%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM623+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 08:17:36 AM UTC 2026
% Result : Theorem 4.80s 6.06s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 69 ( 35 unt; 0 def)
% Number of atoms : 141 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 52 ~; 49 |; 13 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(mDefMin,axiom,
! [W0] :
( ( W0 != slcrc0
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,W0) ) ) ),
file('theBenchmark.p',mDefMin) ).
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3671,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('theBenchmark.p',m__3671) ).
fof(m__5093,axiom,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ),
file('theBenchmark.p',m__5093) ).
fof(m__5365,axiom,
( aElementOf0(xx,xO)
& aElementOf0(xx,szNzAzT0) ),
file('theBenchmark.p',m__5365) ).
fof(m__5389,axiom,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ),
file('theBenchmark.p',m__5389) ).
fof(m__5481,axiom,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
file('theBenchmark.p',m__5481) ).
fof(m__,conjecture,
xp = xx,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
xp != xx,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_100,plain,
( ~ aElementOf0(B,A)
| slcrc0 != A ),
inference(clausify,[status(thm)],[mDefEmp]) ).
cnf(c_105,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_106,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_137,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_152,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_168,plain,
( sdtlseqdt0(B,C)
| ~ aElementOf0(C,A)
| szmzizndt0(A) != B
| slcrc0 = A
| ~ aSubsetOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mDefMin]) ).
cnf(c_240,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_259,plain,
( aSubsetOf0(sdtlpdtrp0(xN,A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3671]) ).
fof(m__4998,axiom,
aSubsetOf0(xO,xS),
file('theBenchmark.p',m__4998) ).
cnf(c_297,plain,
aSubsetOf0(xO,xS),
inference(clausify,[status(thm)],[m__4998]) ).
cnf(c_300,plain,
xQ != slcrc0,
inference(clausify,[status(thm)],[m__5093]) ).
fof(m__5106,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('theBenchmark.p',m__5106) ).
cnf(c_301,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(clausify,[status(thm)],[m__5106]) ).
fof(m__5147,axiom,
xp = szmzizndt0(xQ),
file('theBenchmark.p',m__5147) ).
cnf(c_303,plain,
xp = szmzizndt0(xQ),
inference(clausify,[status(thm)],[m__5147]) ).
cnf(c_304,plain,
szmzizndt0(xQ) = xp,
inference(copy,[status(thm)],[c_303]) ).
fof(m__5182,axiom,
aElementOf0(xp,xO),
file('theBenchmark.p',m__5182) ).
cnf(c_309,plain,
aElementOf0(xp,xO),
inference(clausify,[status(thm)],[m__5182]) ).
cnf(c_319,plain,
aElementOf0(xx,szNzAzT0),
inference(clausify,[status(thm)],[m__5365]) ).
cnf(c_321,plain,
aElementOf0(xm,szNzAzT0),
inference(clausify,[status(thm)],[m__5389]) ).
fof(m__5401,axiom,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('theBenchmark.p',m__5401) ).
cnf(c_323,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(clausify,[status(thm)],[m__5401]) ).
cnf(c_324,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = xx,
inference(copy,[status(thm)],[c_323]) ).
cnf(c_327,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(clausify,[status(thm)],[m__5481]) ).
cnf(c_328,plain,
aElementOf0(xx,xQ),
inference(clausify,[status(thm)],[m__5481]) ).
cnf(c_329,negated_conjecture,
xx != xp,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_330,negated_conjecture,
xp != xx,
inference(copy,[status(thm)],[c_329]) ).
cnf(c_3410,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_240,c_106]) ).
cnf(c_784,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS) ),
inference(resolve,[status(thm)],[c_137,c_3410]) ).
cnf(c_3411,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_240,c_105]) ).
cnf(c_785,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_137,c_3411]) ).
cnf(c_3412,plain,
( aElementOf0(A,xS)
| ~ aElementOf0(A,xO)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_297,c_106]) ).
cnf(c_1419,plain,
( aElementOf0(A,xS)
| ~ aElementOf0(A,xO) ),
inference(resolve,[status(thm)],[c_785,c_3412]) ).
cnf(c_3413,plain,
( sdtlseqdt0(xp,A)
| ~ aElementOf0(A,xQ)
| slcrc0 = xQ
| ~ aSubsetOf0(xQ,szNzAzT0) ),
inference(resolve,[status(thm)],[c_304,c_168]) ).
cnf(c_3414,plain,
( sdtlseqdt0(xp,A)
| ~ aElementOf0(A,xQ)
| xQ = slcrc0
| ~ aSubsetOf0(xQ,szNzAzT0) ),
inference(copy,[status(thm)],[c_3413]) ).
cnf(c_3415,plain,
( sdtlseqdt0(xp,A)
| ~ aElementOf0(A,xQ)
| xQ = slcrc0 ),
inference(resolve,[status(thm)],[c_301,c_3414]) ).
cnf(c_1528,plain,
( sdtlseqdt0(xp,A)
| ~ aElementOf0(A,xQ) ),
inference(resolve,[status(thm)],[c_300,c_3415]) ).
cnf(c_2093,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(resolve,[status(thm)],[c_321,c_259]) ).
cnf(c_3416,plain,
( sdtlseqdt0(A,xp)
| szmzizndt0(sdtlpdtrp0(xN,xm)) != A
| slcrc0 = sdtlpdtrp0(xN,xm)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(resolve,[status(thm)],[c_327,c_168]) ).
cnf(c_3417,plain,
( sdtlseqdt0(A,xp)
| xx != A
| slcrc0 = sdtlpdtrp0(xN,xm)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(paramod,[status(thm)],[c_324,c_3416]) ).
cnf(c_3418,plain,
( sdtlseqdt0(A,xp)
| xx != A
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
inference(copy,[status(thm)],[c_3417]) ).
cnf(c_2221,plain,
( sdtlseqdt0(A,xp)
| xx != A
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolve,[status(thm)],[c_2093,c_3418]) ).
cnf(c_3419,plain,
slcrc0 != sdtlpdtrp0(xN,xm),
inference(resolve,[status(thm)],[c_327,c_100]) ).
cnf(c_2230,plain,
sdtlpdtrp0(xN,xm) != slcrc0,
inference(copy,[status(thm)],[c_3419]) ).
cnf(c_2231,plain,
( sdtlseqdt0(A,xp)
| xx != A ),
inference(resolve,[status(thm)],[c_2230,c_2221]) ).
cnf(c_3176,plain,
aElementOf0(xp,xS),
inference(resolve,[status(thm)],[c_1419,c_309]) ).
cnf(c_3198,plain,
aElementOf0(xp,szNzAzT0),
inference(resolve,[status(thm)],[c_3176,c_784]) ).
cnf(c_3376,plain,
sdtlseqdt0(xp,xx),
inference(resolve,[status(thm)],[c_1528,c_328]) ).
cnf(c_3420,plain,
( xp = xx
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(resolve,[status(thm)],[c_3376,c_152]) ).
cnf(c_3421,plain,
( xp = xx
| ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(resolve,[status(thm)],[c_319,c_3420]) ).
cnf(c_3422,plain,
( xp = xx
| ~ sdtlseqdt0(xx,xp) ),
inference(resolve,[status(thm)],[c_3198,c_3421]) ).
cnf(c_3381,negated_conjecture,
~ sdtlseqdt0(xx,xp),
inference(resolve,[status(thm)],[c_330,c_3422]) ).
cnf(c_3423,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(copy,[status(thm)],[c_324]) ).
cnf(c_3424,plain,
sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xm)),xp),
inference(resolve,[status(thm)],[c_2231,c_3423]) ).
cnf(c_3425,plain,
sdtlseqdt0(xx,xp),
inference(paramod,[status(thm)],[c_324,c_3424]) ).
cnf(c_3409,plain,
$false,
inference(resolve,[status(thm)],[c_3381,c_3425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM623+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n013.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 03:29:12 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1838945 was started by sandbox on n013,
% 0.11/5.39 % Sat Sep 26 03:29:12 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.41
% 0.16/5.41 % From the command line: assign(max_seconds, 300).
% 4.80/6.06
% 4.80/6.06 % SZS status Theorem for theBenchmark
% 4.80/6.06
% 4.80/6.06 % Proof 1 at 0.41 (+ 0.11) seconds.
% 4.80/6.06 % Length of proof is 47.
% 4.80/6.06 % Level of proof is 7.
% 4.80/6.06 % Maximum clause weight is 26.000.
% 4.80/6.06 % Given clauses 387.
% 4.80/6.06
% 4.80/6.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------