%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM558+3 : 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 : n006.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 08:17:24 AM UTC 2026
% Result : Theorem 0.50s 0.49s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 94 ( 14 equ)
% Maximal formula atoms : 43 ( 3 avg)
% Number of connectives : 86 ( 16 ~; 15 |; 36 &)
% ( 2 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(m__2202_02,axiom,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('theBenchmark.p',m__2202_02) ).
fof(m__2227,axiom,
( ~ ( ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xT)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xT)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,xS)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,xS)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSet0(W0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ),
file('theBenchmark.p',m__2227) ).
fof(m__2357,axiom,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( ( W0 = xx
| aElementOf0(W0,sdtmndt0(xQ,xy)) )
& aElement0(W0) ) )
& aSet0(xP)
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( W0 != xy
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& aSet0(sdtmndt0(xQ,xy)) ),
file('theBenchmark.p',m__2357) ).
fof(m__2378,axiom,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) ) ),
file('theBenchmark.p',m__2378) ).
fof(m__,conjecture,
aElementOf0(xx,xT),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xx,xT),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_66,negated_conjecture,
~ aElementOf0(xx,xT),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_67,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(clausify,[status(thm)],[m__2378]) ).
cnf(c_73,plain,
( xx != A
| ~ aElement0(A)
| aElementOf0(A,xP) ),
inference(clausify,[status(thm)],[m__2357]) ).
fof(m__2256,axiom,
aElementOf0(xx,xS),
file('theBenchmark.p',m__2256) ).
cnf(c_94,plain,
aElementOf0(xx,xS),
inference(clausify,[status(thm)],[m__2256]) ).
cnf(c_105,plain,
( aElementOf0(A,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(A,slbdtsldtrb0(xS,xk)) ),
inference(clausify,[status(thm)],[m__2227]) ).
cnf(c_111,plain,
( aElementOf0(B,xT)
| ~ aElementOf0(B,A)
| ~ aElementOf0(A,slbdtsldtrb0(xT,xk)) ),
inference(clausify,[status(thm)],[m__2227]) ).
cnf(c_119,plain,
aSet0(xS),
inference(clausify,[status(thm)],[m__2202_02]) ).
cnf(c_225,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_285,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(resolve,[status(thm)],[c_105,c_67]) ).
cnf(c_952,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_225,c_94]) ).
cnf(c_594,plain,
aElement0(xx),
inference(resolve,[status(thm)],[c_119,c_952]) ).
cnf(c_953,plain,
( xx != xx
| aElementOf0(xx,xP) ),
inference(resolve,[status(thm)],[c_594,c_73]) ).
cnf(c_737,plain,
aElementOf0(xx,xP),
inference(copy,[status(thm)],[c_953]) ).
cnf(c_954,plain,
( aElementOf0(xx,xT)
| ~ aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
inference(resolve,[status(thm)],[c_737,c_111]) ).
cnf(c_955,plain,
aElementOf0(xx,xT),
inference(resolve,[status(thm)],[c_285,c_954]) ).
cnf(c_951,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_955]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 03:13:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 255691 was started by sandbox2 on n006,
% 0.12/0.38 % Sat Sep 26 03:13:12 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 0.50/0.49
% 0.50/0.49 % SZS status Theorem for theBenchmark
% 0.50/0.49
% 0.50/0.49 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.50/0.49 % Length of proof is 18.
% 0.50/0.49 % Level of proof is 4.
% 0.50/0.49 % Maximum clause weight is 21.000.
% 0.50/0.49 % Given clauses 227.
% 0.50/0.49
% 0.50/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------