%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM605+1 : 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 : n017.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 08:17:32 AM UTC 2026
% Result : Theorem 0.47s 0.56s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 21 unt; 0 def)
% Number of atoms : 48 ( 24 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 35 ( 16 ~; 11 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCardSeg,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(W0)) = W0 ),
file('theBenchmark.p',mCardSeg) ).
fof(mDefSel,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aSet0(W0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( ! [W3] :
( aElementOf0(W3,W2)
<=> ( sbrdtbr0(W3) = W1
& aSubsetOf0(W3,W0) ) )
& aSet0(W2) ) ) ),
file('theBenchmark.p',mDefSel) ).
fof(m__4891,axiom,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ),
file('theBenchmark.p',m__4891) ).
fof(m__,conjecture,
xQ != slcrc0,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xQ != slcrc0 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_133,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',mSegZero) ).
cnf(c_178,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[mSegZero]) ).
cnf(c_186,plain,
( sbrdtbr0(slbdtrb0(A)) = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mCardSeg]) ).
cnf(c_189,plain,
( sbrdtbr0(D) = B
| ~ aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
fof(m__3418,axiom,
aElementOf0(xK,szNzAzT0),
file('theBenchmark.p',m__3418) ).
cnf(c_233,plain,
aElementOf0(xK,szNzAzT0),
inference(clausify,[status(thm)],[m__3418]) ).
fof(m__3462,axiom,
xK != sz00,
file('theBenchmark.p',m__3462) ).
cnf(c_245,plain,
xK != sz00,
inference(clausify,[status(thm)],[m__3462]) ).
cnf(c_285,plain,
aSet0(xO),
inference(clausify,[status(thm)],[m__4891]) ).
fof(m__5078,axiom,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('theBenchmark.p',m__5078) ).
cnf(c_292,plain,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(clausify,[status(thm)],[m__5078]) ).
cnf(c_293,negated_conjecture,
xQ = slcrc0,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_323,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xO,xK)),
inference(paramod,[status(thm)],[c_293,c_292]) ).
cnf(c_898,plain,
sbrdtbr0(slbdtrb0(sz00)) = sz00,
inference(resolve,[status(thm)],[c_186,c_133]) ).
cnf(c_369,plain,
sbrdtbr0(slcrc0) = sz00,
inference(paramod,[status(thm)],[c_178,c_898]) ).
cnf(c_899,plain,
( sbrdtbr0(C) = A
| ~ aElementOf0(C,B)
| slbdtsldtrb0(xO,A) != B
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_189,c_285]) ).
cnf(c_900,plain,
( sbrdtbr0(B) = xK
| ~ aElementOf0(B,A)
| slbdtsldtrb0(xO,xK) != A ),
inference(resolve,[status(thm)],[c_899,c_233]) ).
cnf(c_901,plain,
( sbrdtbr0(A) = xK
| ~ aElementOf0(A,slbdtsldtrb0(xO,xK)) ),
inference(xxres,[status(thm)],[c_900]) ).
cnf(c_902,plain,
sbrdtbr0(slcrc0) = xK,
inference(resolve,[status(thm)],[c_901,c_323]) ).
cnf(c_903,plain,
sz00 = xK,
inference(paramod,[status(thm)],[c_369,c_902]) ).
cnf(c_904,plain,
xK = sz00,
inference(copy,[status(thm)],[c_903]) ).
cnf(c_897,plain,
$false,
inference(resolve,[status(thm)],[c_245,c_904]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM605+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:20:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3872830 was started by sandbox2 on n017,
% 0.10/0.37 % Sat Sep 26 03:20:47 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 0.47/0.56
% 0.47/0.56 % SZS status Theorem for theBenchmark
% 0.47/0.56
% 0.47/0.56 % Proof 1 at 0.10 (+ 0.03) seconds.
% 0.47/0.56 % Length of proof is 16.
% 0.47/0.56 % Level of proof is 3.
% 0.47/0.56 % Maximum clause weight is 27.000.
% 0.47/0.56 % Given clauses 218.
% 0.47/0.56
% 0.47/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------