) ),
inference(component_clause,[status(thm)],[f1387]) ).
fof(f1411,definition,
( sQ195_spl
<=> sdtasdt0(sK40_skl,xu) = xc ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1412,plain,
( ~ sQ195_spl
| sdtasdt0(sK40_skl,xu) = xc ),
inference(component_clause,[status(thm)],[f1411]) ).
fof(f1414,plain,
( sQ195_spl
| ~ sQ134_spl
| ~ sQ189_spl ),
inference(split_clause,[status(thm)],[f1381,f1387,f1084,f1411]) ).
fof(f1417,plain,
( sQ189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1389,f288]) ).
fof(f1418,plain,
sQ189_spl,
inference(contradiction_clause,[status(thm)],[f1417]) ).
fof(f1430,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[f94,f274]) ).
fof(f1462,plain,
( sQ134_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1430,f390,f1084]) ).
fof(f4756,definition,
( sQ558_spl
<=> aElementOf0(xu,xI) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f4758,plain,
( sQ558_spl
| ~ aElementOf0(xu,xI) ),
inference(component_clause,[status(thm)],[f4756]) ).
fof(f4896,plain,
( ~ sQ195_spl
| aElementOf0(xc,xI)
| ~ aElement0(sK40_skl)
| ~ aElementOf0(xu,xI) ),
inference(paramodulation,[status(thm)],[f1412,f229]) ).
fof(f4909,definition,
( sQ574_spl
<=> aElementOf0(xc,xI) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f4910,plain,
( ~ sQ574_spl
| aElementOf0(xc,xI) ),
inference(component_clause,[status(thm)],[f4909]) ).
fof(f4913,plain,
( ~ sQ195_spl
| sQ574_spl
| ~ sQ189_spl
| ~ sQ558_spl ),
inference(split_clause,[status(thm)],[f4896,f4756,f1387,f4909,f1411]) ).
fof(f4926,plain,
( sQ558_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4758,f274]) ).
fof(f4927,plain,
sQ558_spl,
inference(contradiction_clause,[status(thm)],[f4926]) ).
fof(f4928,plain,
( ~ sQ574_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4910,f371]) ).
fof(f4929,plain,
~ sQ574_spl,
inference(contradiction_clause,[status(thm)],[f4928]) ).
fof(f4930,plain,
$false,
inference(sat_refutation,[status(thm)],[f393,f399,f401,f1414,f1418,f1462,f4913,f4927,f4929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG126+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n026.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 04:24:22 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.59 % Drodi V4.1.1
% 0.15/0.88 % Refutation found
% 0.15/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.91 % Elapsed time: 0.327205 seconds
% 0.15/0.91 % CPU time: 2.327745 seconds
% 0.15/0.91 % Total memory used: 142.216 MB
% 0.15/0.91 % Net memory used: 139.894 MB
%------------------------------------------------------------------------------