%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM558+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 01:40:59 PM UTC 2026
% Result : Theorem 1.29s 0.71s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 123 ( 25 unt; 20 def)
% Number of atoms : 491 ( 80 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 597 ( 229 ~; 229 |; 99 &)
% ( 33 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 15 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 161 ( 150 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
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(f15,definition,
! [W0,W1] :
( ( aElement0(W1)
& aSet0(W0) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) ) )
& aSet0(W2) ) ) ),
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(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(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
( slbdtsldtrb0(xS,xk) != slcrc0
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,hypothesis,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f80,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f81,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f85,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f87,plain,
( ! [W0] :
( aElementOf0(sK0_skl(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f98,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(f99,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)],[f98]) ).
fof(f100,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)],[f99]) ).
fof(f101,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))],[f100]) ).
fof(f103,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f114,plain,
! [W0,W1] :
( ! [W2] :
( W2 = sdtpldt0(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)],[f15]) ).
fof(f115,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ( ( ! [W3] :
( ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) ) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [W0,W1] :
( ( ! [W2] :
( ? [W3] :
( ( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| aElementOf0(W3,W2) )
& ( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| ~ aElementOf0(W3,W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
! [W0,W1] :
( ( ! [W2] :
( ( ( ( ( sK2_skl(W2,W1,W0) = W1
| aElementOf0(sK2_skl(W2,W1,W0),W0) )
& aElement0(sK2_skl(W2,W1,W0)) )
| aElementOf0(sK2_skl(W2,W1,W0),W2) )
& ( ( sK2_skl(W2,W1,W0) != W1
& ~ aElementOf0(sK2_skl(W2,W1,W0),W0) )
| ~ aElement0(sK2_skl(W2,W1,W0))
| ~ aElementOf0(sK2_skl(W2,W1,W0),W2) ) )
| ~ aSet0(W2)
| W2 = sdtpldt0(W0,W1) )
& ! [W2] :
( ( ! [W3] :
( ( W3 != W1
& ~ aElementOf0(W3,W0) )
| ~ aElement0(W3)
| aElementOf0(W3,W2) )
& ! [W3] :
( ( ( W3 = W1
| aElementOf0(W3,W0) )
& aElement0(W3) )
| ~ aElementOf0(W3,W2) )
& aSet0(W2) )
| W2 != sdtpldt0(W0,W1) ) )
| ~ aElement0(W1)
| ~ aSet0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W3,sK2_skl(W2,W1,W0))],[f116]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| ~ aElement0(X3)
| aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f127,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(f128,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f129,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)],[f127,f128]) ).
fof(f130,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)],[f129]) ).
fof(f131,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)],[f130]) ).
fof(f132,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))],[f131]) ).
fof(f133,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtmndt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f255,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(f256,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)],[f255]) ).
fof(f257,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)],[f256]) ).
fof(f258,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))],[f257]) ).
fof(f259,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f260,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)],[f258]) ).
fof(f272,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f273,plain,
aSet0(xS),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f274,plain,
aSet0(xT),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f276,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f277,plain,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f278,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f280,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f284,plain,
aElementOf0(xy,xQ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f287,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f288,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f289,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f297,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f89]) ).
fof(f307,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f122]) ).
fof(f308,plain,
! [X0,X1] :
( aElementOf0(X1,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f307]) ).
fof(f312,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f133]) ).
fof(f328,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f259]) ).
fof(f329,plain,
! [X0,X1,X2] :
( aSubsetOf0(X2,X0)
| ~ aElementOf0(X2,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f260]) ).
fof(f333,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f81,f278]) ).
fof(f334,definition,
( sQ0_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( sQ0_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
( sQ1_spl
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f333,f334,f337]) ).
fof(f341,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f273]) ).
fof(f342,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f353,plain,
( aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f284,f81]) ).
fof(f354,definition,
( sQ4_spl
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ4_spl
| ~ aSet0(xQ) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,definition,
( sQ5_spl
<=> aElement0(xy) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f353,f354,f357]) ).
fof(f361,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f280]) ).
fof(f362,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f373,plain,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(resolution,[status(thm)],[f103,f276]) ).
fof(f375,definition,
( sQ8_spl
<=> aSet0(slbdtsldtrb0(xT,xk)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ8_spl
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
! [X0] :
( sQ9_spl
<=> ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f379,plain,
! [X0] :
( ~ sQ9_spl
| aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f373,f375,f378]) ).
fof(f646,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f287,f308]) ).
fof(f647,definition,
( sQ39_spl
<=> aSet0(sdtmndt0(xQ,xy)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( sQ39_spl
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(component_clause,[status(thm)],[f647]) ).
fof(f650,definition,
( sQ40_spl
<=> aElementOf0(xx,xP) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( ~ sQ40_spl
| aElementOf0(xx,xP) ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( sQ40_spl
| ~ sQ1_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f646,f647,f337,f650]) ).
fof(f764,definition,
( sQ52_spl
<=> xQ = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( ~ sQ52_spl
| xQ = slcrc0 ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f873,plain,
( sQ39_spl
| ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f312,f649]) ).
fof(f874,plain,
( sQ39_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f873,f354,f357,f647]) ).
fof(f1071,definition,
( sQ95_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1073,plain,
( sQ95_spl
| ~ aElementOf0(xk,szNzAzT0) ),
inference(component_clause,[status(thm)],[f1071]) ).
fof(f1079,plain,
( sQ95_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1073,f272]) ).
fof(f1080,plain,
sQ95_spl,
inference(contradiction_clause,[status(thm)],[f1079]) ).
fof(f1288,plain,
( sQ8_spl
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f328,f377]) ).
fof(f1290,definition,
( sQ125_spl
<=> aSet0(xT) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1292,plain,
( sQ125_spl
| ~ aSet0(xT) ),
inference(component_clause,[status(thm)],[f1290]) ).
fof(f1293,plain,
( sQ8_spl
| ~ sQ95_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f1288,f1290,f1071,f375]) ).
fof(f1300,plain,
( sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1292,f274]) ).
fof(f1301,plain,
sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1300]) ).
fof(f1302,plain,
( ~ sQ9_spl
| aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
inference(resolution,[status(thm)],[f379,f288]) ).
fof(f1320,definition,
( sQ130_spl
<=> slbdtsldtrb0(xS,xk) = slcrc0 ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1321,plain,
( ~ sQ130_spl
| slbdtsldtrb0(xS,xk) = slcrc0 ),
inference(component_clause,[status(thm)],[f1320]) ).
fof(f1340,plain,
( ~ sQ130_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1321,f277]) ).
fof(f1341,plain,
~ sQ130_spl,
inference(contradiction_clause,[status(thm)],[f1340]) ).
fof(f1517,plain,
( ~ sQ9_spl
| aSubsetOf0(xP,xT)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f329,f1302]) ).
fof(f1529,definition,
( sQ159_spl
<=> aSubsetOf0(xP,xT) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( ~ sQ159_spl
| aSubsetOf0(xP,xT) ),
inference(component_clause,[status(thm)],[f1529]) ).
fof(f1532,plain,
( ~ sQ9_spl
| sQ159_spl
| ~ sQ95_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f1517,f1290,f1071,f1529,f378]) ).
fof(f1685,plain,
! [X0] :
( ~ sQ159_spl
| aElementOf0(X0,xT)
| ~ aElementOf0(X0,xP)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[f1530,f103]) ).
fof(f1695,definition,
! [X0] :
( sQ185_spl
<=> ( aElementOf0(X0,xT)
| ~ aElementOf0(X0,xP) ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1696,plain,
! [X0] :
( ~ sQ185_spl
| aElementOf0(X0,xT)
| ~ aElementOf0(X0,xP) ),
inference(component_clause,[status(thm)],[f1695]) ).
fof(f1698,plain,
( ~ sQ159_spl
| sQ185_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f1685,f1290,f1695,f1529]) ).
fof(f1774,plain,
( ~ sQ52_spl
| aElementOf0(xy,slcrc0) ),
inference(backward_demodulation,[status(thm)],[f765,f284]) ).
fof(f1785,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1774,f297]) ).
fof(f1786,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1785]) ).
fof(f1992,plain,
( ~ sQ40_spl
| ~ sQ185_spl
| aElementOf0(xx,xT) ),
inference(resolution,[status(thm)],[f1696,f651]) ).
fof(f2017,plain,
( ~ sQ40_spl
| ~ sQ185_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1992,f289]) ).
fof(f2018,plain,
( ~ sQ40_spl
| ~ sQ185_spl ),
inference(contradiction_clause,[status(thm)],[f2017]) ).
fof(f2019,plain,
$false,
inference(sat_refutation,[status(thm)],[f340,f342,f360,f362,f381,f653,f874,f1080,f1293,f1301,f1341,f1532,f1698,f1786,f2018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM558+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:45:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.29/0.71 % Refutation found
% 1.29/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.29/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.29/0.73 % Elapsed time: 0.369004 seconds
% 1.29/0.73 % CPU time: 2.526726 seconds
% 1.29/0.73 % Total memory used: 142.036 MB
% 1.29/0.73 % Net memory used: 138.015 MB
%------------------------------------------------------------------------------