%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM482+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 : n017.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 08:17:09 AM UTC 2026
% Result : Theorem 0.23s 0.55s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 64 ( 28 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 66 ( 18 ~; 17 |; 24 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 18 ( 0 sgn 5 !; 8 ?)
% 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(m__,conjecture,
( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [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,
~ ( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [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__]) ).
cnf(c_48,negated_conjecture,
isPrime0(xk),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_49,negated_conjecture,
( ~ isPrime0(A)
| sdtasdt0(A,B) != xk
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_70,negated_conjecture,
( sdtasdt0(xk,A) != xk
| ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(xk) ),
inference(resolve,[status(thm)],[c_49,c_48]) ).
fof(m__1716,axiom,
aNaturalNumber0(xk),
file('theBenchmark.p',m__1716) ).
cnf(c_117,plain,
aNaturalNumber0(xk),
inference(clausify,[status(thm)],[m__1716]) ).
cnf(c_168,plain,
( sdtasdt0(A,sz10) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulUnit]) ).
cnf(c_178,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_203,negated_conjecture,
( sdtasdt0(xk,A) != xk
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_117,c_70]) ).
cnf(c_467,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolve,[status(thm)],[c_168,c_117]) ).
cnf(c_798,negated_conjecture,
sdtasdt0(xk,sz10) != xk,
inference(resolve,[status(thm)],[c_203,c_178]) ).
cnf(c_799,negated_conjecture,
xk != xk,
inference(paramod,[status(thm)],[c_467,c_798]) ).
cnf(c_797,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 02:51:17 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3825888 was started by sandbox2 on n017,
% 0.18/0.45 % Sat Sep 26 02:51:17 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 0.23/0.55
% 0.23/0.55 % SZS status Theorem for theBenchmark
% 0.23/0.55
% 0.23/0.55 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.23/0.55 % Length of proof is 12.
% 0.23/0.55 % Level of proof is 4.
% 0.23/0.55 % Maximum clause weight is 19.000.
% 0.23/0.55 % Given clauses 115.
% 0.23/0.55
% 0.23/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------