%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM487+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 : n016.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 5.38s 1.17s
% Output : CNFRefutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 24 unt; 0 def)
% Number of atoms : 136 ( 60 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 66 ~; 51 |; 16 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',m_AddZero) ).
fof(mAddCanc,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('theBenchmark.p',mAddCanc) ).
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(mDefPrime,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('theBenchmark.p',mDefPrime) ).
fof(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__1860,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('theBenchmark.p',m__1860) ).
fof(m__,conjecture,
( sdtlseqdt0(xr,xn)
& xr != xn ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_45,plain,
( sz00 != A
| ~ isPrime0(A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefPrime]) ).
cnf(c_51,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_52,plain,
( sz00 != xp
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_51,c_45]) ).
cnf(c_53,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_82,negated_conjecture,
( ~ sdtlseqdt0(xr,xn)
| xr = xn ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__1883,axiom,
xr = sdtmndt0(xn,xp),
file('theBenchmark.p',m__1883) ).
cnf(c_83,plain,
xr = sdtmndt0(xn,xp),
inference(clausify,[status(thm)],[m__1883]) ).
cnf(c_84,plain,
sdtmndt0(xn,xp) = xr,
inference(copy,[status(thm)],[c_83]) ).
fof(m__1870,axiom,
sdtlseqdt0(xp,xn),
file('theBenchmark.p',m__1870) ).
cnf(c_85,plain,
sdtlseqdt0(xp,xn),
inference(clausify,[status(thm)],[m__1870]) ).
cnf(c_87,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_89,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_121,plain,
( sdtpldt0(A,C) = B
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_122,plain,
( aNaturalNumber0(C)
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_123,plain,
( sdtpldt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefLE]) ).
cnf(c_134,plain,
( C = B
| sdtpldt0(A,C) != sdtpldt0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAddCanc]) ).
cnf(c_146,plain,
( sdtpldt0(A,sz00) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_AddZero]) ).
cnf(c_148,plain,
( sdtpldt0(B,A) = sdtpldt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAddComm]) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_153,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_180,plain,
xp != sz00,
inference(resolve,[status(thm)],[c_87,c_53]) ).
cnf(c_1900,plain,
( sdtpldt0(xp,B) = A
| sdtmndt0(A,xp) != B
| ~ sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_121,c_87]) ).
cnf(c_1901,plain,
( sdtpldt0(xp,A) = xn
| sdtmndt0(xn,xp) != A
| ~ sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_1900,c_89]) ).
cnf(c_1902,plain,
( sdtpldt0(xp,A) = xn
| sdtmndt0(xn,xp) != A ),
inference(resolve,[status(thm)],[c_1901,c_85]) ).
cnf(c_368,plain,
sdtpldt0(xp,xr) = xn,
inference(resolve,[status(thm)],[c_1902,c_84]) ).
cnf(c_1903,plain,
( aNaturalNumber0(B)
| sdtmndt0(A,xp) != B
| ~ sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_122,c_87]) ).
cnf(c_1904,plain,
( aNaturalNumber0(A)
| sdtmndt0(xn,xp) != A
| ~ sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_1903,c_89]) ).
cnf(c_1905,plain,
( aNaturalNumber0(A)
| sdtmndt0(xn,xp) != A ),
inference(resolve,[status(thm)],[c_1904,c_85]) ).
cnf(c_370,plain,
aNaturalNumber0(xr),
inference(resolve,[status(thm)],[c_1905,c_84]) ).
cnf(c_1411,plain,
sdtpldt0(xr,sz00) = xr,
inference(resolve,[status(thm)],[c_370,c_146]) ).
cnf(c_1906,plain,
( sdtpldt0(A,xp) = sdtpldt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_148,c_87]) ).
cnf(c_1907,plain,
sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
inference(resolve,[status(thm)],[c_1906,c_370]) ).
cnf(c_1572,plain,
sdtpldt0(xr,xp) = xn,
inference(paramod,[status(thm)],[c_368,c_1907]) ).
cnf(c_1908,plain,
( B = A
| sdtpldt0(xr,B) != sdtpldt0(xr,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_134,c_370]) ).
cnf(c_1909,plain,
( A = sz00
| sdtpldt0(xr,A) != sdtpldt0(xr,sz00)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1908,c_153]) ).
cnf(c_1910,plain,
( xp = sz00
| sdtpldt0(xr,xp) != sdtpldt0(xr,sz00) ),
inference(resolve,[status(thm)],[c_1909,c_87]) ).
cnf(c_1911,plain,
sdtpldt0(xr,xp) != sdtpldt0(xr,sz00),
inference(resolve,[status(thm)],[c_1910,c_180]) ).
cnf(c_1912,plain,
xn != sdtpldt0(xr,sz00),
inference(paramod,[status(thm)],[c_1572,c_1911]) ).
cnf(c_1913,plain,
xn != xr,
inference(paramod,[status(thm)],[c_1411,c_1912]) ).
cnf(c_1731,plain,
xr != xn,
inference(copy,[status(thm)],[c_1913]) ).
cnf(c_1761,negated_conjecture,
~ sdtlseqdt0(xr,xn),
inference(resolve,[status(thm)],[c_1731,c_82]) ).
cnf(c_1914,plain,
( sdtpldt0(xr,B) != A
| ~ aNaturalNumber0(B)
| sdtlseqdt0(xr,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_123,c_370]) ).
cnf(c_1915,plain,
( sdtpldt0(xr,A) != xn
| ~ aNaturalNumber0(A)
| sdtlseqdt0(xr,xn) ),
inference(resolve,[status(thm)],[c_1914,c_89]) ).
cnf(c_1916,negated_conjecture,
( sdtpldt0(xr,A) != xn
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1915,c_1761]) ).
cnf(c_1917,negated_conjecture,
sdtpldt0(xr,xp) != xn,
inference(resolve,[status(thm)],[c_1916,c_87]) ).
cnf(c_1918,negated_conjecture,
xn != xn,
inference(paramod,[status(thm)],[c_1572,c_1917]) ).
cnf(c_1899,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1918]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM487+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:02:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 4056570 was started by sandbox on n016,
% 0.09/0.37 % Sat Sep 26 03:02:01 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 5.38/1.17
% 5.38/1.17 % SZS status Theorem for theBenchmark
% 5.38/1.17
% 5.38/1.17 % Proof 1 at 0.54 (+ 0.07) seconds.
% 5.38/1.17 % Length of proof is 34.
% 5.38/1.17 % Level of proof is 7.
% 5.38/1.17 % Maximum clause weight is 27.000.
% 5.38/1.17 % Given clauses 171.
% 5.38/1.17
% 5.38/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------