%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM504+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 : n008.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 08:17:12 AM UTC 2026
% Result : Theorem 24.65s 3.68s
% Output : CNFRefutation 24.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 119 ( 36 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 132 ( 59 ~; 49 |; 15 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mLEAsym,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLEAsym) ).
fof(mDefQuot,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefQuot) ).
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__2414,axiom,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('theBenchmark.p',m__2414) ).
cnf(c_51,plain,
( sz00 != A
| ~ isPrime0(A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefPrime]) ).
cnf(c_57,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_66,plain,
( sz00 != xp
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_57,c_51]) ).
cnf(c_67,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_96,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(clausify,[status(thm)],[m__2414]) ).
cnf(c_97,plain,
sdtasdt0(xp,xk) != sdtasdt0(xp,xm),
inference(clausify,[status(thm)],[m__2414]) ).
cnf(c_98,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(clausify,[status(thm)],[m__2414]) ).
fof(m__2306,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('theBenchmark.p',m__2306) ).
cnf(c_108,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(clausify,[status(thm)],[m__2306]) ).
cnf(c_117,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_118,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_119,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_120,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_130,plain,
( sdtasdt0(A,C) = B
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_149,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLEAsym]) ).
cnf(c_180,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_220,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) != sdtasdt0(xp,xm),
inference(paramod,[status(thm)],[c_108,c_97]) ).
cnf(c_221,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))),
inference(paramod,[status(thm)],[c_108,c_96]) ).
cnf(c_225,plain,
xp != sz00,
inference(resolve,[status(thm)],[c_118,c_67]) ).
cnf(c_17803,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(copy,[status(thm)],[c_108]) ).
cnf(c_17804,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xn,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_130,c_17803]) ).
cnf(c_17805,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_108,c_17804]) ).
cnf(c_17806,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_17805]) ).
cnf(c_17807,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_118,c_17806]) ).
cnf(c_17808,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_225,c_17807]) ).
cnf(c_709,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolve,[status(thm)],[c_117,c_17808]) ).
cnf(c_1244,plain,
( aNaturalNumber0(sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_180,c_120]) ).
cnf(c_1246,plain,
( aNaturalNumber0(sdtasdt0(xp,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_180,c_118]) ).
cnf(c_17809,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ sdtlseqdt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(resolve,[status(thm)],[c_221,c_149]) ).
cnf(c_17810,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(copy,[status(thm)],[c_17809]) ).
cnf(c_1693,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))) ),
inference(resolve,[status(thm)],[c_220,c_17810]) ).
cnf(c_16616,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolve,[status(thm)],[c_1244,c_119]) ).
cnf(c_16645,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm),
inference(resolve,[status(thm)],[c_16616,c_709]) ).
cnf(c_17811,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(paramod,[status(thm)],[c_16645,c_1693]) ).
cnf(c_17812,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(paramod,[status(thm)],[c_16645,c_17811]) ).
cnf(c_17813,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolve,[status(thm)],[c_16616,c_17812]) ).
cnf(c_16705,plain,
~ aNaturalNumber0(sdtasdt0(xp,xm)),
inference(resolve,[status(thm)],[c_98,c_17813]) ).
cnf(c_17814,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(resolve,[status(thm)],[c_1246,c_119]) ).
cnf(c_17802,plain,
$false,
inference(resolve,[status(thm)],[c_16705,c_17814]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM504+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 03:01:39 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 2646972 was started by sandbox2 on n008,
% 0.11/0.39 % Sat Sep 26 03:01:39 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 24.65/3.68
% 24.65/3.68 % given #500 (F,wt=22): 5511 sdtpldt0(f1(xr,xr),xp) != sz00. [resolve(1980,a,1052,a)].
% 24.65/3.68
% 24.65/3.68 % given #1000 (T,wt=16): 772 -aNaturalNumber0(A) | xm = A | -sdtlseqdt0(xm,A) | iLess0(xm,A). [resolve(135,a,119,a),flip(b)].
% 24.65/3.68
% 24.65/3.68 % SZS status Theorem for theBenchmark
% 24.65/3.68
% 24.65/3.68 % Proof 1 at 2.35 (+ 0.66) seconds.
% 24.65/3.68 % Length of proof is 33.
% 24.65/3.68 % Level of proof is 8.
% 24.65/3.68 % Maximum clause weight is 43.000.
% 24.65/3.68 % Given clauses 1065.
% 24.65/3.68
% 24.65/3.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------