%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM482+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 : n020.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 08:17:08 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 47 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 14 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 3 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',m_MulUnit) ).
fof(mDefDiv,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(m__,conjecture,
( isPrime0(xk)
=> ? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( isPrime0(xk)
=> ? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_48,negated_conjecture,
isPrime0(xk),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_49,negated_conjecture,
( ~ isPrime0(A)
| ~ doDivides0(A,xk)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_59,negated_conjecture,
( ~ doDivides0(xk,xk)
| ~ aNaturalNumber0(xk) ),
inference(resolve,[status(thm)],[c_49,c_48]) ).
fof(m__1716,axiom,
aNaturalNumber0(xk),
file('theBenchmark.p',m__1716) ).
cnf(c_84,plain,
aNaturalNumber0(xk),
inference(clausify,[status(thm)],[m__1716]) ).
cnf(c_94,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiv]) ).
cnf(c_135,plain,
( sdtasdt0(A,sz10) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulUnit]) ).
cnf(c_145,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_153,negated_conjecture,
~ doDivides0(xk,xk),
inference(resolve,[status(thm)],[c_84,c_59]) ).
cnf(c_290,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolve,[status(thm)],[c_135,c_84]) ).
cnf(c_481,plain,
( sdtasdt0(xk,B) != A
| ~ aNaturalNumber0(B)
| doDivides0(xk,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_94,c_84]) ).
cnf(c_482,plain,
( sdtasdt0(xk,A) != xk
| ~ aNaturalNumber0(A)
| doDivides0(xk,xk) ),
inference(resolve,[status(thm)],[c_481,c_84]) ).
cnf(c_483,negated_conjecture,
( sdtasdt0(xk,A) != xk
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_482,c_153]) ).
cnf(c_484,negated_conjecture,
sdtasdt0(xk,sz10) != xk,
inference(resolve,[status(thm)],[c_483,c_145]) ).
cnf(c_480,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_290,c_484]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM482+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n020.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 26 02:56:48 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.34 % Process 459433 was started by sandbox2 on n020,
% 0.10/0.34 % Sat Sep 26 02:56:48 2026
% 0.10/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.35
% 0.10/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.40 % Length of proof is 14.
% 0.13/0.40 % Level of proof is 4.
% 0.13/0.40 % Maximum clause weight is 24.000.
% 0.13/0.40 % Given clauses 77.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------