%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM612+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 : n001.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 01:41:11 PM UTC 2026
% Result : Theorem 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 49
% Syntax : Number of formulae : 173 ( 37 unt; 26 def)
% Number of atoms : 528 ( 76 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 581 ( 226 ~; 224 |; 77 &)
% ( 37 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 23 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 14 con; 0-3 aty)
% Number of variables : 151 ( 145 !; 6 ?)
% 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(f11,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
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(f17,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
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(f51,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> isFinite0(slbdtrb0(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(f64,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,hypothesis,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,conjecture,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f110,negated_conjecture,
~ ( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
fof(f117,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f118,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f135,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(f136,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)],[f135]) ).
fof(f137,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)],[f136]) ).
fof(f138,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))],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f143,plain,
! [W0] :
( ! [W1] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f144,plain,
! [X0,X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f164,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(f165,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f166,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)],[f164,f165]) ).
fof(f167,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)],[f166]) ).
fof(f168,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)],[f167]) ).
fof(f169,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))],[f168]) ).
fof(f171,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)],[f169]) ).
fof(f175,plain,
! [W0] :
( ! [W1] :
( sdtpldt0(sdtmndt0(W0,W1),W1) = W0
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f176,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f187,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f189,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f190,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f191,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f227,plain,
! [W0] :
( ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f228,plain,
! [W0] :
( ( ( ~ isFinite0(W0)
| aElementOf0(sbrdtbr0(W0),szNzAzT0) )
& ( isFinite0(W0)
| ~ aElementOf0(sbrdtbr0(W0),szNzAzT0) ) )
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f227]) ).
fof(f229,plain,
! [X0] :
( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0] :
( ~ isFinite0(X0)
| aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f235,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(f236,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f274,plain,
! [W0] :
( isFinite0(slbdtrb0(W0))
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f275,plain,
! [X0] :
( isFinite0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f292,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(f293,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)],[f292]) ).
fof(f294,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)],[f293]) ).
fof(f295,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))],[f294]) ).
fof(f298,plain,
! [X0,X1,X2,X3] :
( sbrdtbr0(X3) = X1
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f295]) ).
fof(f319,plain,
! [W0] :
( aSet0(szDzozmdt0(W0))
| ~ aFunction0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f64]) ).
fof(f320,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[status(thm)],[f319]) ).
fof(f369,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f370,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f372,plain,
aFunction0(xc),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f383,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f384,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f431,plain,
aSet0(xO),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f441,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f443,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f444,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f446,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f448,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f449,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f451,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f453,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ),
inference(pre_NNF_transformation,[status(thm)],[f110]) ).
fof(f454,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| szszuzczcdt0(sbrdtbr0(xP)) != sbrdtbr0(xQ) ),
inference(cnf_transformation,[status(thm)],[f453]) ).
fof(f455,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)],[f165]) ).
fof(f456,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)],[f455]) ).
fof(f459,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f456]) ).
fof(f461,definition,
( sQ0_spl
<=> szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f464,definition,
( sQ1_spl
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ1_spl
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f454,f461,f464]) ).
fof(f478,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f171]) ).
fof(f493,plain,
! [X0,X1,X2] :
( sbrdtbr0(X2) = X1
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f298]) ).
fof(f508,plain,
! [X0,X1] : ~ sP0_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f459]) ).
fof(f517,definition,
( sQ2_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ2_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f535,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f187]) ).
fof(f536,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f560,plain,
( sbrdtbr0(xQ) = xK
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xO) ),
inference(resolution,[status(thm)],[f493,f441]) ).
fof(f561,definition,
( sQ11_spl
<=> aSet0(xO) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ11_spl
| ~ aSet0(xO) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,definition,
( sQ12_spl
<=> aElementOf0(xK,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f567,definition,
( sQ13_spl
<=> sbrdtbr0(xQ) = xK ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( ~ sQ13_spl
| sbrdtbr0(xQ) = xK ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,plain,
( sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f560,f561,f564,f567]) ).
fof(f576,plain,
( ~ sQ13_spl
| isFinite0(xQ)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f568,f229]) ).
fof(f578,definition,
( sQ14_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f581,definition,
( sQ15_spl
<=> isFinite0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ13_spl
| sQ15_spl
| ~ sQ12_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f576,f578,f564,f581,f567]) ).
fof(f598,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f431]) ).
fof(f599,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f598]) ).
fof(f655,plain,
( aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f384,f191]) ).
fof(f659,definition,
( sQ26_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f661,plain,
( sQ26_spl
| ~ aElementOf0(xk,szNzAzT0) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f693,plain,
( sQ12_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f655,f659,f564]) ).
fof(f694,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f661,f383]) ).
fof(f695,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f694]) ).
fof(f732,definition,
( sQ43_spl
<=> isFinite0(xP) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( aSet0(xP)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f139,f451]) ).
fof(f744,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f139,f444]) ).
fof(f750,definition,
( sQ45_spl
<=> aSet0(xP) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( sQ45_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f743,f578,f750]) ).
fof(f755,plain,
( sQ14_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f744,f517,f578]) ).
fof(f843,plain,
xP = sdtmndt0(xQ,xp),
inference(backward_demodulation,[status(thm)],[f446,f448]) ).
fof(f933,plain,
( aElement0(xp)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f449,f118]) ).
fof(f934,definition,
( sQ71_spl
<=> aElement0(xp) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f937,plain,
( sQ71_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f933,f578,f934]) ).
fof(f976,definition,
( sQ78_spl
<=> aSubsetOf0(xS,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f978,plain,
( sQ78_spl
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(component_clause,[status(thm)],[f976]) ).
fof(f1005,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f144,f451]) ).
fof(f1014,plain,
( sQ43_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1005,f578,f581,f732]) ).
fof(f1555,plain,
! [X0] :
( sP0_prd(X0,xp,xQ)
| ~ aElementOf0(X0,xP)
| ~ aElement0(xp)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f843,f478]) ).
fof(f1558,definition,
! [X0] :
( sQ127_spl
<=> ( sP0_prd(X0,xp,xQ)
| ~ aElementOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1559,plain,
! [X0] :
( ~ sQ127_spl
| sP0_prd(X0,xp,xQ)
| ~ aElementOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f1558]) ).
fof(f1561,plain,
( sQ127_spl
| ~ sQ71_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1555,f578,f934,f1558]) ).
fof(f1569,plain,
( ~ sQ127_spl
| ~ aElementOf0(xp,xP) ),
inference(resolution,[status(thm)],[f1559,f508]) ).
fof(f1763,definition,
( sQ151_spl
<=> isFinite0(slbdtrb0(xK)) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1765,plain,
( sQ151_spl
| ~ isFinite0(slbdtrb0(xK)) ),
inference(component_clause,[status(thm)],[f1763]) ).
fof(f1771,definition,
( sQ153_spl
<=> isFinite0(slbdtrb0(xk)) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1773,plain,
( sQ153_spl
| ~ isFinite0(slbdtrb0(xk)) ),
inference(component_clause,[status(thm)],[f1771]) ).
fof(f1790,plain,
( sdtpldt0(xP,xp) = xQ
| ~ aElementOf0(xp,xQ)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f843,f176]) ).
fof(f1791,definition,
( sQ156_spl
<=> aElementOf0(xp,xQ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1793,plain,
( sQ156_spl
| ~ aElementOf0(xp,xQ) ),
inference(component_clause,[status(thm)],[f1791]) ).
fof(f1794,definition,
( sQ157_spl
<=> sdtpldt0(xP,xp) = xQ ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1795,plain,
( ~ sQ157_spl
| sdtpldt0(xP,xp) = xQ ),
inference(component_clause,[status(thm)],[f1794]) ).
fof(f1797,plain,
( sQ157_spl
| ~ sQ156_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1790,f578,f1791,f1794]) ).
fof(f1798,plain,
( sQ156_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1793,f449]) ).
fof(f1799,plain,
sQ156_spl,
inference(contradiction_clause,[status(thm)],[f1798]) ).
fof(f1857,definition,
! [X0] :
( sQ168_spl
<=> ~ aElementOf0(X0,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1858,plain,
! [X0] :
( ~ sQ168_spl
| ~ aElementOf0(X0,szNzAzT0) ),
inference(component_clause,[status(thm)],[f1857]) ).
fof(f1862,plain,
( ~ sQ168_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f189,f1858]) ).
fof(f1868,plain,
~ sQ168_spl,
inference(contradiction_clause,[status(thm)],[f1862]) ).
fof(f1916,plain,
isFinite0(slbdtrb0(xk)),
inference(resolution,[status(thm)],[f275,f383]) ).
fof(f1917,plain,
isFinite0(slbdtrb0(xK)),
inference(resolution,[status(thm)],[f275,f369]) ).
fof(f1921,plain,
( sQ153_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1916,f1773]) ).
fof(f1922,plain,
sQ153_spl,
inference(contradiction_clause,[status(thm)],[f1921]) ).
fof(f1923,plain,
( sQ151_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1917,f1765]) ).
fof(f1924,plain,
sQ151_spl,
inference(contradiction_clause,[status(thm)],[f1923]) ).
fof(f1936,definition,
( sQ174_spl
<=> aSet0(szDzozmdt0(xc)) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1938,plain,
( sQ174_spl
| ~ aSet0(szDzozmdt0(xc)) ),
inference(component_clause,[status(thm)],[f1936]) ).
fof(f1944,plain,
( sQ174_spl
| ~ aFunction0(xc) ),
inference(resolution,[status(thm)],[f1938,f320]) ).
fof(f1945,plain,
( sQ174_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1944,f372]) ).
fof(f1946,plain,
sQ174_spl,
inference(contradiction_clause,[status(thm)],[f1945]) ).
fof(f1956,definition,
( sQ178_spl
<=> aElementOf0(xp,xP) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1957,plain,
( ~ sQ178_spl
| aElementOf0(xp,xP) ),
inference(component_clause,[status(thm)],[f1956]) ).
fof(f1963,plain,
( ~ sQ178_spl
| ~ sQ127_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1957,f1569]) ).
fof(f1964,plain,
( ~ sQ178_spl
| ~ sQ127_spl ),
inference(contradiction_clause,[status(thm)],[f1963]) ).
fof(f2153,definition,
( sQ191_spl
<=> xQ = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2154,plain,
( ~ sQ191_spl
| xQ = slcrc0 ),
inference(component_clause,[status(thm)],[f2153]) ).
fof(f2157,plain,
( ~ sQ191_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2154,f443]) ).
fof(f2158,plain,
~ sQ191_spl,
inference(contradiction_clause,[status(thm)],[f2157]) ).
fof(f2419,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f978,f370]) ).
fof(f2420,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f2419]) ).
fof(f2620,plain,
( ~ sQ157_spl
| sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP))
| aElementOf0(xp,xP)
| ~ aElement0(xp)
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(paramodulation,[status(thm)],[f1795,f236]) ).
fof(f2621,plain,
( ~ sQ157_spl
| sQ0_spl
| sQ178_spl
| ~ sQ71_spl
| ~ sQ43_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f2620,f750,f732,f934,f1956,f461,f1794]) ).
fof(f2627,plain,
( sQ1_spl
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(resolution,[status(thm)],[f466,f230]) ).
fof(f2628,plain,
( sQ1_spl
| ~ sQ43_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f2627,f750,f732,f464]) ).
fof(f2629,plain,
$false,
inference(sat_refutation,[status(thm)],[f467,f536,f570,f593,f599,f693,f695,f754,f755,f937,f1014,f1561,f1797,f1799,f1868,f1922,f1924,f1946,f1964,f2158,f2420,f2621,f2628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM612+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:49:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.49 % Refutation found
% 0.14/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.52 % Elapsed time: 0.148883 seconds
% 0.14/0.52 % CPU time: 0.898576 seconds
% 0.14/0.52 % Total memory used: 125.810 MB
% 0.14/0.52 % Net memory used: 124.555 MB
%------------------------------------------------------------------------------