%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM574+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 08:13:12 AM UTC 2026
% Result : Theorem 20.68s 13.13s
% Output : CNFRefutation 20.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 110 ( 29 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 103 ( 32 ~; 33 |; 21 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNatExtra,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ) ) ).
fof(mZeroLess,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ) ).
fof(mLessASymm,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ) ).
fof(m__3623,hypothesis,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ) ).
fof(m__3786,hypothesis,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ) ).
fof(m__3786_02,hypothesis,
( ( ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ) ) ).
fof(m__,conjecture,
( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c58,plain,
( aElementOf0(sK51(X0),szNzAzT0)
| X0 = sz00
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mNatExtra]) ).
cnf(c59,plain,
( X0 = szszuzczcdt0(sK51(X0))
| X0 = sz00
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mNatExtra]) ).
cnf(c61,plain,
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mZeroLess]) ).
cnf(c67,plain,
( ~ aElementOf0(X0,szNzAzT0)
| X1 = X0
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(clausification,[status(esa)],[mLessASymm]) ).
cnf(c229,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(clausification,[status(esa)],[m__3623]) ).
cnf(c248,plain,
aElementOf0(xj,szNzAzT0),
inference(clausification,[status(esa)],[m__3786]) ).
cnf(c249,plain,
aElementOf0(xi,szNzAzT0),
inference(clausification,[status(esa)],[m__3786]) ).
cnf(c253,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| szszuzczcdt0(X0) != xi
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(clausification,[status(esa)],[m__3786_02]) ).
cnf(c254,plain,
sdtlseqdt0(xj,xi),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c255,plain,
aElementOf0(sK201,sdtlpdtrp0(xN,xi)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c256,plain,
~ aElementOf0(sK201,sdtlpdtrp0(xN,xj)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c257,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xi ),
inference(resolution,[status(thm)],[c254,c253]) ).
cnf(d1,plain,
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xi ),
inference(resolution,[status(thm)],[c257,d0]) ).
cnf(d2,plain,
( xi = szszuzczcdt0(sK51(xi))
| xi = sz00 ),
inference(resolution,[status(thm)],[c59,c249]) ).
cnf(d3,plain,
( xi = sz00
| ~ aElementOf0(sK51(xi),szNzAzT0)
| xi != xi ),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ aElementOf0(sK51(xi),szNzAzT0)
| xi = sz00 ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ aElementOf0(xi,szNzAzT0)
| xi = sz00
| xi = sz00 ),
inference(resolution,[status(thm)],[d4,c58]) ).
cnf(d6,plain,
xi = sz00,
inference(resolution,[status(thm)],[c249,d5]) ).
cnf(d7,plain,
( ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| xi = xj ),
inference(resolution,[status(thm)],[c67,c254]) ).
cnf(d8,plain,
( ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xi,szNzAzT0)
| xi = xj ),
inference(resolution,[status(thm)],[c248,d7]) ).
cnf(d9,plain,
( ~ sdtlseqdt0(xi,xj)
| xi = xj ),
inference(resolution,[status(thm)],[c249,d8]) ).
cnf(d10,plain,
( ~ sdtlseqdt0(xi,xj)
| sz00 = xj ),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ sdtlseqdt0(sz00,xj)
| sz00 = xj ),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
sdtlseqdt0(sz00,xj),
inference(resolution,[status(thm)],[c61,c248]) ).
cnf(d13,plain,
sz00 = xj,
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
~ aElementOf0(sK201,sdtlpdtrp0(xN,sz00)),
inference(demodulation,[status(thm)],[c256,d13]) ).
cnf(d15,plain,
~ aElementOf0(sK201,xS),
inference(demodulation,[status(thm)],[d14,c229]) ).
cnf(d16,plain,
aElementOf0(sK201,sdtlpdtrp0(xN,sz00)),
inference(demodulation,[status(thm)],[c255,d6]) ).
cnf(d17,plain,
aElementOf0(sK201,xS),
inference(demodulation,[status(thm)],[d16,c229]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM574+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n013.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 26 03:17:02 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.68/13.13 % SZS status Theorem for theBenchmark.p
% 20.68/13.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------