%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM539+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 : 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 : Sun Sep 27 08:17:20 AM UTC 2026
% Result : Theorem 5.74s 1.13s
% Output : CNFRefutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 103 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 48 ~; 44 |; 10 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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__1779,axiom,
( xT != slcrc0
& xS != slcrc0
& aSubsetOf0(xT,szNzAzT0)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__1779) ).
fof(m__1802,axiom,
( aElementOf0(szmzizndt0(xT),xS)
& aElementOf0(szmzizndt0(xS),xT) ),
file('theBenchmark.p',m__1802) ).
fof(m__,conjecture,
szmzizndt0(xS) = szmzizndt0(xT),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
szmzizndt0(xS) != szmzizndt0(xT),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_50,negated_conjecture,
szmzizndt0(xT) != szmzizndt0(xS),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_51,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(clausify,[status(thm)],[m__1802]) ).
cnf(c_52,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(clausify,[status(thm)],[m__1802]) ).
cnf(c_53,plain,
xT != slcrc0,
inference(clausify,[status(thm)],[m__1779]) ).
cnf(c_54,plain,
xS != slcrc0,
inference(clausify,[status(thm)],[m__1779]) ).
cnf(c_55,plain,
aSubsetOf0(xT,szNzAzT0),
inference(clausify,[status(thm)],[m__1779]) ).
cnf(c_56,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__1779]) ).
cnf(c_63,plain,
( sdtlseqdt0(B,C)
| ~ aElementOf0(C,A)
| szmzizndt0(A) != B
| slcrc0 = A
| ~ aSubsetOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mDefMin]) ).
cnf(c_78,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_93,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_124,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_1817,plain,
( sdtlseqdt0(A,B)
| ~ aElementOf0(B,xS)
| szmzizndt0(xS) != A
| slcrc0 = xS ),
inference(resolve,[status(thm)],[c_63,c_56]) ).
cnf(c_1818,plain,
( sdtlseqdt0(A,B)
| ~ aElementOf0(B,xS)
| szmzizndt0(xS) != A
| xS = slcrc0 ),
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_154,plain,
( sdtlseqdt0(A,B)
| ~ aElementOf0(B,xS)
| szmzizndt0(xS) != A ),
inference(resolve,[status(thm)],[c_54,c_1818]) ).
cnf(c_1819,plain,
( sdtlseqdt0(A,B)
| ~ aElementOf0(B,xT)
| szmzizndt0(xT) != A
| slcrc0 = xT ),
inference(resolve,[status(thm)],[c_63,c_55]) ).
cnf(c_1820,plain,
( sdtlseqdt0(A,B)
| ~ aElementOf0(B,xT)
| szmzizndt0(xT) != A
| xT = slcrc0 ),
inference(copy,[status(thm)],[c_1819]) ).
cnf(c_155,plain,
( sdtlseqdt0(A,B)
| ~ aElementOf0(B,xT)
| szmzizndt0(xT) != A ),
inference(resolve,[status(thm)],[c_53,c_1820]) ).
cnf(c_1821,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_124,c_56]) ).
cnf(c_211,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xS) ),
inference(resolve,[status(thm)],[c_93,c_1821]) ).
cnf(c_1822,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xT)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_124,c_55]) ).
cnf(c_212,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xT) ),
inference(resolve,[status(thm)],[c_93,c_1822]) ).
cnf(c_340,plain,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(resolve,[status(thm)],[c_211,c_51]) ).
cnf(c_341,plain,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(resolve,[status(thm)],[c_212,c_52]) ).
cnf(c_343,plain,
( sdtlseqdt0(A,szmzizndt0(xT))
| szmzizndt0(xS) != A ),
inference(resolve,[status(thm)],[c_154,c_51]) ).
cnf(c_1811,plain,
sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)),
inference(xxres,[status(thm)],[c_343]) ).
cnf(c_1823,plain,
( szmzizndt0(xS) = szmzizndt0(xT)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(resolve,[status(thm)],[c_1811,c_78]) ).
cnf(c_1824,plain,
( szmzizndt0(xT) = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(copy,[status(thm)],[c_1823]) ).
cnf(c_1825,plain,
( szmzizndt0(xT) = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0) ),
inference(resolve,[status(thm)],[c_340,c_1824]) ).
cnf(c_1826,plain,
( szmzizndt0(xT) = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ),
inference(resolve,[status(thm)],[c_341,c_1825]) ).
cnf(c_1813,negated_conjecture,
~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(resolve,[status(thm)],[c_50,c_1826]) ).
cnf(c_1827,plain,
( sdtlseqdt0(A,szmzizndt0(xS))
| szmzizndt0(xT) != A ),
inference(resolve,[status(thm)],[c_155,c_52]) ).
cnf(c_1828,plain,
szmzizndt0(xT) != szmzizndt0(xT),
inference(resolve,[status(thm)],[c_1827,c_1813]) ).
cnf(c_1816,plain,
$false,
inference(copy,[status(thm)],[c_1828]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM539+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 : Sat Sep 26 03:09:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2014527 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 03:09:01 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 5.74/1.13
% 5.74/1.13 % SZS status Theorem for theBenchmark
% 5.74/1.13
% 5.74/1.13 % Proof 1 at 0.68 (+ 0.05) seconds.
% 5.74/1.13 % Length of proof is 28.
% 5.74/1.13 % Level of proof is 6.
% 5.74/1.13 % Maximum clause weight is 26.000.
% 5.74/1.13 % Given clauses 299.
% 5.74/1.13
% 5.74/1.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------