%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM588+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 01:41:06 PM UTC 2026
% Result : Theorem 12.97s 12.30s
% Output : CNFRefutation 12.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 98 ( 14 unt; 5 def)
% Number of atoms : 442 ( 71 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 564 ( 220 ~; 221 |; 90 &)
% ( 15 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 174 ( 163 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aSet0(W2)
& aSet0(W1)
& aSet0(W0) )
=> ( ( aSubsetOf0(W1,W2)
& aSubsetOf0(W0,W1) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,definition,
! [W0] :
( ( W0 != slcrc0
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,conjecture,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
=> aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,negated_conjecture,
~ ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
=> ! [W2] :
( ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
=> aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f96,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f97,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f107,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f110,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f111,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,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(f115,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)],[f114]) ).
fof(f116,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)],[f115]) ).
fof(f117,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))],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f128,plain,
! [W0,W1,W2] :
( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X2)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f143,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(f144,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f145,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)],[f143,f144]) ).
fof(f146,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)],[f145]) ).
fof(f147,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)],[f146]) ).
fof(f148,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))],[f147]) ).
fof(f149,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f166,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f224,plain,
! [W0] :
( ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f225,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(NNF_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ~ sdtlseqdt0(W1,W2)
& aElementOf0(W2,W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(miniscoping,[status(thm)],[f225]) ).
fof(f227,plain,
! [W0] :
( ( ! [W1] :
( ( ~ sdtlseqdt0(W1,sK6_skl(W1,W0))
& aElementOf0(sK6_skl(W1,W0),W0) )
| ~ aElementOf0(W1,W0)
| W1 = szmzizndt0(W0) )
& ! [W1] :
( ( ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,W0) )
| W1 != szmzizndt0(W0) ) )
| W0 = slcrc0
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W2,sK6_skl(W1,W0))],[f226]) ).
fof(f228,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| X1 != szmzizndt0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f271,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(f272,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)],[f271]) ).
fof(f273,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)],[f272]) ).
fof(f274,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))],[f273]) ).
fof(f276,plain,
! [X0,X1,X2,X3] :
( aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f277,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)],[f274]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| aElementOf0(X3,X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f362,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f370,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f371,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f372,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f387,plain,
? [W0] :
( ? [W1] :
( ? [W2] :
( ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
& aElementOf0(W2,slbdtsldtrb0(W1,xk))
& aSet0(W2) )
& isCountable0(W1)
& aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f89]) ).
fof(f388,plain,
( ~ aElementOf0(sK23_skl,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl))),xk))
& aElementOf0(sK23_skl,slbdtsldtrb0(sK22_skl,xk))
& aSet0(sK23_skl)
& isCountable0(sK22_skl)
& aSubsetOf0(sK22_skl,sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl))))
& aElementOf0(sK21_skl,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl]),skolemize(W0,sK21_skl),skolemize(W1,sK22_skl),skolemize(W2,sK23_skl)],[f387]) ).
fof(f389,plain,
aElementOf0(sK21_skl,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f390,plain,
aSubsetOf0(sK22_skl,sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f393,plain,
aElementOf0(sK23_skl,slbdtsldtrb0(sK22_skl,xk)),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f394,plain,
~ aElementOf0(sK23_skl,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl))),xk)),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f410,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f149]) ).
fof(f414,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f228]) ).
fof(f425,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X0)
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f426,plain,
! [X0,X1,X2] :
( sbrdtbr0(X2) = X1
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f277]) ).
fof(f427,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aElementOf0(X1,slbdtsldtrb0(X0,sbrdtbr0(X1)))
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f278]) ).
fof(f445,plain,
( aSet0(sK22_skl)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))) ),
inference(resolution,[status(thm)],[f118,f390]) ).
fof(f447,plain,
! [X0] :
( ~ isFinite0(sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f372,f111]) ).
fof(f476,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))
| ~ aSet0(sdtlpdtrp0(xN,sK21_skl))
| aSet0(sK22_skl) ),
inference(resolution,[status(thm)],[f445,f410]) ).
fof(f487,plain,
! [X0] :
( aElement0(szmzizndt0(X0))
| ~ aSet0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f414,f97]) ).
fof(f493,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X1)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X2,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f118]) ).
fof(f550,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[f371,f118]) ).
fof(f555,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f166]) ).
fof(f640,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElement0(szmzizndt0(sdtlpdtrp0(xN,X0)))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| sdtlpdtrp0(xN,X0) = slcrc0 ),
inference(resolution,[status(thm)],[f487,f371]) ).
fof(f643,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElement0(szmzizndt0(sdtlpdtrp0(xN,X0)))
| sdtlpdtrp0(xN,X0) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f555]) ).
fof(f660,plain,
( aSubsetOf0(sK23_skl,sK22_skl)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(sK22_skl) ),
inference(resolution,[status(thm)],[f425,f393]) ).
fof(f664,plain,
( aSubsetOf0(sK23_skl,sK22_skl)
| ~ aSet0(sK22_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f362]) ).
fof(f688,plain,
! [X0] :
( aSubsetOf0(sK23_skl,X0)
| ~ aSubsetOf0(sK22_skl,X0)
| ~ aSet0(X0)
| ~ aSet0(sK22_skl)
| ~ aSet0(sK22_skl) ),
inference(resolution,[status(thm)],[f664,f493]) ).
fof(f693,plain,
! [X0] :
( aSubsetOf0(sK23_skl,X0)
| ~ aSubsetOf0(sK22_skl,X0)
| ~ aSet0(X0)
| ~ aSet0(sK22_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f688]) ).
fof(f694,plain,
! [X0] :
( aSubsetOf0(sK23_skl,X0)
| ~ aSubsetOf0(sK22_skl,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f693,f118]) ).
fof(f757,plain,
( aSubsetOf0(sK23_skl,sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))) ),
inference(resolution,[status(thm)],[f694,f390]) ).
fof(f944,plain,
! [X0] :
( ~ isFinite0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f555]) ).
fof(f1884,plain,
( sbrdtbr0(sK23_skl) = xk
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(sK22_skl) ),
inference(resolution,[status(thm)],[f426,f393]) ).
fof(f1890,plain,
( sbrdtbr0(sK23_skl) = xk
| ~ aSet0(sK22_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1884,f362]) ).
fof(f5986,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK21_skl))
| aSet0(sK22_skl)
| ~ aElementOf0(sK21_skl,szNzAzT0)
| sdtlpdtrp0(xN,sK21_skl) = slcrc0 ),
inference(resolution,[status(thm)],[f643,f476]) ).
fof(f5990,plain,
( ~ aSet0(sdtlpdtrp0(xN,sK21_skl))
| aSet0(sK22_skl)
| sdtlpdtrp0(xN,sK21_skl) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f5986,f389]) ).
fof(f5992,plain,
( ~ aElementOf0(sK21_skl,szNzAzT0)
| aSet0(sK22_skl)
| sdtlpdtrp0(xN,sK21_skl) = slcrc0 ),
inference(resolution,[status(thm)],[f5990,f555]) ).
fof(f5993,plain,
( aSet0(sK22_skl)
| sdtlpdtrp0(xN,sK21_skl) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f5992,f389]) ).
fof(f6057,plain,
( aSet0(sK22_skl)
| ~ isFinite0(slcrc0)
| ~ aElementOf0(sK21_skl,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f5993,f944]) ).
fof(f6089,plain,
( aSet0(sK22_skl)
| ~ isFinite0(slcrc0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6057,f389]) ).
fof(f6102,plain,
sbrdtbr0(sK23_skl) = xk,
inference(backward_subsumption_resolution,[status(thm)],[f1890,f6115]) ).
fof(f6115,plain,
aSet0(sK22_skl),
inference(forward_subsumption_resolution,[status(thm)],[f6089,f107]) ).
fof(f6125,plain,
! [X0] :
( ~ aSubsetOf0(sK23_skl,X0)
| aElementOf0(sK23_skl,slbdtsldtrb0(X0,xk))
| ~ aElementOf0(sbrdtbr0(sK23_skl),szNzAzT0)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f6102,f427]) ).
fof(f6159,plain,
! [X0] :
( ~ aSubsetOf0(sK23_skl,X0)
| aElementOf0(sK23_skl,slbdtsldtrb0(X0,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f6102,f6125]) ).
fof(f6160,plain,
! [X0] :
( ~ aSubsetOf0(sK23_skl,X0)
| aElementOf0(sK23_skl,slbdtsldtrb0(X0,xk))
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6159,f362]) ).
fof(f6302,plain,
( ~ aSubsetOf0(sK23_skl,sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))) ),
inference(resolution,[status(thm)],[f6160,f394]) ).
fof(f6307,plain,
~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK21_skl),szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))),
inference(forward_subsumption_resolution,[status(thm)],[f6302,f757]) ).
fof(f6326,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,sK21_skl)))
| ~ aSet0(sdtlpdtrp0(xN,sK21_skl)) ),
inference(resolution,[status(thm)],[f6307,f410]) ).
fof(f6327,plain,
( ~ aElementOf0(sK21_skl,szNzAzT0)
| sdtlpdtrp0(xN,sK21_skl) = slcrc0
| ~ aSet0(sdtlpdtrp0(xN,sK21_skl)) ),
inference(resolution,[status(thm)],[f6326,f643]) ).
fof(f6328,plain,
( ~ aElementOf0(sK21_skl,szNzAzT0)
| sdtlpdtrp0(xN,sK21_skl) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f6327,f555]) ).
fof(f6442,plain,
sdtlpdtrp0(xN,sK21_skl) = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f6328,f389]) ).
fof(f6466,plain,
( ~ isFinite0(slcrc0)
| ~ aElementOf0(sK21_skl,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f6442,f944]) ).
fof(f6538,plain,
~ isFinite0(slcrc0),
inference(forward_subsumption_resolution,[status(thm)],[f6466,f389]) ).
fof(f6557,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6538,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM588+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.54 % Computer : n006.cluster.edu
% 0.08/10.54 % Model : x86_64 x86_64
% 0.08/10.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.54 % Memory : 8046.5625MB
% 0.08/10.54 % OS : Linux 6.8.0-71-generic
% 0.08/10.54 % CPULimit : 300
% 0.08/10.54 % WCLimit : 300
% 0.08/10.54 % DateTime : Mon Sep 21 02:42:25 UTC 2026
% 0.08/10.54 % CPUTime :
% 0.08/10.56 % Drodi V4.1.1
% 12.97/12.30 % Refutation found
% 12.97/12.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.97/12.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.16/12.35 % Elapsed time: 1.787231 seconds
% 5.16/12.35 % CPU time: 13.831851 seconds
% 5.16/12.35 % Total memory used: 230.227 MB
% 5.16/12.35 % Net memory used: 217.334 MB
%------------------------------------------------------------------------------