%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM489+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 : n001.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 08:17:10 AM UTC 2026
% Result : Theorem 0.03s 0.41s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 37 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 10 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__,conjecture,
xn = sdtpldt0(xp,xr),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_83,negated_conjecture,
sdtpldt0(xp,xr) != xn,
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__1883,axiom,
xr = sdtmndt0(xn,xp),
file('theBenchmark.p',m__1883) ).
cnf(c_86,plain,
xr = sdtmndt0(xn,xp),
inference(clausify,[status(thm)],[m__1883]) ).
fof(m__1870,axiom,
sdtlseqdt0(xp,xn),
file('theBenchmark.p',m__1870) ).
cnf(c_87,plain,
sdtlseqdt0(xp,xn),
inference(clausify,[status(thm)],[m__1870]) ).
cnf(c_89,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_91,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_123,plain,
( sdtpldt0(A,C) = B
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_181,negated_conjecture,
sdtpldt0(xp,sdtmndt0(xn,xp)) != xn,
inference(paramod,[status(thm)],[c_86,c_83]) ).
cnf(c_374,plain,
( sdtpldt0(xp,B) = A
| sdtmndt0(A,xp) != B
| ~ sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_123,c_89]) ).
cnf(c_375,plain,
( sdtpldt0(xp,A) = xn
| sdtmndt0(xn,xp) != A
| ~ sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_374,c_91]) ).
cnf(c_376,plain,
( sdtpldt0(xp,A) = xn
| sdtmndt0(xn,xp) != A ),
inference(resolve,[status(thm)],[c_375,c_87]) ).
cnf(c_377,plain,
sdtmndt0(xn,xp) = xr,
inference(copy,[status(thm)],[c_86]) ).
cnf(c_378,plain,
sdtpldt0(xp,xr) = xn,
inference(resolve,[status(thm)],[c_376,c_377]) ).
cnf(c_379,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
inference(paramod,[status(thm)],[c_86,c_378]) ).
cnf(c_373,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_181,c_379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM489+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 03:03:26 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 752482 was started by sandbox2 on n001,
% 0.03/0.36 % Sat Sep 26 03:03:26 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.37
% 0.03/0.37 % From the command line: assign(max_seconds, 300).
% 0.03/0.41
% 0.03/0.41 % SZS status Theorem for theBenchmark
% 0.03/0.41
% 0.03/0.41 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.03/0.41 % Length of proof is 11.
% 0.03/0.41 % Level of proof is 3.
% 0.03/0.41 % Maximum clause weight is 27.000.
% 0.03/0.41 % Given clauses 45.
% 0.03/0.41
% 0.03/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------