%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM458+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 : n005.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 08:17:03 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 35 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 11 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 3 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',m_AddZero) ).
fof(mDefLE,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefLE) ).
fof(m__,conjecture,
sdtlseqdt0(xm,xm),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_20,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_27,plain,
( sdtpldt0(A,sz00) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_AddZero]) ).
cnf(c_48,plain,
( sdtpldt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefLE]) ).
fof(m__718,axiom,
aNaturalNumber0(xm),
file('theBenchmark.p',m__718) ).
cnf(c_52,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__718]) ).
cnf(c_53,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_236,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolve,[status(thm)],[c_52,c_27]) ).
cnf(c_271,plain,
( sdtpldt0(xm,B) != A
| ~ aNaturalNumber0(B)
| sdtlseqdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_48,c_52]) ).
cnf(c_272,plain,
( sdtpldt0(xm,A) != xm
| ~ aNaturalNumber0(A)
| sdtlseqdt0(xm,xm) ),
inference(resolve,[status(thm)],[c_271,c_52]) ).
cnf(c_273,negated_conjecture,
( sdtpldt0(xm,A) != xm
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_272,c_53]) ).
cnf(c_274,negated_conjecture,
sdtpldt0(xm,sz00) != xm,
inference(resolve,[status(thm)],[c_273,c_20]) ).
cnf(c_275,negated_conjecture,
xm != xm,
inference(paramod,[status(thm)],[c_236,c_274]) ).
cnf(c_270,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:49:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1044928 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 02:49:31 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 10.
% 0.09/0.40 % Level of proof is 3.
% 0.09/0.40 % Maximum clause weight is 14.000.
% 0.09/0.40 % Given clauses 32.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------