%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM565+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 : n019.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 08:17:25 AM UTC 2026
% Result : Theorem 0.22s 10.65s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 23 unt; 0 def)
% Number of atoms : 98 ( 40 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 86 ( 36 ~; 30 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 10 !; 1 ?)
% 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(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ),
file('theBenchmark.p',mCardEmpty) ).
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__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3453,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('theBenchmark.p',m__3453) ).
fof(m__,conjecture,
! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_82,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_114,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('theBenchmark.p',mZeroNum) ).
cnf(c_116,plain,
aElementOf0(sz00,szNzAzT0),
inference(clausify,[status(thm)],[mZeroNum]) ).
cnf(c_136,plain,
( slcrc0 = A
| sbrdtbr0(A) != sz00
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCardEmpty]) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0,
file('theBenchmark.p',mSegZero) ).
cnf(c_161,plain,
slbdtrb0(sz00) = slcrc0,
inference(clausify,[status(thm)],[mSegZero]) ).
cnf(c_162,plain,
slcrc0 = slbdtrb0(sz00),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_172,plain,
( aSubsetOf0(D,A)
| ~ aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
cnf(c_173,plain,
( sbrdtbr0(D) = B
| ~ aElementOf0(D,C)
| slbdtsldtrb0(A,B) != C
| ~ aElementOf0(B,szNzAzT0)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSel]) ).
cnf(c_220,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_223,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(clausify,[status(thm)],[m__3453]) ).
cnf(c_224,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(copy,[status(thm)],[c_223]) ).
fof(m__3462,axiom,
xK = sz00,
file('theBenchmark.p',m__3462) ).
cnf(c_231,plain,
xK = sz00,
inference(clausify,[status(thm)],[m__3462]) ).
fof(nnf_74,plain,
? [W0] :
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,W0)
& aElementOf0(W0,slbdtsldtrb0(xS,sz00)) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK0)
& aElementOf0(sK0,slbdtsldtrb0(xS,sz00)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_74]) ).
cnf(c_234,negated_conjecture,
aElementOf0(sK0,slbdtsldtrb0(xS,sz00)),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_235,negated_conjecture,
sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,sK0),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_236,negated_conjecture,
sdtlpdtrp0(xc,slbdtrb0(sz00)) != sdtlpdtrp0(xc,sK0),
inference(paramod,[status(thm)],[c_162,c_235]) ).
cnf(c_262,plain,
( slbdtrb0(sz00) = A
| sbrdtbr0(A) != sz00
| ~ aSet0(A) ),
inference(paramod,[status(thm)],[c_162,c_136]) ).
cnf(c_285,plain,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(paramod,[status(thm)],[c_231,c_224]) ).
cnf(c_286,negated_conjecture,
aElementOf0(sK0,szDzozmdt0(xc)),
inference(paramod,[status(thm)],[c_285,c_234]) ).
cnf(c_786,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_220,c_82]) ).
cnf(c_366,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_114,c_786]) ).
cnf(c_787,plain,
( sbrdtbr0(C) = A
| ~ aElementOf0(C,B)
| slbdtsldtrb0(xS,A) != B
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_173,c_366]) ).
cnf(c_788,plain,
( sbrdtbr0(B) = sz00
| ~ aElementOf0(B,A)
| slbdtsldtrb0(xS,sz00) != A ),
inference(resolve,[status(thm)],[c_787,c_116]) ).
cnf(c_789,plain,
( sbrdtbr0(A) = sz00
| ~ aElementOf0(A,szDzozmdt0(xc)) ),
inference(resolve,[status(thm)],[c_788,c_285]) ).
cnf(c_542,negated_conjecture,
sbrdtbr0(sK0) = sz00,
inference(resolve,[status(thm)],[c_789,c_286]) ).
cnf(c_790,plain,
( aSubsetOf0(C,xS)
| ~ aElementOf0(C,B)
| slbdtsldtrb0(xS,A) != B
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_172,c_366]) ).
cnf(c_791,plain,
( aSubsetOf0(B,xS)
| ~ aElementOf0(B,A)
| slbdtsldtrb0(xS,sz00) != A ),
inference(resolve,[status(thm)],[c_790,c_116]) ).
cnf(c_792,plain,
( aSubsetOf0(A,xS)
| ~ aElementOf0(A,szDzozmdt0(xc)) ),
inference(resolve,[status(thm)],[c_791,c_285]) ).
cnf(c_544,negated_conjecture,
aSubsetOf0(sK0,xS),
inference(resolve,[status(thm)],[c_792,c_286]) ).
cnf(c_793,plain,
( aSet0(sK0)
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_544,c_82]) ).
cnf(c_657,plain,
aSet0(sK0),
inference(resolve,[status(thm)],[c_366,c_793]) ).
cnf(c_794,plain,
( slbdtrb0(sz00) = sK0
| sbrdtbr0(sK0) != sz00 ),
inference(resolve,[status(thm)],[c_657,c_262]) ).
cnf(c_795,plain,
( slbdtrb0(sz00) = sK0
| sz00 != sz00 ),
inference(paramod,[status(thm)],[c_542,c_794]) ).
cnf(c_664,plain,
slbdtrb0(sz00) = sK0,
inference(copy,[status(thm)],[c_795]) ).
cnf(c_796,negated_conjecture,
sdtlpdtrp0(xc,sK0) != sdtlpdtrp0(xc,sK0),
inference(paramod,[status(thm)],[c_664,c_236]) ).
cnf(c_785,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_796]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM565+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/10.45 % Computer : n019.cluster.edu
% 0.18/10.45 % Model : x86_64 x86_64
% 0.18/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.45 % Memory : 8046.5625MB
% 0.18/10.45 % OS : Linux 6.8.0-71-generic
% 0.18/10.45 % CPULimit : 300
% 0.18/10.45 % WCLimit : 300
% 0.18/10.45 % DateTime : Sat Sep 26 03:15:15 UTC 2026
% 0.18/10.45 % CPUTime :
% 0.18/10.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/10.46 % Process 274093 was started by sandbox2 on n019,
% 0.18/10.46 % Sat Sep 26 03:15:15 2026
% 0.18/10.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/10.47
% 0.18/10.47 % From the command line: assign(max_seconds, 300).
% 0.22/10.65
% 0.22/10.65 % SZS status Theorem for theBenchmark
% 0.22/10.65
% 0.22/10.65 % Proof 1 at 0.12 (+ 0.03) seconds.
% 0.22/10.65 % Length of proof is 31.
% 0.22/10.65 % Level of proof is 8.
% 0.22/10.65 % Maximum clause weight is 27.000.
% 0.22/10.65 % Given clauses 194.
% 0.22/10.65
% 0.22/10.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------