%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM512+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 : n018.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 08:17:14 AM UTC 2026
% Result : Theorem 42.79s 6.64s
% Output : CNFRefutation 42.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 32 unt; 0 def)
% Number of atoms : 201 ( 108 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 196 ( 80 ~; 85 |; 19 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 15 !; 0 ?)
% 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(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
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(mDivAsso,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( aNaturalNumber0(W2)
=> sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ),
file('theBenchmark.p',mDivAsso) ).
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__2342,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('theBenchmark.p',m__2342) ).
fof(m__,conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_52,plain,
( sz00 != A
| ~ isPrime0(A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefPrime]) ).
cnf(c_58,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_59,plain,
isPrime0(xr),
inference(clausify,[status(thm)],[m__2342]) ).
cnf(c_60,plain,
( sz00 != xr
| ~ aNaturalNumber0(xr) ),
inference(resolve,[status(thm)],[c_59,c_52]) ).
cnf(c_61,plain,
( xr != sz00
| ~ aNaturalNumber0(xr) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_67,plain,
( sz00 != xp
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_58,c_52]) ).
cnf(c_68,plain,
( xp != sz00
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_97,negated_conjecture,
( sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__2487,axiom,
doDivides0(xr,xn),
file('theBenchmark.p',m__2487) ).
cnf(c_100,plain,
doDivides0(xr,xn),
inference(clausify,[status(thm)],[m__2487]) ).
cnf(c_106,plain,
aNaturalNumber0(xr),
inference(clausify,[status(thm)],[m__2342]) ).
fof(m__2306,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('theBenchmark.p',m__2306) ).
cnf(c_109,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(clausify,[status(thm)],[m__2306]) ).
cnf(c_118,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(clausify,[status(thm)],[m__1860]) ).
cnf(c_119,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_120,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_121,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_124,plain,
( sdtsldt0(sdtasdt0(C,B),A) = sdtasdt0(C,sdtsldt0(B,A))
| ~ aNaturalNumber0(C)
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDivAsso]) ).
cnf(c_131,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_132,plain,
( aNaturalNumber0(C)
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_175,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_176,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_181,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_215,plain,
xr != sz00,
inference(resolve,[status(thm)],[c_106,c_61]) ).
cnf(c_222,negated_conjecture,
( sdtasdt0(sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ),
inference(paramod,[status(thm)],[c_109,c_97]) ).
cnf(c_226,plain,
xp != sz00,
inference(resolve,[status(thm)],[c_119,c_68]) ).
cnf(c_14518,plain,
( sdtsldt0(sdtasdt0(B,A),xr) = sdtasdt0(B,sdtsldt0(A,xr))
| ~ aNaturalNumber0(B)
| ~ doDivides0(xr,A)
| sz00 = xr
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_124,c_106]) ).
cnf(c_14519,plain,
( sdtsldt0(sdtasdt0(A,xn),xr) = sdtasdt0(A,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(A)
| ~ doDivides0(xr,xn)
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14518,c_121]) ).
cnf(c_14520,plain,
( sdtsldt0(sdtasdt0(A,xn),xr) = sdtasdt0(A,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(A)
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14519,c_100]) ).
cnf(c_14521,plain,
( sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,sdtsldt0(xn,xr))
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14520,c_120]) ).
cnf(c_14522,plain,
( sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,sdtsldt0(xn,xr))
| xr = sz00 ),
inference(copy,[status(thm)],[c_14521]) ).
cnf(c_342,plain,
sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(resolve,[status(thm)],[c_215,c_14522]) ).
cnf(c_14523,plain,
( sdtasdt0(xr,B) = A
| sdtsldt0(A,xr) != B
| ~ doDivides0(xr,A)
| sz00 = xr
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_131,c_106]) ).
cnf(c_14524,plain,
( sdtasdt0(xr,A) = xn
| sdtsldt0(xn,xr) != A
| ~ doDivides0(xr,xn)
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14523,c_121]) ).
cnf(c_14525,plain,
( sdtasdt0(xr,A) = xn
| sdtsldt0(xn,xr) != A
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14524,c_100]) ).
cnf(c_14526,plain,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| sz00 = xr ),
inference(xxres,[status(thm)],[c_14525]) ).
cnf(c_14527,plain,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| xr = sz00 ),
inference(copy,[status(thm)],[c_14526]) ).
cnf(c_375,plain,
sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
inference(resolve,[status(thm)],[c_215,c_14527]) ).
cnf(c_14528,plain,
( aNaturalNumber0(B)
| sdtsldt0(A,xr) != B
| ~ doDivides0(xr,A)
| sz00 = xr
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_132,c_106]) ).
cnf(c_14529,plain,
( aNaturalNumber0(A)
| sdtsldt0(xn,xr) != A
| ~ doDivides0(xr,xn)
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14528,c_121]) ).
cnf(c_14530,plain,
( aNaturalNumber0(A)
| sdtsldt0(xn,xr) != A
| sz00 = xr ),
inference(resolve,[status(thm)],[c_14529,c_100]) ).
cnf(c_14531,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| sz00 = xr ),
inference(xxres,[status(thm)],[c_14530]) ).
cnf(c_14532,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| xr = sz00 ),
inference(copy,[status(thm)],[c_14531]) ).
cnf(c_380,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(resolve,[status(thm)],[c_215,c_14532]) ).
cnf(c_14533,plain,
( sdtasdt0(A,xn) = sdtasdt0(xn,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_176,c_121]) ).
cnf(c_932,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(resolve,[status(thm)],[c_14533,c_120]) ).
cnf(c_961,plain,
sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(paramod,[status(thm)],[c_932,c_342]) ).
cnf(c_14534,plain,
( aNaturalNumber0(sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_181,c_121]) ).
cnf(c_1351,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolve,[status(thm)],[c_14534,c_120]) ).
cnf(c_14535,plain,
( sdtasdt0(A,xm) = sdtasdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_176,c_120]) ).
cnf(c_7424,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(resolve,[status(thm)],[c_14535,c_380]) ).
cnf(c_14536,plain,
( sdtasdt0(A,xr) = sdtasdt0(xr,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_176,c_106]) ).
cnf(c_14537,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(resolve,[status(thm)],[c_14536,c_380]) ).
cnf(c_7426,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = xn,
inference(paramod,[status(thm)],[c_375,c_14537]) ).
cnf(c_14538,plain,
( sdtasdt0(sdtasdt0(xm,A),B) = sdtasdt0(xm,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_175,c_120]) ).
cnf(c_14539,plain,
( sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),A) = sdtasdt0(xm,sdtasdt0(sdtsldt0(xn,xr),A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_14538,c_380]) ).
cnf(c_14540,plain,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) = sdtasdt0(xm,sdtasdt0(sdtsldt0(xn,xr),xr)),
inference(resolve,[status(thm)],[c_14539,c_106]) ).
cnf(c_14541,plain,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) = sdtasdt0(xm,xn),
inference(paramod,[status(thm)],[c_7426,c_14540]) ).
cnf(c_7535,plain,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) = sdtasdt0(xn,xm),
inference(paramod,[status(thm)],[c_932,c_14541]) ).
cnf(c_14542,negated_conjecture,
( sdtasdt0(sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr),xr) != sdtasdt0(xn,xm)
| sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xn,xm) ),
inference(paramod,[status(thm)],[c_7424,c_222]) ).
cnf(c_14543,negated_conjecture,
( sdtasdt0(sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr),xr) != sdtasdt0(xn,xm)
| sdtasdt0(xn,xm) != sdtasdt0(xn,xm) ),
inference(paramod,[status(thm)],[c_7535,c_14542]) ).
cnf(c_8103,negated_conjecture,
sdtasdt0(sdtsldt0(sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)),xr),xr) != sdtasdt0(xn,xm),
inference(copy,[status(thm)],[c_14543]) ).
cnf(c_14544,plain,
( sdtasdt0(xp,B) = A
| sdtsldt0(A,xp) != B
| ~ doDivides0(xp,A)
| sz00 = xp
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_131,c_119]) ).
cnf(c_14545,plain,
( sdtasdt0(xp,A) = sdtasdt0(xn,xm)
| sdtsldt0(sdtasdt0(xn,xm),xp) != A
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| sz00 = xp ),
inference(resolve,[status(thm)],[c_14544,c_1351]) ).
cnf(c_14546,plain,
( sdtasdt0(xp,A) = sdtasdt0(xn,xm)
| sdtsldt0(sdtasdt0(xn,xm),xp) != A
| sz00 = xp ),
inference(resolve,[status(thm)],[c_14545,c_118]) ).
cnf(c_14547,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(copy,[status(thm)],[c_109]) ).
cnf(c_14548,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xn,xm)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_14546,c_14547]) ).
cnf(c_14549,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| sz00 = xp ),
inference(paramod,[status(thm)],[c_109,c_14548]) ).
cnf(c_14550,plain,
( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm)
| xp = sz00 ),
inference(copy,[status(thm)],[c_14549]) ).
cnf(c_14438,plain,
sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm),
inference(resolve,[status(thm)],[c_226,c_14550]) ).
cnf(c_14551,negated_conjecture,
sdtasdt0(sdtsldt0(sdtasdt0(xn,xm),xr),xr) != sdtasdt0(xn,xm),
inference(paramod,[status(thm)],[c_14438,c_8103]) ).
cnf(c_14552,negated_conjecture,
sdtasdt0(sdtasdt0(xm,sdtsldt0(xn,xr)),xr) != sdtasdt0(xn,xm),
inference(paramod,[status(thm)],[c_961,c_14551]) ).
cnf(c_14553,negated_conjecture,
sdtasdt0(xn,xm) != sdtasdt0(xn,xm),
inference(paramod,[status(thm)],[c_7535,c_14552]) ).
cnf(c_14517,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_14553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM512+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 03:05:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3568178 was started by sandbox on n018,
% 0.10/0.36 % Sat Sep 26 03:05:21 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 42.79/6.64
% 42.79/6.64 % SZS status Theorem for theBenchmark
% 42.79/6.64
% 42.79/6.64 % Proof 1 at 5.36 (+ 0.84) seconds.
% 42.79/6.64 % Length of proof is 46.
% 42.79/6.64 % Level of proof is 9.
% 42.79/6.64 % Maximum clause weight is 61.000.
% 42.79/6.64 % Given clauses 350.
% 42.79/6.64
% 42.79/6.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------