%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM490+1 : 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 : n019.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 134.09s 17.51s
% Output : CNFRefutation 134.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 25 unt; 0 def)
% Number of atoms : 113 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 54 ~; 46 |; 8 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mDefLE,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefLE) ).
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,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_83,negated_conjecture,
sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) != sdtasdt0(xr,xm),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__1951,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('theBenchmark.p',m__1951) ).
cnf(c_84,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(clausify,[status(thm)],[m__1951]) ).
cnf(c_85,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(copy,[status(thm)],[c_84]) ).
fof(m__1883,axiom,
xr = sdtmndt0(xn,xp),
file('theBenchmark.p',m__1883) ).
cnf(c_90,plain,
xr = sdtmndt0(xn,xp),
inference(clausify,[status(thm)],[m__1883]) ).
cnf(c_91,plain,
sdtmndt0(xn,xp) = xr,
inference(copy,[status(thm)],[c_90]) ).
fof(m__1870,axiom,
sdtlseqdt0(xp,xn),
file('theBenchmark.p',m__1870) ).
cnf(c_92,plain,
sdtlseqdt0(xp,xn),
inference(clausify,[status(thm)],[m__1870]) ).
cnf(c_94,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_95,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_96,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_127,plain,
( sdtpldt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtmndt0(B,A) = C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_129,plain,
( aNaturalNumber0(C)
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_130,plain,
( sdtpldt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefLE]) ).
cnf(c_149,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_154,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_2891,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) = sdtasdt0(xr,xm)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolve,[status(thm)],[c_127,c_85]) ).
cnf(c_770,negated_conjecture,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolve,[status(thm)],[c_83,c_2891]) ).
cnf(c_2892,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_129,c_91]) ).
cnf(c_2893,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_94,c_2892]) ).
cnf(c_2894,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_96,c_2893]) ).
cnf(c_801,plain,
aNaturalNumber0(xr),
inference(resolve,[status(thm)],[c_92,c_2894]) ).
cnf(c_829,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolve,[status(thm)],[c_130,c_85]) ).
cnf(c_2895,plain,
( sdtasdt0(A,xm) = sdtasdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_149,c_95]) ).
cnf(c_2896,plain,
sdtasdt0(xp,xm) = sdtasdt0(xm,xp),
inference(resolve,[status(thm)],[c_2895,c_94]) ).
cnf(c_1067,plain,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(copy,[status(thm)],[c_2896]) ).
cnf(c_2897,plain,
( aNaturalNumber0(sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_154,c_96]) ).
cnf(c_1502,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolve,[status(thm)],[c_2897,c_95]) ).
cnf(c_2898,plain,
( aNaturalNumber0(sdtasdt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_154,c_95]) ).
cnf(c_2899,plain,
aNaturalNumber0(sdtasdt0(xm,xp)),
inference(resolve,[status(thm)],[c_2898,c_94]) ).
cnf(c_1505,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(paramod,[status(thm)],[c_1067,c_2899]) ).
cnf(c_2900,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_1505,c_829]) ).
cnf(c_1507,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_1502,c_2900]) ).
cnf(c_2901,negated_conjecture,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_1505,c_770]) ).
cnf(c_1508,negated_conjecture,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_1502,c_2901]) ).
cnf(c_2902,plain,
( aNaturalNumber0(sdtasdt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_154,c_95]) ).
cnf(c_2696,plain,
aNaturalNumber0(sdtasdt0(xm,xr)),
inference(resolve,[status(thm)],[c_2902,c_801]) ).
cnf(c_2903,plain,
( sdtasdt0(A,xm) = sdtasdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_149,c_95]) ).
cnf(c_2746,plain,
sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
inference(resolve,[status(thm)],[c_2903,c_801]) ).
cnf(c_2904,negated_conjecture,
( ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(paramod,[status(thm)],[c_2746,c_1508]) ).
cnf(c_2889,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
inference(resolve,[status(thm)],[c_2696,c_2904]) ).
cnf(c_2905,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xr))
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) ),
inference(paramod,[status(thm)],[c_2746,c_1507]) ).
cnf(c_2906,plain,
~ aNaturalNumber0(sdtasdt0(xm,xr)),
inference(resolve,[status(thm)],[c_2889,c_2905]) ).
cnf(c_2890,plain,
$false,
inference(resolve,[status(thm)],[c_2696,c_2906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 02:58:06 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 248381 was started by sandbox on n019,
% 0.18/0.45 % Sat Sep 26 02:58:06 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 134.09/17.51
% 134.09/17.51 % SZS status Theorem for theBenchmark
% 134.09/17.51
% 134.09/17.51 % Proof 1 at 0.81 (+ 0.16) seconds.
% 134.09/17.51 % Length of proof is 32.
% 134.09/17.51 % Level of proof is 6.
% 134.09/17.51 % Maximum clause weight is 29.000.
% 134.09/17.51 % Given clauses 167.
% 134.09/17.51
% 134.09/17.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------