%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM539+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 71 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 70 ( 22 ~; 20 |; 16 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 17 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(m__1779,axiom,
( ~ ( xT = slcrc0
| ~ ? [W0] : aElementOf0(W0,xT) )
& ~ ( xS = slcrc0
| ~ ? [W0] : aElementOf0(W0,xS) )
& aSubsetOf0(xT,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xT)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xT)
& aSubsetOf0(xS,szNzAzT0)
& ! [W0] :
( aElementOf0(W0,xS)
=> aElementOf0(W0,szNzAzT0) )
& aSet0(xS) ),
file('theBenchmark.p',m__1779) ).
fof(m__1802,axiom,
( aElementOf0(szmzizndt0(xT),xS)
& ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xT),W0) )
& aElementOf0(szmzizndt0(xT),xT)
& aElementOf0(szmzizndt0(xS),xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xS) ),
file('theBenchmark.p',m__1802) ).
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xS) )
=> ( szmzizndt0(xS) = szmzizndt0(xT)
| ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xS),W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(szmzizndt0(xS),W0) )
& aElementOf0(szmzizndt0(xS),xS) )
=> ( szmzizndt0(xS) = szmzizndt0(xT)
| ! [W0] :
( aElementOf0(W0,xT)
=> sdtlseqdt0(szmzizndt0(xS),W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_50,negated_conjecture,
szmzizndt0(xT) != szmzizndt0(xS),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_53,negated_conjecture,
( sdtlseqdt0(szmzizndt0(xS),A)
| ~ aElementOf0(A,xS) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_55,plain,
aElementOf0(szmzizndt0(xT),xS),
inference(clausify,[status(thm)],[m__1802]) ).
cnf(c_56,plain,
( sdtlseqdt0(szmzizndt0(xT),A)
| ~ aElementOf0(A,xT) ),
inference(clausify,[status(thm)],[m__1802]) ).
cnf(c_57,plain,
aElementOf0(szmzizndt0(xT),xT),
inference(clausify,[status(thm)],[m__1802]) ).
cnf(c_58,plain,
aElementOf0(szmzizndt0(xS),xT),
inference(clausify,[status(thm)],[m__1802]) ).
cnf(c_64,plain,
( aElementOf0(A,szNzAzT0)
| ~ aElementOf0(A,xT) ),
inference(clausify,[status(thm)],[m__1779]) ).
cnf(c_90,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_158,plain,
sdtlseqdt0(szmzizndt0(xS),szmzizndt0(xT)),
inference(resolve,[status(thm)],[c_55,c_53]) ).
cnf(c_161,plain,
sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)),
inference(resolve,[status(thm)],[c_58,c_56]) ).
cnf(c_165,plain,
aElementOf0(szmzizndt0(xS),szNzAzT0),
inference(resolve,[status(thm)],[c_64,c_58]) ).
cnf(c_166,plain,
aElementOf0(szmzizndt0(xT),szNzAzT0),
inference(resolve,[status(thm)],[c_64,c_57]) ).
cnf(c_354,plain,
( szmzizndt0(xS) = szmzizndt0(xT)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(resolve,[status(thm)],[c_158,c_90]) ).
cnf(c_355,plain,
( szmzizndt0(xT) = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0)
| ~ aElementOf0(szmzizndt0(xT),szNzAzT0) ),
inference(copy,[status(thm)],[c_354]) ).
cnf(c_356,plain,
( szmzizndt0(xT) = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS))
| ~ aElementOf0(szmzizndt0(xS),szNzAzT0) ),
inference(resolve,[status(thm)],[c_166,c_355]) ).
cnf(c_357,plain,
( szmzizndt0(xT) = szmzizndt0(xS)
| ~ sdtlseqdt0(szmzizndt0(xT),szmzizndt0(xS)) ),
inference(resolve,[status(thm)],[c_165,c_356]) ).
cnf(c_358,plain,
szmzizndt0(xT) = szmzizndt0(xS),
inference(resolve,[status(thm)],[c_161,c_357]) ).
cnf(c_353,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_50,c_358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM539+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:09:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2348338 was started by sandbox2 on n010,
% 0.09/0.36 % Sat Sep 26 03:09:29 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.46 % Length of proof is 17.
% 0.13/0.46 % Level of proof is 3.
% 0.13/0.46 % Maximum clause weight is 20.000.
% 0.13/0.46 % Given clauses 106.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------