%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM500+3 : 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 : 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 08:17:12 AM UTC 2026
% Result : Theorem 19.37s 3.02s
% Output : CNFRefutation 19.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 7 unt; 0 def)
% Number of atoms : 127 ( 63 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 126 ( 32 ~; 62 |; 29 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mPrimDiv,axiom,
! [W0] :
( ( W0 != sz10
& W0 != sz00
& aNaturalNumber0(W0) )
=> ? [W1] :
( isPrime0(W1)
& doDivides0(W1,W0)
& aNaturalNumber0(W1) ) ),
file('theBenchmark.p',mPrimDiv) ).
fof(m__2306,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('theBenchmark.p',m__2306) ).
fof(m__2327,axiom,
( xk != sz10
& xk != sz00 ),
file('theBenchmark.p',m__2327) ).
fof(m__,conjecture,
? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_37,plain,
! [W0] :
( ? [W1] :
( isPrime0(W1)
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| sz10 = W0
| sz00 = W0
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mPrimDiv]) ).
fof(sk_mPrimDiv_sk,plain,
! [W0] :
( ( isPrime0(sK0(W0))
& doDivides0(sK0(W0),W0)
& aNaturalNumber0(sK0(W0)) )
| sz10 = W0
| sz00 = W0
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_37]) ).
fof(sk_mPrimDiv,plain,
( ! [VAR_0] :
( isPrime0(sK0(VAR_0))
| sz10 = VAR_0
| sz00 = VAR_0
| ~ aNaturalNumber0(VAR_0) )
& ! [VAR_0] :
( doDivides0(sK0(VAR_0),VAR_0)
| sz10 = VAR_0
| sz00 = VAR_0
| ~ aNaturalNumber0(VAR_0) )
& ! [VAR_0] :
( aNaturalNumber0(sK0(VAR_0))
| sz10 = VAR_0
| sz00 = VAR_0
| ~ aNaturalNumber0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mPrimDiv_sk]) ).
cnf(c_55,plain,
( isPrime0(sK0(A))
| sz10 = A
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mPrimDiv]) ).
cnf(c_76,negated_conjecture,
( ~ isPrime0(A)
| ~ doDivides0(A,xk)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_85,negated_conjecture,
( sz10 = A
| sz00 = A
| ~ aNaturalNumber0(A)
| ~ doDivides0(sK0(A),xk)
| ~ aNaturalNumber0(sK0(A)) ),
inference(resolve,[status(thm)],[c_76,c_55]) ).
cnf(c_307,plain,
xk != sz10,
inference(clausify,[status(thm)],[m__2327]) ).
cnf(c_308,plain,
xk != sz00,
inference(clausify,[status(thm)],[m__2327]) ).
cnf(c_313,plain,
aNaturalNumber0(xk),
inference(clausify,[status(thm)],[m__2306]) ).
cnf(c_559,plain,
( doDivides0(sK0(A),A)
| sz10 = A
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mPrimDiv]) ).
cnf(c_560,plain,
( aNaturalNumber0(sK0(A))
| sz10 = A
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mPrimDiv]) ).
cnf(c_9473,plain,
( doDivides0(sK0(xk),xk)
| sz10 = xk
| sz00 = xk ),
inference(resolve,[status(thm)],[c_559,c_313]) ).
cnf(c_9474,plain,
( doDivides0(sK0(xk),xk)
| sz10 = xk
| xk = sz00 ),
inference(copy,[status(thm)],[c_9473]) ).
cnf(c_9475,plain,
( doDivides0(sK0(xk),xk)
| xk = sz10
| xk = sz00 ),
inference(copy,[status(thm)],[c_9474]) ).
cnf(c_9476,plain,
( doDivides0(sK0(xk),xk)
| xk = sz10 ),
inference(resolve,[status(thm)],[c_308,c_9475]) ).
cnf(c_2830,plain,
doDivides0(sK0(xk),xk),
inference(resolve,[status(thm)],[c_307,c_9476]) ).
cnf(c_9477,plain,
( aNaturalNumber0(sK0(xk))
| sz10 = xk
| sz00 = xk ),
inference(resolve,[status(thm)],[c_560,c_313]) ).
cnf(c_9478,plain,
( aNaturalNumber0(sK0(xk))
| sz10 = xk
| xk = sz00 ),
inference(copy,[status(thm)],[c_9477]) ).
cnf(c_9479,plain,
( aNaturalNumber0(sK0(xk))
| xk = sz10
| xk = sz00 ),
inference(copy,[status(thm)],[c_9478]) ).
cnf(c_9480,plain,
( aNaturalNumber0(sK0(xk))
| xk = sz10 ),
inference(resolve,[status(thm)],[c_308,c_9479]) ).
cnf(c_2837,plain,
aNaturalNumber0(sK0(xk)),
inference(resolve,[status(thm)],[c_307,c_9480]) ).
cnf(c_9481,negated_conjecture,
( sz10 = xk
| sz00 = xk
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sK0(xk)) ),
inference(resolve,[status(thm)],[c_2830,c_85]) ).
cnf(c_9482,negated_conjecture,
( sz10 = xk
| xk = sz00
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sK0(xk)) ),
inference(copy,[status(thm)],[c_9481]) ).
cnf(c_9483,negated_conjecture,
( xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sK0(xk)) ),
inference(copy,[status(thm)],[c_9482]) ).
cnf(c_9484,negated_conjecture,
( xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk) ),
inference(resolve,[status(thm)],[c_2837,c_9483]) ).
cnf(c_9485,negated_conjecture,
( xk = sz10
| xk = sz00 ),
inference(resolve,[status(thm)],[c_313,c_9484]) ).
cnf(c_9486,negated_conjecture,
xk = sz10,
inference(resolve,[status(thm)],[c_308,c_9485]) ).
cnf(c_9472,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_307,c_9486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 03:00:44 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 3236878 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 03:00:44 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.44
% 0.13/0.44 % From the command line: assign(max_seconds, 300).
% 19.37/3.02
% 19.37/3.02 % given #500 (I,wt=70): 893 -aNaturalNumber0(A) | -aNaturalNumber0(B) | -aNaturalNumber0(f4(C)) | sdtasdt0(f4(C),f4(C)) != sdtasdt0(A,B) | -iLess0(sdtpldt0(sdtpldt0(A,B),f4(C)),sdtpldt0(sdtpldt0(xn,xm),xp)) | doDivides0(f4(C),A) | sdtasdt0(f4(C),f8(A,B,f4(C))) = B | -aNaturalNumber0(C) | sz00 = C | sz10 = C. [factor(217,c,d)].
% 19.37/3.02
% 19.37/3.02 % given #1000 (I,wt=66): 1532 -aNaturalNumber0(A) | -aNaturalNumber0(B) | sz00 = B | sz10 = B | aNaturalNumber0(f5(A,B,B)) | -aNaturalNumber0(C) | sdtasdt0(B,C) != sdtasdt0(A,B) | -iLess0(sdtpldt0(sdtpldt0(A,B),B),sdtpldt0(sdtpldt0(xn,xm),xp)) | sdtasdt0(B,f7(A,B,B)) = A | sdtasdt0(B,f8(A,B,B)) = B. [factor(547,b,c)].
% 19.37/3.02
% 19.37/3.02 % given #1500 (I,wt=55): 2183 -aNaturalNumber0(A) | -aNaturalNumber0(B) | sz00 = B | sz10 = B | f5(A,B,B) != sz10 | sdtasdt0(A,B) != sdtasdt0(B,A) | -iLess0(sdtpldt0(sdtpldt0(A,B),B),sdtpldt0(sdtpldt0(xn,xm),xp)) | doDivides0(B,A) | doDivides0(B,B). [factor(1218,b,c)].
% 19.37/3.02
% 19.37/3.02 % given #2000 (A,wt=27): 2657 -aNaturalNumber0(A) | sdtasdt0(A,c3) != xk | sz00 = A | sz10 = A | f9(A) != sz10. [resolve(317,a,302,b)].
% 19.37/3.02
% 19.37/3.02 % SZS status Theorem for theBenchmark
% 19.37/3.02
% 19.37/3.02 % Proof 1 at 2.19 (+ 0.24) seconds.
% 19.37/3.02 % Length of proof is 15.
% 19.37/3.02 % Level of proof is 3.
% 19.37/3.02 % Maximum clause weight is 25.000.
% 19.37/3.02 % Given clauses 2284.
% 19.37/3.02
% 19.37/3.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------