%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM525+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 : n002.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 08:17:17 AM UTC 2026
% Result : Theorem 28.14s 4.08s
% Output : CNFRefutation 28.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 32 unt; 0 def)
% Number of atoms : 126 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 113 ( 47 ~; 49 |; 12 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__2987,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__2987) ).
fof(m__3046,axiom,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('theBenchmark.p',m__3046) ).
fof(m__,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_96,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__3059,axiom,
xq = sdtsldt0(xn,xp),
file('theBenchmark.p',m__3059) ).
cnf(c_97,plain,
xq = sdtsldt0(xn,xp),
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_98,plain,
doDivides0(xp,xn),
inference(clausify,[status(thm)],[m__3046]) ).
fof(m__3014,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('theBenchmark.p',m__3014) ).
cnf(c_100,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausify,[status(thm)],[m__3014]) ).
cnf(c_101,plain,
xp != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_104,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_106,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_116,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_117,plain,
( aNaturalNumber0(C)
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_160,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_161,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_5498,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),xq))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(paramod,[status(thm)],[c_97,c_96]) ).
cnf(c_5499,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(paramod,[status(thm)],[c_97,c_5498]) ).
cnf(c_214,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp)))) != sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_100,c_5499]) ).
cnf(c_288,plain,
( sdtasdt0(sdtasdt0(A,B),B) = sdtasdt0(A,sdtasdt0(B,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_160]) ).
cnf(c_5500,plain,
( sdtasdt0(xp,B) = A
| sdtsldt0(A,xp) != B
| ~ doDivides0(xp,A)
| sz00 = xp
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_116,c_104]) ).
cnf(c_5501,plain,
( sdtasdt0(xp,A) = xn
| sdtsldt0(xn,xp) != A
| ~ doDivides0(xp,xn)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_5500,c_106]) ).
cnf(c_5502,plain,
( sdtasdt0(xp,A) = xn
| sdtsldt0(xn,xp) != A
| sz00 = xp ),
inference(resolve,[status(thm)],[c_5501,c_98]) ).
cnf(c_5503,plain,
sdtsldt0(xn,xp) = xq,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_5504,plain,
( sdtasdt0(xp,xq) = xn
| sz00 = xp ),
inference(resolve,[status(thm)],[c_5502,c_5503]) ).
cnf(c_5505,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| sz00 = xp ),
inference(paramod,[status(thm)],[c_97,c_5504]) ).
cnf(c_5506,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| xp = sz00 ),
inference(copy,[status(thm)],[c_5505]) ).
cnf(c_366,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = xn,
inference(resolve,[status(thm)],[c_101,c_5506]) ).
cnf(c_5507,plain,
( aNaturalNumber0(B)
| sdtsldt0(A,xp) != B
| ~ doDivides0(xp,A)
| sz00 = xp
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_117,c_104]) ).
cnf(c_5508,plain,
( aNaturalNumber0(A)
| sdtsldt0(xn,xp) != A
| ~ doDivides0(xp,xn)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_5507,c_106]) ).
cnf(c_5509,plain,
( aNaturalNumber0(A)
| sdtsldt0(xn,xp) != A
| sz00 = xp ),
inference(resolve,[status(thm)],[c_5508,c_98]) ).
cnf(c_5510,plain,
sdtsldt0(xn,xp) = xq,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_5511,plain,
( aNaturalNumber0(xq)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_5509,c_5510]) ).
cnf(c_5512,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| sz00 = xp ),
inference(paramod,[status(thm)],[c_97,c_5511]) ).
cnf(c_5513,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| xp = sz00 ),
inference(copy,[status(thm)],[c_5512]) ).
cnf(c_370,plain,
aNaturalNumber0(sdtsldt0(xn,xp)),
inference(resolve,[status(thm)],[c_101,c_5513]) ).
cnf(c_5514,plain,
( sdtasdt0(A,xn) = sdtasdt0(xn,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_161,c_106]) ).
cnf(c_5515,plain,
sdtasdt0(xp,xn) = sdtasdt0(xn,xp),
inference(resolve,[status(thm)],[c_5514,c_104]) ).
cnf(c_681,plain,
sdtasdt0(xn,xp) = sdtasdt0(xp,xn),
inference(copy,[status(thm)],[c_5515]) ).
cnf(c_5516,plain,
( sdtasdt0(sdtasdt0(xp,A),A) = sdtasdt0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_288,c_104]) ).
cnf(c_5517,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(resolve,[status(thm)],[c_5516,c_370]) ).
cnf(c_5518,plain,
sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(paramod,[status(thm)],[c_366,c_5517]) ).
cnf(c_4891,plain,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) = sdtasdt0(xn,sdtsldt0(xn,xp)),
inference(copy,[status(thm)],[c_5518]) ).
cnf(c_5519,plain,
( sdtasdt0(sdtasdt0(xn,A),B) = sdtasdt0(xn,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_160,c_106]) ).
cnf(c_5520,plain,
( sdtasdt0(sdtasdt0(xn,xp),A) = sdtasdt0(xn,sdtasdt0(xp,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_5519,c_104]) ).
cnf(c_5521,plain,
sdtasdt0(sdtasdt0(xn,xp),sdtsldt0(xn,xp)) = sdtasdt0(xn,sdtasdt0(xp,sdtsldt0(xn,xp))),
inference(resolve,[status(thm)],[c_5520,c_370]) ).
cnf(c_5522,plain,
sdtasdt0(sdtasdt0(xp,xn),sdtsldt0(xn,xp)) = sdtasdt0(xn,sdtasdt0(xp,sdtsldt0(xn,xp))),
inference(paramod,[status(thm)],[c_681,c_5521]) ).
cnf(c_5172,plain,
sdtasdt0(sdtasdt0(xp,xn),sdtsldt0(xn,xp)) = sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_366,c_5522]) ).
cnf(c_5523,plain,
( sdtasdt0(sdtasdt0(xp,A),B) = sdtasdt0(xp,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_160,c_104]) ).
cnf(c_5524,plain,
( sdtasdt0(sdtasdt0(xp,xn),A) = sdtasdt0(xp,sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_5523,c_106]) ).
cnf(c_5525,plain,
sdtasdt0(sdtasdt0(xp,xn),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(xn,sdtsldt0(xn,xp))),
inference(resolve,[status(thm)],[c_5524,c_370]) ).
cnf(c_5526,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xn,sdtsldt0(xn,xp))),
inference(paramod,[status(thm)],[c_5172,c_5525]) ).
cnf(c_5179,plain,
sdtasdt0(xp,sdtasdt0(xn,sdtsldt0(xn,xp))) = sdtasdt0(xn,xn),
inference(copy,[status(thm)],[c_5526]) ).
cnf(c_5527,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xn,sdtsldt0(xn,xp))) != sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_4891,c_214]) ).
cnf(c_5528,negated_conjecture,
sdtasdt0(xn,xn) != sdtasdt0(xn,xn),
inference(paramod,[status(thm)],[c_5179,c_5527]) ).
cnf(c_5497,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_5528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM525+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 03:09:07 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 700885 was started by sandbox on n002,
% 0.16/0.43 % Sat Sep 26 03:09:07 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 28.14/4.08
% 28.14/4.08 % SZS status Theorem for theBenchmark
% 28.14/4.08
% 28.14/4.08 % Proof 1 at 3.39 (+ 0.20) seconds.
% 28.14/4.08 % Length of proof is 26.
% 28.14/4.08 % Level of proof is 5.
% 28.14/4.08 % Maximum clause weight is 50.000.
% 28.14/4.08 % Given clauses 406.
% 28.14/4.08
% 28.14/4.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------