%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM514+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:17:14 AM UTC 2026
% Result : Theorem 23.09s 13.58s
% Output : CNFRefutation 23.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 81 ( 32 unt; 0 def)
% Number of atoms : 227 ( 67 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 261 ( 115 ~; 117 |; 20 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mDefDiv,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(mDefQuot,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefQuot) ).
fof(mDefPrime,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('theBenchmark.p',mDefPrime) ).
fof(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__1860,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('theBenchmark.p',m__1860) ).
fof(m__2342,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('theBenchmark.p',m__2342) ).
fof(m__,conjecture,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_53,plain,
( sz00 != A
| ~ isPrime0(A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefPrime]) ).
cnf(c_59,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_60,plain,
isPrime0(xr),
inference(clausify,[status(thm)],[m__2342]) ).
cnf(c_61,plain,
( sz00 != xr
| ~ aNaturalNumber0(xr) ),
inference(resolve,[status(thm)],[c_60,c_53]) ).
cnf(c_62,plain,
( xr != sz00
| ~ aNaturalNumber0(xr) ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_68,plain,
( sz00 != xp
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_59,c_53]) ).
cnf(c_69,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_98,negated_conjecture,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__2613,axiom,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
file('theBenchmark.p',m__2613) ).
cnf(c_99,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(clausify,[status(thm)],[m__2613]) ).
fof(m__2487,axiom,
doDivides0(xr,xn),
file('theBenchmark.p',m__2487) ).
cnf(c_104,plain,
doDivides0(xr,xn),
inference(clausify,[status(thm)],[m__2487]) ).
cnf(c_109,plain,
doDivides0(xr,xk),
inference(clausify,[status(thm)],[m__2342]) ).
cnf(c_110,plain,
aNaturalNumber0(xr),
inference(clausify,[status(thm)],[m__2342]) ).
fof(m__2306,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('theBenchmark.p',m__2306) ).
cnf(c_113,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(clausify,[status(thm)],[m__2306]) ).
cnf(c_122,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_123,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_124,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_125,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_134,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtsldt0(B,A) = C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_136,plain,
( aNaturalNumber0(C)
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
fof(nnf_29,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [X0] :
( sdtasdt0(W0,X0) = W1
& aNaturalNumber0(X0) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiv]) ).
fof(sk_mDefDiv_sk,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( sdtasdt0(W0,sK0(W0,W1)) = W1
& aNaturalNumber0(sK0(W0,W1)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(W0,W1))],[nnf_29]) ).
fof(sk_mDefDiv,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sdtasdt0(VAR_0,VAR_2) != VAR_1
| ~ aNaturalNumber0(VAR_2)
| doDivides0(VAR_0,VAR_1)
| ~ aNaturalNumber0(VAR_1)
| ~ aNaturalNumber0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK0(VAR_0,VAR_1)) = VAR_1
| ~ doDivides0(VAR_0,VAR_1)
| ~ aNaturalNumber0(VAR_1)
| ~ aNaturalNumber0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aNaturalNumber0(sK0(VAR_0,VAR_1))
| ~ doDivides0(VAR_0,VAR_1)
| ~ aNaturalNumber0(VAR_1)
| ~ aNaturalNumber0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefDiv_sk]) ).
cnf(c_137,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefDiv]) ).
cnf(c_138,plain,
( sdtasdt0(A,sK0(A,B)) = B
| ~ doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefDiv]) ).
cnf(c_139,plain,
( aNaturalNumber0(sK0(A,B))
| ~ doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefDiv]) ).
cnf(c_183,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_217,plain,
xr != sz00,
inference(resolve,[status(thm)],[c_110,c_62]) ).
cnf(c_220,plain,
doDivides0(xr,sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(paramod,[status(thm)],[c_113,c_109]) ).
cnf(c_225,plain,
sdtasdt0(xp,sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(paramod,[status(thm)],[c_113,c_99]) ).
cnf(c_229,plain,
xp != sz00,
inference(resolve,[status(thm)],[c_123,c_69]) ).
cnf(c_23714,plain,
( sdtasdt0(xr,A) != xn
| ~ aNaturalNumber0(A)
| sdtsldt0(xn,xr) = A
| sz00 = xr
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolve,[status(thm)],[c_134,c_104]) ).
cnf(c_23715,plain,
( sdtasdt0(xr,A) != xn
| ~ aNaturalNumber0(A)
| sdtsldt0(xn,xr) = A
| xr = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(copy,[status(thm)],[c_23714]) ).
cnf(c_23716,plain,
( sdtasdt0(xr,A) != xn
| ~ aNaturalNumber0(A)
| sdtsldt0(xn,xr) = A
| xr = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_110,c_23715]) ).
cnf(c_23717,plain,
( sdtasdt0(xr,A) != xn
| ~ aNaturalNumber0(A)
| sdtsldt0(xn,xr) = A
| xr = sz00 ),
inference(resolve,[status(thm)],[c_125,c_23716]) ).
cnf(c_695,plain,
( sdtasdt0(xr,A) != xn
| ~ aNaturalNumber0(A)
| sdtsldt0(xn,xr) = A ),
inference(resolve,[status(thm)],[c_217,c_23717]) ).
cnf(c_23718,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(copy,[status(thm)],[c_113]) ).
cnf(c_23719,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_136,c_23718]) ).
cnf(c_23720,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_113,c_23719]) ).
cnf(c_23721,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_23720]) ).
cnf(c_23722,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_123,c_23721]) ).
cnf(c_23723,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_229,c_23722]) ).
cnf(c_745,plain,
( aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_122,c_23723]) ).
cnf(c_746,plain,
( aNaturalNumber0(sdtsldt0(B,A))
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(xxres,[status(thm)],[c_136]) ).
cnf(c_23724,plain,
( sdtasdt0(xr,sK0(xr,xn)) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolve,[status(thm)],[c_138,c_104]) ).
cnf(c_23725,plain,
( sdtasdt0(xr,sK0(xr,xn)) = xn
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_110,c_23724]) ).
cnf(c_788,plain,
sdtasdt0(xr,sK0(xr,xn)) = xn,
inference(resolve,[status(thm)],[c_125,c_23725]) ).
cnf(c_23726,plain,
( aNaturalNumber0(sK0(xr,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolve,[status(thm)],[c_139,c_104]) ).
cnf(c_23727,plain,
( aNaturalNumber0(sK0(xr,xn))
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_110,c_23726]) ).
cnf(c_799,plain,
aNaturalNumber0(sK0(xr,xn)),
inference(resolve,[status(thm)],[c_125,c_23727]) ).
cnf(c_1272,plain,
( aNaturalNumber0(sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_183,c_125]) ).
cnf(c_1277,plain,
( aNaturalNumber0(sdtasdt0(A,xm))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_183,c_124]) ).
cnf(c_23728,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_225,c_137]) ).
cnf(c_23729,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(resolve,[status(thm)],[c_123,c_23728]) ).
cnf(c_1721,negated_conjecture,
( ~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| ~ aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(resolve,[status(thm)],[c_98,c_23729]) ).
cnf(c_19255,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolve,[status(thm)],[c_1272,c_124]) ).
cnf(c_19286,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)),
inference(resolve,[status(thm)],[c_19255,c_745]) ).
cnf(c_23730,plain,
( sdtasdt0(xr,sK0(xr,xn)) != xn
| sdtsldt0(xn,xr) = sK0(xr,xn) ),
inference(resolve,[status(thm)],[c_695,c_799]) ).
cnf(c_23731,plain,
( xn != xn
| sdtsldt0(xn,xr) = sK0(xr,xn) ),
inference(paramod,[status(thm)],[c_788,c_23730]) ).
cnf(c_23732,plain,
( xn != xn
| sK0(xr,xn) = sdtsldt0(xn,xr) ),
inference(copy,[status(thm)],[c_23731]) ).
cnf(c_21186,plain,
sK0(xr,xn) = sdtsldt0(xn,xr),
inference(copy,[status(thm)],[c_23732]) ).
cnf(c_21307,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(paramod,[status(thm)],[c_21186,c_799]) ).
cnf(c_21352,plain,
aNaturalNumber0(sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(resolve,[status(thm)],[c_1277,c_21307]) ).
cnf(c_21375,negated_conjecture,
~ aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)),
inference(resolve,[status(thm)],[c_21352,c_1721]) ).
cnf(c_23733,plain,
( aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| sz00 = xr
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr) ),
inference(resolve,[status(thm)],[c_746,c_220]) ).
cnf(c_23734,plain,
( aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| xr = sz00
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xr) ),
inference(copy,[status(thm)],[c_23733]) ).
cnf(c_23735,plain,
( aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| xr = sz00
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)) ),
inference(resolve,[status(thm)],[c_110,c_23734]) ).
cnf(c_23736,plain,
( aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr))
| xr = sz00 ),
inference(resolve,[status(thm)],[c_19286,c_23735]) ).
cnf(c_23737,plain,
aNaturalNumber0(sdtsldt0(sdtsldt0(sdtasdt0(xn,xm),xp),xr)),
inference(resolve,[status(thm)],[c_217,c_23736]) ).
cnf(c_23713,plain,
$false,
inference(resolve,[status(thm)],[c_21375,c_23737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM514+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.58 % Computer : n013.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Sat Sep 26 03:03:32 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.59 % Process 1805167 was started by sandbox on n013,
% 0.10/10.59 % Sat Sep 26 03:03:32 2026
% 0.10/10.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/10.60
% 0.14/10.60 % From the command line: assign(max_seconds, 300).
% 23.09/13.58
% 23.09/13.58 % given #500 (A,wt=31): 421 xm = sz00 | xm = sz10 | doDivides0(f3(xm),xm) | -aNaturalNumber0(A) | -doDivides0(A,xm) | sz10 = A | xm = A. [resolve(124,a,95,a),flip(a),flip(b),flip(g)].
% 23.09/13.58
% 23.09/13.58 % given #1000 (T,wt=15): 1240 sdtpldt0(xn,sz00) = xn. [resolve(180,a,125,a)].
% 23.09/13.58
% 23.09/13.58 % given #1500 (A,wt=28): 724 -aNaturalNumber0(A) | sz00 = A | -doDivides0(A,xn) | sdtsldt0(xn,A) != B | sdtasdt0(A,B) = xn. [resolve(135,b,125,a)].
% 23.09/13.58
% 23.09/13.58 % SZS status Theorem for theBenchmark
% 23.09/13.58
% 23.09/13.58 % Proof 1 at 2.24 (+ 0.70) seconds.
% 23.09/13.58 % Length of proof is 50.
% 23.09/13.58 % Level of proof is 10.
% 23.09/13.58 % Maximum clause weight is 45.000.
% 23.09/13.58 % Given clauses 1566.
% 23.09/13.58
% 23.09/13.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------