%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM622+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 : n014.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 01:41:14 PM UTC 2026
% Result : Theorem 23.72s 3.84s
% Output : CNFRefutation 23.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 17 unt; 3 def)
% Number of atoms : 200 ( 42 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 233 ( 93 ~; 85 |; 42 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 71 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
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(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,hypothesis,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,conjecture,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,negated_conjecture,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(negated_conjecture,[status(cth)],[f119]) ).
fof(f131,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f132,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,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))],[f133]) ).
fof(f135,plain,
! [X0] :
( aSet0(X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f143,plain,
! [W0] :
( W0 != slcrc0
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f144,plain,
! [X0] :
( X0 != slcrc0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,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(f146,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)],[f145]) ).
fof(f147,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)],[f146]) ).
fof(f148,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))],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1,X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f197,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f255,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(f256,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)],[f255]) ).
fof(f257,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)],[f256]) ).
fof(f258,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))],[f257]) ).
fof(f259,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| X1 != szmzizndt0(X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f401,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f402,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f403,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f430,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(f433,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f466,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f467,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f472,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f476,plain,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f477,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f484,plain,
aSet0(slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f135]) ).
fof(f486,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(destructive_equality_resolution,[status(thm)],[f144]) ).
fof(f497,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(destructive_equality_resolution,[status(thm)],[f259]) ).
fof(f529,plain,
~ isCountable0(slcrc0),
inference(forward_subsumption_resolution,[status(thm)],[f486,f484]) ).
fof(f532,plain,
! [X0] :
( ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[status(thm)],[f150,f477]) ).
fof(f538,plain,
! [X0,X1] :
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),X1)
| ~ aSet0(X1)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(resolution,[status(thm)],[f532,f149]) ).
fof(f539,plain,
! [X0] :
( ~ aElementOf0(xm,szNzAzT0)
| ~ aSet0(szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(resolution,[status(thm)],[f538,f402]) ).
fof(f541,plain,
! [X0] :
( ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f197]) ).
fof(f543,plain,
! [X0] :
( ~ aElementOf0(xp,X0)
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f472]) ).
fof(f544,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(resolution,[status(thm)],[f543,f476]) ).
fof(f1397,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
| sdtlpdtrp0(xN,X0) = slcrc0 ),
inference(resolution,[status(thm)],[f497,f402]) ).
fof(f3856,plain,
sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(resolution,[status(thm)],[f433,f466]) ).
fof(f3867,plain,
xp = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_demodulation,[status(thm)],[f467,f3856]) ).
fof(f3900,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aElementOf0(xp,sdtlpdtrp0(xN,xn))
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(paramodulation,[status(thm)],[f3867,f1397]) ).
fof(f3913,plain,
( ~ aElementOf0(xn,szNzAzT0)
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f3900,f544]) ).
fof(f4101,plain,
sdtlpdtrp0(xN,xn) = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f3913,f466]) ).
fof(f4126,plain,
( isCountable0(slcrc0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f4101,f403]) ).
fof(f4266,plain,
isCountable0(slcrc0),
inference(forward_subsumption_resolution,[status(thm)],[f4126,f466]) ).
fof(f4300,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4266,f529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM622+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.64 % Computer : n014.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Mon Sep 21 02:45:05 UTC 2026
% 0.17/0.65 % CPUTime :
% 0.20/0.67 % Drodi V4.1.1
% 23.72/3.84 % Refutation found
% 23.72/3.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.72/3.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.72/3.91 % Elapsed time: 3.245358 seconds
% 23.72/3.91 % CPU time: 24.813907 seconds
% 23.72/3.91 % Total memory used: 229.768 MB
% 23.72/3.91 % Net memory used: 217.594 MB
%------------------------------------------------------------------------------