%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM556+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 : n015.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 3.51s 0.89s
% Output : CNFRefutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 19
% Syntax : Number of formulae : 141 ( 24 unt; 5 def)
% Number of atoms : 633 ( 103 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 818 ( 326 ~; 356 |; 103 &)
% ( 17 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 212 ( 204 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
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(f11,axiom,
! [W0] :
( ( isFinite0(W0)
& aSet0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox2/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/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(f21,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtpldt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( isFinite0(W1)
& aSet0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/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/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(f61,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,hypothesis,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,conjecture,
( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS) ),
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(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(f104,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f106,plain,
! [W0] :
( ! [W1] :
( isFinite0(W1)
| ~ aSubsetOf0(W1,W0) )
| ~ isFinite0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f107,plain,
! [X0,X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
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(f118,plain,
! [X0,X1,X2] :
( aSet0(X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2)
| X2 != sdtpldt0(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( ~ aElementOf0(X3,X0)
| ~ 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(f134,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)],[f132]) ).
fof(f146,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtpldt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f147,plain,
! [X0,X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f148,plain,
! [W0] :
( ! [W1] :
( isFinite0(sdtmndt0(W1,W0))
| ~ isFinite0(W1)
| ~ aSet0(W1) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f149,plain,
! [X0,X1] :
( isFinite0(sdtmndt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f198,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(f199,plain,
! [X0,X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
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(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(f278,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f279,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f280,plain,
aSet0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f281,plain,
isFinite0(xQ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f283,plain,
aElement0(xy),
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(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f289,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk,
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f290,plain,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f291,plain,
( sbrdtbr0(xP) != xk
| ~ aSubsetOf0(xP,xS) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f292,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)],[f128]) ).
fof(f293,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)],[f292]) ).
fof(f295,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f301,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f303,plain,
! [X0,X1,X2] :
( X2 = X1
| aElementOf0(X2,X0)
| ~ aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f120]) ).
fof(f304,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| ~ aElement0(X2)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f121]) ).
fof(f307,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f133]) ).
fof(f308,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f322,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(f348,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f81,f278]) ).
fof(f353,plain,
aElement0(xx),
inference(forward_subsumption_resolution,[status(thm)],[f348,f273]) ).
fof(f439,plain,
( aSet0(xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f287,f301]) ).
fof(f440,plain,
( aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f353]) ).
fof(f465,plain,
( ~ aElement0(xy)
| ~ aSet0(xQ)
| aSet0(xP) ),
inference(resolution,[status(thm)],[f440,f307]) ).
fof(f466,plain,
( ~ aElement0(xy)
| aSet0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f280]) ).
fof(f467,plain,
aSet0(xP),
inference(forward_subsumption_resolution,[status(thm)],[f466,f283]) ).
fof(f499,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f287,f303]) ).
fof(f502,plain,
! [X0] :
( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f353]) ).
fof(f558,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,X0)
| aElementOf0(X2,sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f81]) ).
fof(f563,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| aElementOf0(X0,xP)
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f287,f558]) ).
fof(f566,plain,
! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,xy))
| aElementOf0(X0,xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f353]) ).
fof(f584,plain,
! [X0] :
( ~ aSet0(sdtmndt0(xQ,xy))
| aSubsetOf0(sdtmndt0(xQ,xy),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xQ,xy),X0),xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[f566,f104]) ).
fof(f587,plain,
! [X0] :
( aSubsetOf0(sdtmndt0(xQ,xy),X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(sdtmndt0(xQ,xy),X0),xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(duplicate_literals_removal,[status(thm)],[f584]) ).
fof(f603,plain,
( ~ aSet0(sdtmndt0(xQ,xy))
| aSubsetOf0(sdtmndt0(xQ,xy),xP)
| ~ aSet0(xP)
| aSubsetOf0(sdtmndt0(xQ,xy),xP)
| ~ aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[f587,f105]) ).
fof(f606,plain,
( aSubsetOf0(sdtmndt0(xQ,xy),xP)
| ~ aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(duplicate_literals_removal,[status(thm)],[f603]) ).
fof(f607,plain,
( aSubsetOf0(sdtmndt0(xQ,xy),xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f467]) ).
fof(f609,plain,
( isFinite0(sdtmndt0(xQ,xy))
| ~ isFinite0(xP)
| ~ aSet0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[f607,f107]) ).
fof(f614,plain,
( isFinite0(sdtmndt0(xQ,xy))
| ~ isFinite0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f467]) ).
fof(f617,plain,
( ~ aElement0(xy)
| ~ aSet0(xQ)
| isFinite0(sdtmndt0(xQ,xy))
| ~ isFinite0(xP) ),
inference(resolution,[status(thm)],[f614,f307]) ).
fof(f618,plain,
( ~ aElement0(xy)
| isFinite0(sdtmndt0(xQ,xy))
| ~ isFinite0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f617,f280]) ).
fof(f619,plain,
( isFinite0(sdtmndt0(xQ,xy))
| ~ isFinite0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f618,f283]) ).
fof(f648,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(paramodulation,[status(thm)],[f287,f147]) ).
fof(f650,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f648,f353]) ).
fof(f730,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xP)
| ~ aSet0(sdtmndt0(xQ,xy))
| sP0_prd(X0,xy,xQ)
| ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f308,f502]) ).
fof(f734,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xP)
| ~ aSet0(sdtmndt0(xQ,xy))
| sP0_prd(X0,xy,xQ)
| ~ aElement0(xy) ),
inference(forward_subsumption_resolution,[status(thm)],[f730,f280]) ).
fof(f740,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy)
| isFinite0(xP)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[f650,f149]) ).
fof(f741,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy)
| isFinite0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f740,f307]) ).
fof(f742,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| isFinite0(xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f741,f283]) ).
fof(f743,plain,
( ~ aSet0(xQ)
| isFinite0(xP) ),
inference(resolution,[status(thm)],[f742,f281]) ).
fof(f744,plain,
isFinite0(xP),
inference(forward_subsumption_resolution,[status(thm)],[f743,f280]) ).
fof(f746,plain,
isFinite0(sdtmndt0(xQ,xy)),
inference(backward_subsumption_resolution,[status(thm)],[f619,f744]) ).
fof(f756,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xP)
| ~ aSet0(sdtmndt0(xQ,xy))
| sP0_prd(X0,xy,xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f734,f283]) ).
fof(f757,plain,
! [X0] :
( ~ aElement0(xy)
| ~ aSet0(xQ)
| X0 = xx
| ~ aElementOf0(X0,xP)
| sP0_prd(X0,xy,xQ) ),
inference(resolution,[status(thm)],[f756,f307]) ).
fof(f758,plain,
! [X0] :
( ~ aElement0(xy)
| X0 = xx
| ~ aElementOf0(X0,xP)
| sP0_prd(X0,xy,xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f757,f280]) ).
fof(f759,plain,
! [X0] :
( X0 = xx
| ~ aElementOf0(X0,xP)
| sP0_prd(X0,xy,xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f283]) ).
fof(f760,plain,
! [X0] :
( aElementOf0(X0,xQ)
| X0 = xx
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f759,f295]) ).
fof(f766,plain,
! [X0] :
( ~ aSet0(xP)
| aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ)
| sK1_skl(xP,X0) = xx ),
inference(resolution,[status(thm)],[f760,f104]) ).
fof(f771,plain,
! [X0] :
( aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ)
| sK1_skl(xP,X0) = xx ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f467]) ).
fof(f1217,plain,
( aSubsetOf0(xQ,xS)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f322,f279]) ).
fof(f1226,plain,
( aSubsetOf0(xQ,xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1217,f273]) ).
fof(f1227,plain,
aSubsetOf0(xQ,xS),
inference(forward_subsumption_resolution,[status(thm)],[f1226,f272]) ).
fof(f1232,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f1227,f103]) ).
fof(f1237,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f1232,f273]) ).
fof(f1243,plain,
! [X0] :
( aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| sK1_skl(xP,X0) = xx
| aElementOf0(sK1_skl(xP,X0),xS) ),
inference(resolution,[status(thm)],[f1237,f771]) ).
fof(f1422,plain,
( sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy)))
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(paramodulation,[status(thm)],[f287,f199]) ).
fof(f1423,plain,
( sbrdtbr0(xP) = xk
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_demodulation,[status(thm)],[f289,f1422]) ).
fof(f1424,plain,
( sbrdtbr0(xP) = xk
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1423,f746]) ).
fof(f2386,plain,
( ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS)
| sK1_skl(xP,xS) = xx ),
inference(resolution,[status(thm)],[f1243,f105]) ).
fof(f2389,plain,
( ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS)
| sK1_skl(xP,xS) = xx ),
inference(duplicate_literals_removal,[status(thm)],[f2386]) ).
fof(f2390,plain,
( ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| sK1_skl(xP,xS) = xx ),
inference(forward_subsumption_resolution,[status(thm)],[f2389,f273]) ).
fof(f2392,plain,
( aSubsetOf0(xP,xS)
| sK1_skl(xP,xS) = xx ),
inference(forward_subsumption_resolution,[status(thm)],[f2390,f467]) ).
fof(f2397,plain,
( aSubsetOf0(xP,xS)
| ~ aElementOf0(xx,xS)
| ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS) ),
inference(paramodulation,[status(thm)],[f2392,f105]) ).
fof(f2403,plain,
( ~ aElementOf0(xx,xS)
| ~ aSet0(xP)
| aSubsetOf0(xP,xS)
| ~ aSet0(xS) ),
inference(duplicate_literals_removal,[status(thm)],[f2397]) ).
fof(f2404,plain,
( ~ aElementOf0(xx,xS)
| ~ aSet0(xP)
| aSubsetOf0(xP,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f2403,f273]) ).
fof(f2406,plain,
( ~ aElementOf0(xx,xS)
| aSubsetOf0(xP,xS) ),
inference(forward_subsumption_resolution,[status(thm)],[f2404,f467]) ).
fof(f2407,plain,
aSubsetOf0(xP,xS),
inference(resolution,[status(thm)],[f2406,f278]) ).
fof(f2408,plain,
sbrdtbr0(xP) != xk,
inference(backward_subsumption_resolution,[status(thm)],[f291,f2407]) ).
fof(f2435,plain,
( sbrdtbr0(xP) = xk
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1424,f353]) ).
fof(f2436,plain,
( sbrdtbr0(xP) = xk
| ~ aSet0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[f2435,f288]) ).
fof(f2440,plain,
~ aSet0(sdtmndt0(xQ,xy)),
inference(forward_subsumption_resolution,[status(thm)],[f2436,f2408]) ).
fof(f2474,plain,
( ~ aElement0(xy)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f2440,f307]) ).
fof(f2475,plain,
~ aElement0(xy),
inference(forward_subsumption_resolution,[status(thm)],[f2474,f280]) ).
fof(f2476,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2475,f283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM556+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:42:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 3.51/0.89 % Refutation found
% 3.51/0.89 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.51/0.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.87/0.91 % Elapsed time: 0.548339 seconds
% 1.87/0.91 % CPU time: 4.016642 seconds
% 1.87/0.91 % Total memory used: 154.753 MB
% 1.87/0.91 % Net memory used: 149.741 MB
%------------------------------------------------------------------------------