%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM568+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 : n009.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 08:17:26 AM UTC 2026
% Result : Theorem 31.05s 5.10s
% Output : CNFRefutation 31.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 46 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 37 ( 12 ~; 18 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 5 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNatExtra,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00 ) ),
file('theBenchmark.p',mNatExtra) ).
fof(m__,conjecture,
? [W0] :
( szszuzczcdt0(W0) = xK
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( szszuzczcdt0(W0) = xK
& aElementOf0(W0,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(m__3418,axiom,
aElementOf0(xK,szNzAzT0),
file('theBenchmark.p',m__3418) ).
cnf(c_499,plain,
aElementOf0(xK,szNzAzT0),
inference(clausify,[status(thm)],[m__3418]) ).
fof(nnf_25,plain,
! [W0] :
( ? [W1] :
( szszuzczcdt0(W1) = W0
& aElementOf0(W1,szNzAzT0) )
| sz00 = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNatExtra]) ).
fof(sk_mNatExtra_sk,plain,
! [W0] :
( ( szszuzczcdt0(sK0(W0)) = W0
& aElementOf0(sK0(W0),szNzAzT0) )
| sz00 = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_25]) ).
fof(sk_mNatExtra,plain,
( ! [VAR_0] :
( szszuzczcdt0(sK0(VAR_0)) = VAR_0
| sz00 = VAR_0
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0] :
( aElementOf0(sK0(VAR_0),szNzAzT0)
| sz00 = VAR_0
| ~ aElementOf0(VAR_0,szNzAzT0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mNatExtra_sk]) ).
cnf(c_595,plain,
( szszuzczcdt0(sK0(A)) = A
| sz00 = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mNatExtra]) ).
cnf(c_596,plain,
( aElementOf0(sK0(A),szNzAzT0)
| sz00 = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mNatExtra]) ).
fof(m__3462,axiom,
xK != sz00,
file('theBenchmark.p',m__3462) ).
cnf(c_643,plain,
xK != sz00,
inference(clausify,[status(thm)],[m__3462]) ).
cnf(c_644,negated_conjecture,
( szszuzczcdt0(A) != xK
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_7657,plain,
( szszuzczcdt0(sK0(xK)) = xK
| sz00 = xK ),
inference(resolve,[status(thm)],[c_595,c_499]) ).
cnf(c_7658,plain,
( szszuzczcdt0(sK0(xK)) = xK
| xK = sz00 ),
inference(copy,[status(thm)],[c_7657]) ).
cnf(c_7199,plain,
szszuzczcdt0(sK0(xK)) = xK,
inference(resolve,[status(thm)],[c_643,c_7658]) ).
cnf(c_7659,plain,
( aElementOf0(sK0(xK),szNzAzT0)
| sz00 = xK ),
inference(resolve,[status(thm)],[c_596,c_499]) ).
cnf(c_7660,plain,
( aElementOf0(sK0(xK),szNzAzT0)
| xK = sz00 ),
inference(copy,[status(thm)],[c_7659]) ).
cnf(c_7200,plain,
aElementOf0(sK0(xK),szNzAzT0),
inference(resolve,[status(thm)],[c_643,c_7660]) ).
cnf(c_7661,negated_conjecture,
szszuzczcdt0(sK0(xK)) != xK,
inference(resolve,[status(thm)],[c_7200,c_644]) ).
cnf(c_7656,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7199,c_7661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 03:15:59 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 3252349 was started by sandbox2 on n009,
% 0.12/0.37 % Sat Sep 26 03:15:59 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/0.48
% 0.23/0.48 % From the command line: assign(max_seconds, 300).
% 31.05/5.10
% 31.05/5.10 % given #500 (I,wt=60): 841 szDzozmdt0(A) != slbdtsldtrb0(B,C) | -aElementOf0(C,szNzAzT0) | -aSet0(B) | aElementOf0(f22(C,B),B) | -isCountable0(B) | -aFunction0(A) | -aElementOf0(f26(C,B,A),xT) | -iLess0(C,xK) | -aElementOf0(D,slbdtsldtrb0(f28(C,B,A),C)) | f27(C,B,A) = sdtlpdtrp0(A,D). [copy(840),flip(j)].
% 31.05/5.10
% 31.05/5.10 % given #1000 (I,wt=69): 1676 -aSet0(f23(A,B,C)) | -aElementOf0(f24(A,B,C),B) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | -aSubsetOf0(sdtlcdtrc0(C,szDzozmdt0(C)),xT) | -iLess0(A,xK) | aSubsetOf0(f28(A,B,C),B). [resolve(268,a,207,f)].
% 31.05/5.10
% 31.05/5.10 % given #1500 (I,wt=84): 2398 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | -aSubsetOf0(sdtlcdtrc0(C,szDzozmdt0(C)),xT) | -iLess0(A,xK) | -aSubsetOf0(D,f28(A,B,C)) | sbrdtbr0(D) != A | f27(A,B,C) = sdtlpdtrp0(C,D). [copy(2397),flip(n)].
% 31.05/5.10
% 31.05/5.10 % given #2000 (I,wt=76): 3120 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aElementOf0(E,f28(A,B,C)) | aElementOf0(E,B). [resolve(273,a,262,f)].
% 31.05/5.10
% 31.05/5.10 % given #2500 (I,wt=77): 3843 aElementOf0(f23(A,B,C),szDzozmdt0(C)) | -aElementOf0(D,f23(A,B,C)) | aElementOf0(D,B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | -aElementOf0(f22(A,B),szNzAzT0) | -isCountable0(B) | -aFunction0(C) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | -aSet0(E) | -aElementOf0(f29(A,B,C,E),f28(A,B,C)) | sbrdtbr0(E) != A | f27(A,B,C) = sdtlpdtrp0(C,E). [copy(3842),flip(n)].
% 31.05/5.10
% 31.05/5.10 % given #3000 (I,wt=118): 4381 -aSet0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | -aElementOf0(f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aElementOf0(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),szNzAzT0) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | -iLess0(A,xK) | -aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)). [factor(1612,j,m)].
% 31.05/5.10
% 31.05/5.10 % given #3500 (I,wt=95): 4891 -aSet0(f23(A,szDzozmdt0(B),B)) | -aElementOf0(f24(A,szDzozmdt0(B),B),szDzozmdt0(B)) | sbrdtbr0(f23(A,szDzozmdt0(B),B)) != A | -aElementOf0(C,f23(A,szDzozmdt0(B),B)) | aElementOf0(C,szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(szDzozmdt0(B)) | -aElementOf0(f22(A,szDzozmdt0(B)),szNzAzT0) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | aElementOf0(D,sdtlcdtrc0(B,szDzozmdt0(B))) | sdtlpdtrp0(B,f24(A,szDzozmdt0(B),B)) != D | -iLess0(A,xK) | aElementOf0(f27(A,szDzozmdt0(B),B),xT). [factor(2173,b,l)].
% 31.05/5.10
% 31.05/5.10 % given #4000 (I,wt=83): 5402 -aSet0(f23(A,B,C)) | aElementOf0(f24(A,B,C),f23(A,B,C)) | sbrdtbr0(f23(A,B,C)) != A | aSubsetOf0(f23(A,B,C),B) | -aElementOf0(A,szNzAzT0) | -aSet0(B) | aElementOf0(f22(A,B),B) | -isCountable0(B) | -aFunction0(C) | aSet0(sdtlcdtrc0(C,szDzozmdt0(C))) | -iLess0(A,xK) | aElementOf0(f29(A,B,C,B),B) | sbrdtbr0(B) != A | f27(A,B,C) = sdtlpdtrp0(C,B). [factor(2844,f,l)].
% 31.05/5.10
% 31.05/5.10 % given #4500 (I,wt=91): 5925 aElementOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),szDzozmdt0(B)) | -aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(f26(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(sdtlcdtrc0(B,szDzozmdt0(B)),szNzAzT0) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | -iLess0(A,xK) | -aElementOf0(C,f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | aElementOf0(C,sdtlcdtrc0(B,szDzozmdt0(B))). [factor(3705,c,h)].
% 31.05/5.10
% 31.05/5.10 % given #5000 (I,wt=117): 6444 -aSet0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) | -aElementOf0(f24(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),sdtlcdtrc0(B,szDzozmdt0(B))) | sbrdtbr0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != A | -aElementOf0(f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B),szDzozmdt0(B)) | -aElementOf0(A,szNzAzT0) | -aSet0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aElementOf0(f22(A,sdtlcdtrc0(B,szDzozmdt0(B))),szNzAzT0) | -isCountable0(sdtlcdtrc0(B,szDzozmdt0(B))) | -aFunction0(B) | aElementOf0(C,sdtlcdtrc0(B,szDzozmdt0(B))) | sdtlpdtrp0(B,f23(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)) != C | -iLess0(A,xK) | -aElementOf0(C,f28(A,sdtlcdtrc0(B,szDzozmdt0(B)),B)). [factor(4401,j,n)].
% 31.05/5.10
% 31.05/5.10 % given #5500 (I,wt=76): 6944 aElementOf0(f23(A,szDzozmdt0(B),B),szDzozmdt0(B)) | -aElementOf0(f23(A,szDzozmdt0(B),B),f23(A,szDzozmdt0(B),B)) | -aElementOf0(A,szNzAzT0) | -aSubsetOf0(szDzozmdt0(B),szNzAzT0) | -isCountable0(szDzozmdt0(B)) | -aFunction0(B) | -aElementOf0(C,sdtlcdtrc0(B,szDzozmdt0(B))) | aElementOf0(f25(A,szDzozmdt0(B),B,C),szDzozmdt0(B)) | -iLess0(A,xK) | -aElementOf0(f25(A,szDzozmdt0(B),B,C),f28(A,szDzozmdt0(B),B)). [factor(5983,h,k)].
% 31.05/5.10
% 31.05/5.10 % SZS status Theorem for theBenchmark
% 31.05/5.10
% 31.05/5.10 % Proof 1 at 4.02 (+ 0.22) seconds.
% 31.05/5.10 % Length of proof is 10.
% 31.05/5.10 % Level of proof is 3.
% 31.05/5.10 % Maximum clause weight is 26.000.
% 31.05/5.10 % Given clauses 5750.
% 31.05/5.10
% 31.05/5.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------