%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM623+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 : n008.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 3.22s 0.91s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 17 unt; 1 def)
% Number of atoms : 125 ( 51 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 138 ( 55 ~; 61 |; 17 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [W0,W1] :
( ( W1 != slcrc0
& W0 != slcrc0
& aSubsetOf0(W1,szNzAzT0)
& aSubsetOf0(W0,szNzAzT0) )
=> ( ( aElementOf0(szmzizndt0(W1),W0)
& aElementOf0(szmzizndt0(W0),W1) )
=> szmzizndt0(W0) = szmzizndt0(W1) ) ),
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(f100,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
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(f115,hypothesis,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,hypothesis,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,conjecture,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f121,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f120]) ).
fof(f132,plain,
! [W0] :
( W0 = slcrc0
<=> ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f133,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( ! [W0] :
( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ! [W0] :
( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,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))],[f134]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f272,plain,
! [W0,W1] :
( szmzizndt0(W0) = szmzizndt0(W1)
| ~ aElementOf0(szmzizndt0(W1),W0)
| ~ aElementOf0(szmzizndt0(W0),W1)
| W1 = slcrc0
| W0 = slcrc0
| ~ aSubsetOf0(W1,szNzAzT0)
| ~ aSubsetOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f273,plain,
! [X0,X1] :
( szmzizndt0(X0) = szmzizndt0(X1)
| ~ aElementOf0(szmzizndt0(X1),X0)
| ~ aElementOf0(szmzizndt0(X0),X1)
| X1 = slcrc0
| X0 = slcrc0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f402,plain,
! [W0] :
( ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f403,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f402]) ).
fof(f454,plain,
xQ != slcrc0,
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f455,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f457,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f473,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f475,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f478,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f479,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f480,plain,
xp != xx,
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f488,plain,
! [X0] : ~ aElementOf0(X0,slcrc0),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f1973,plain,
! [X0] :
( szmzizndt0(X0) = szmzizndt0(xQ)
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| xQ = slcrc0
| X0 = slcrc0
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f457,f273]) ).
fof(f1975,plain,
! [X0] :
( szmzizndt0(X0) = xp
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| xQ = slcrc0
| X0 = slcrc0
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f457,f1973]) ).
fof(f1976,plain,
! [X0] :
( szmzizndt0(X0) = xp
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| xQ = slcrc0
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1975,f455]) ).
fof(f1986,plain,
! [X0] :
( szmzizndt0(X0) = xp
| ~ aElementOf0(xp,X0)
| ~ aElementOf0(szmzizndt0(X0),xQ)
| X0 = slcrc0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1976,f454]) ).
fof(f1989,plain,
( szmzizndt0(sdtlpdtrp0(xN,xm)) = xp
| ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xx,xQ)
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(paramodulation,[status(thm)],[f475,f1986]) ).
fof(f1992,plain,
( xx = xp
| ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xx,xQ)
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f475,f1989]) ).
fof(f1993,plain,
( xx = xp
| ~ aElementOf0(xp,sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1992,f479]) ).
fof(f3781,plain,
( xx = xp
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1993,f478]) ).
fof(f3782,plain,
( ~ aElementOf0(xm,szNzAzT0)
| xx = xp
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[f3781,f403]) ).
fof(f3783,plain,
( ~ aElementOf0(xm,szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(forward_subsumption_resolution,[status(thm)],[f3782,f480]) ).
fof(f3796,plain,
aElementOf0(xp,slcrc0),
inference(backward_demodulation,[status(thm)],[f3797,f478]) ).
fof(f3797,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(forward_subsumption_resolution,[status(thm)],[f3783,f473]) ).
fof(f3804,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3796,f488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM623+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:46:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.43 % Drodi V4.1.1
% 3.22/0.91 % Refutation found
% 3.22/0.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.22/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.22/0.94 % Elapsed time: 0.537609 seconds
% 3.22/0.94 % CPU time: 3.707493 seconds
% 3.22/0.94 % Total memory used: 159.889 MB
% 3.22/0.94 % Net memory used: 155.817 MB
%------------------------------------------------------------------------------