%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM609+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 : n009.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 0.11s 0.62s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 17 unt; 3 def)
% Number of atoms : 205 ( 22 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 248 ( 96 ~; 97 |; 41 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 89 ( 85 !; 4 ?)
% 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(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(f101,hypothesis,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,hypothesis,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f105,hypothesis,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f107,conjecture,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,negated_conjecture,
~ aSubsetOf0(xP,xQ),
inference(negated_conjecture,[status(cth)],[f107]) ).
fof(f115,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f116,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f133,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(f134,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)],[f133]) ).
fof(f135,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)],[f134]) ).
fof(f136,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))],[f135]) ).
fof(f137,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [X0,X1] :
( aElementOf0(sK1_skl(X1,X0),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aElementOf0(sK1_skl(X1,X0),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f162,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(f163,definition,
! [W0,W1,W3] :
( sP0_prd(W3,W1,W0)
<=> ( W3 != W1
& aElementOf0(W3,W0)
& aElement0(W3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f164,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)],[f162,f163]) ).
fof(f165,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)],[f164]) ).
fof(f166,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)],[f165]) ).
fof(f167,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))],[f166]) ).
fof(f169,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)],[f167]) ).
fof(f185,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f442,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f444,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f445,plain,
aSet0(xP),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f446,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f447,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f449,plain,
~ aSubsetOf0(xP,xQ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f450,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)],[f163]) ).
fof(f451,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)],[f450]) ).
fof(f453,plain,
! [X0,X1,X2] :
( aElementOf0(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f451]) ).
fof(f466,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ aElementOf0(X2,sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f169]) ).
fof(f497,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f137,f442]) ).
fof(f520,plain,
aSet0(xQ),
inference(backward_subsumption_resolution,[status(thm)],[f497,f185]) ).
fof(f576,plain,
xP = sdtmndt0(xQ,xp),
inference(backward_demodulation,[status(thm)],[f444,f446]) ).
fof(f579,plain,
( aElement0(xp)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f447,f116]) ).
fof(f580,plain,
aElement0(xp),
inference(forward_subsumption_resolution,[status(thm)],[f579,f520]) ).
fof(f871,plain,
! [X0] :
( sP0_prd(X0,xp,xQ)
| ~ aElementOf0(X0,xP)
| ~ aElement0(xp)
| ~ aSet0(xQ) ),
inference(paramodulation,[status(thm)],[f576,f466]) ).
fof(f875,plain,
! [X0] :
( sP0_prd(X0,xp,xQ)
| ~ aElementOf0(X0,xP)
| ~ aElement0(xp) ),
inference(forward_subsumption_resolution,[status(thm)],[f871,f520]) ).
fof(f878,plain,
! [X0] :
( sP0_prd(X0,xp,xQ)
| ~ aElementOf0(X0,xP) ),
inference(forward_subsumption_resolution,[status(thm)],[f875,f580]) ).
fof(f879,plain,
! [X0] :
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,xP) ),
inference(resolution,[status(thm)],[f878,f453]) ).
fof(f890,plain,
! [X0] :
( ~ aSet0(xP)
| aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ) ),
inference(resolution,[status(thm)],[f879,f139]) ).
fof(f893,plain,
! [X0] :
( aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(sK1_skl(xP,X0),xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f890,f445]) ).
fof(f1021,plain,
( ~ aSet0(xP)
| aSubsetOf0(xP,xQ)
| ~ aSet0(xQ)
| aSubsetOf0(xP,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[f893,f140]) ).
fof(f1026,plain,
( ~ aSet0(xP)
| aSubsetOf0(xP,xQ)
| ~ aSet0(xQ) ),
inference(duplicate_literals_removal,[status(thm)],[f1021]) ).
fof(f1027,plain,
( ~ aSet0(xP)
| aSubsetOf0(xP,xQ) ),
inference(forward_subsumption_resolution,[status(thm)],[f1026,f520]) ).
fof(f1029,plain,
~ aSet0(xP),
inference(forward_subsumption_resolution,[status(thm)],[f1027,f449]) ).
fof(f1030,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f445,f1029]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM609+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:44:27 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.62 % Refutation found
% 0.11/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.15/0.67 % Elapsed time: 0.288144 seconds
% 1.15/0.67 % CPU time: 1.954808 seconds
% 1.15/0.67 % Total memory used: 126.794 MB
% 1.15/0.67 % Net memory used: 125.107 MB
%------------------------------------------------------------------------------