%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM604+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 : n004.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 01:41:09 PM UTC 2026
% Result : Theorem 62.83s 8.63s
% Output : CNFRefutation 62.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 19 unt; 3 def)
% Number of atoms : 187 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 207 ( 78 ~; 75 |; 41 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 69 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,hypothesis,
( sdtlpdtrp0(xe,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,conjecture,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,negated_conjecture,
~ aElementOf0(xx,xS),
inference(negated_conjecture,[status(cth)],[f101]) ).
fof(f113,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f114,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,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))],[f115]) ).
fof(f117,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f125,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f126,plain,
! [X0] :
( X0 != slcrc0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,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(f128,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)],[f127]) ).
fof(f129,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)],[f128]) ).
fof(f130,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))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f179,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f237,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(f238,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)],[f237]) ).
fof(f239,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)],[f238]) ).
fof(f240,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))],[f239]) ).
fof(f241,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| X1 != szmzizndt0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f362,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f383,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f384,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f412,plain,
( ! [W0] :
( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f415,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f412]) ).
fof(f433,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f434,plain,
sdtlpdtrp0(xe,xi) = xx,
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f435,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f436,plain,
~ aElementOf0(xx,xS),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f468,plain,
! [X0] :
( X0 != slcrc0
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f117]) ).
fof(f472,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f131,f362]) ).
fof(f473,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[status(thm)],[f472,f179]) ).
fof(f3240,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f435,f132]) ).
fof(f3244,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3240,f473]) ).
fof(f7448,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(resolution,[status(thm)],[f384,f433]) ).
fof(f7477,plain,
isCountable0(sdtlpdtrp0(xN,xi)),
inference(resolution,[status(thm)],[f385,f433]) ).
fof(f7534,plain,
sdtlpdtrp0(xN,xi) != slcrc0,
inference(resolution,[status(thm)],[f7477,f468]) ).
fof(f8935,plain,
sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(resolution,[status(thm)],[f415,f433]) ).
fof(f8941,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(forward_demodulation,[status(thm)],[f434,f8935]) ).
fof(f10519,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| X0 != szmzizndt0(sdtlpdtrp0(xN,xi))
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(resolution,[status(thm)],[f7448,f241]) ).
fof(f10531,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| X0 != xx
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(forward_demodulation,[status(thm)],[f8941,f10519]) ).
fof(f10532,plain,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
| X0 != xx ),
inference(forward_subsumption_resolution,[status(thm)],[f10531,f7534]) ).
fof(f23741,plain,
aElementOf0(sdtlpdtrp0(xe,xi),sdtlpdtrp0(xN,xi)),
inference(resolution,[status(thm)],[f10532,f434]) ).
fof(f23744,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xi)),
inference(forward_demodulation,[status(thm)],[f434,f23741]) ).
fof(f24225,plain,
aElementOf0(xx,xS),
inference(resolution,[status(thm)],[f23744,f3244]) ).
fof(f24260,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f24225,f436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM604+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n004.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 02:44:04 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 62.83/8.63 % Refutation found
% 62.83/8.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 62.83/8.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.52/9.35 % Elapsed time: 8.921797 seconds
% 4.52/9.35 % CPU time: 65.709579 seconds
% 4.52/9.35 % Total memory used: 351.819 MB
% 4.52/9.35 % Net memory used: 320.578 MB
%------------------------------------------------------------------------------