%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM584+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 : n003.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 01:41:05 PM UTC 2026
% Result : Theorem 7.87s 1.46s
% Output : CNFRefutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 17 unt; 8 def)
% Number of atoms : 213 ( 32 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 246 ( 95 ~; 94 |; 41 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 61 ( 57 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) ) ),
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(f75,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,hypothesis,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,hypothesis,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f115,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(f116,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)],[f115]) ).
fof(f117,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)],[f116]) ).
fof(f118,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))],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f167,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f170,plain,
! [W0] :
( ( szszuzczcdt0(W0) != sz00
& aElementOf0(szszuzczcdt0(W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f171,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f272,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(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) )
& ( ( ! [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)],[f272]) ).
fof(f274,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)],[f273]) ).
fof(f275,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))],[f274]) ).
fof(f279,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)],[f275]) ).
fof(f350,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f353,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f363,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f364,plain,
szszuzczcdt0(xk) = xK,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f380,plain,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f381,plain,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f382,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f415,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aElementOf0(X1,slbdtsldtrb0(X0,sbrdtbr0(X1)))
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f279]) ).
fof(f472,definition,
( sQ7_spl
<=> aSet0(szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ7_spl
| ~ aSet0(szNzAzT0) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f479,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f167]) ).
fof(f480,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f605,definition,
( sQ29_spl
<=> aElementOf0(xk,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ29_spl
| ~ aElementOf0(xk,szNzAzT0) ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f618,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f363]) ).
fof(f619,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f715,definition,
( sQ42_spl
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f717,plain,
( sQ42_spl
| ~ aSet0(xS) ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f740,plain,
! [X0] :
( sQ42_spl
| ~ aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[f717,f119]) ).
fof(f810,plain,
( sQ42_spl
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[f740,f350]) ).
fof(f811,plain,
( sQ42_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f810,f472,f715]) ).
fof(f826,plain,
( aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f364,f171]) ).
fof(f827,definition,
( sQ59_spl
<=> aElementOf0(xK,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( sQ59_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f826,f605,f827]) ).
fof(f2426,plain,
! [X0] :
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),X0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(X0,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))))
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(X0) ),
inference(paramodulation,[status(thm)],[f380,f415]) ).
fof(f2431,definition,
! [X0] :
( sQ294_spl
<=> ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),X0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(X0,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))))
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2432,plain,
! [X0] :
( ~ sQ294_spl
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),X0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(X0,sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))))
| ~ aSet0(X0) ),
inference(component_clause,[status(thm)],[f2431]) ).
fof(f2434,plain,
( ~ sQ59_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f2426,f2431,f827]) ).
fof(f2435,plain,
! [X0] :
( ~ sQ294_spl
| ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),X0)
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(X0,xK))
| ~ aSet0(X0) ),
inference(forward_demodulation,[status(thm)],[f380,f2432]) ).
fof(f2949,plain,
~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(backward_demodulation,[status(thm)],[f353,f382]) ).
fof(f6762,plain,
( ~ sQ294_spl
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[f2435,f381]) ).
fof(f6765,definition,
( sQ733_spl
<=> aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
introduced(definition,[new_symbols(definition,[sQ733_spl])],[split_symbol_definition]) ).
fof(f6766,plain,
( ~ sQ733_spl
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
inference(component_clause,[status(thm)],[f6765]) ).
fof(f6768,plain,
( ~ sQ294_spl
| sQ733_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f6762,f715,f6765,f2431]) ).
fof(f6780,plain,
( ~ sQ733_spl
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)) ),
inference(forward_demodulation,[status(thm)],[f353,f6766]) ).
fof(f6781,plain,
( ~ sQ733_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6780,f2949]) ).
fof(f6782,plain,
~ sQ733_spl,
inference(contradiction_clause,[status(thm)],[f6781]) ).
fof(f6783,plain,
$false,
inference(sat_refutation,[status(thm)],[f480,f619,f811,f830,f2434,f6768,f6782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM584+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 : n003.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 02:43:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 7.87/1.46 % Refutation found
% 7.87/1.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.87/1.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.87/1.50 % Elapsed time: 1.129255 seconds
% 7.87/1.50 % CPU time: 8.364527 seconds
% 7.87/1.50 % Total memory used: 164.849 MB
% 7.87/1.50 % Net memory used: 158.182 MB
%------------------------------------------------------------------------------