%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM524+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 : n005.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 08:17:16 AM UTC 2026
% Result : Theorem 168.17s 21.78s
% Output : CNFRefutation 168.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 68 ( 28 unt; 0 def)
% Number of atoms : 193 ( 78 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 215 ( 90 ~; 103 |; 14 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 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 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
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(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(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_96,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xq,xq)) != 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]) ).
cnf(c_99,plain,
doDivides0(xp,sdtasdt0(xn,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_105,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_106,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_109,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_115,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtsldt0(B,A) = C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
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_166,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_4719,negated_conjecture,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),xq)) != sdtasdt0(xm,xm),
inference(paramod,[status(thm)],[c_97,c_96]) ).
cnf(c_214,negated_conjecture,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) != sdtasdt0(xm,xm),
inference(paramod,[status(thm)],[c_97,c_4719]) ).
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_4720,plain,
( sdtsldt0(sdtasdt0(B,A),xp) = sdtasdt0(B,sdtsldt0(A,xp))
| ~ aNaturalNumber0(B)
| ~ doDivides0(xp,A)
| sz00 = xp
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_109,c_104]) ).
cnf(c_4721,plain,
( sdtsldt0(sdtasdt0(A,xn),xp) = sdtasdt0(A,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(A)
| ~ doDivides0(xp,xn)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_4720,c_106]) ).
cnf(c_4722,plain,
( sdtsldt0(sdtasdt0(A,xn),xp) = sdtasdt0(A,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(A)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_4721,c_98]) ).
cnf(c_4723,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,sdtsldt0(xn,xp))
| sz00 = xp ),
inference(resolve,[status(thm)],[c_4722,c_106]) ).
cnf(c_4724,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,sdtsldt0(xn,xp))
| xp = sz00 ),
inference(copy,[status(thm)],[c_4723]) ).
cnf(c_611,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,sdtsldt0(xn,xp)),
inference(resolve,[status(thm)],[c_101,c_4724]) ).
cnf(c_4725,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_115,c_100]) ).
cnf(c_4726,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_611,c_4725]) ).
cnf(c_4727,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_4726]) ).
cnf(c_4728,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_104,c_4727]) ).
cnf(c_4729,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_101,c_4728]) ).
cnf(c_708,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_99,c_4729]) ).
cnf(c_4730,plain,
sdtsldt0(xn,xp) = xq,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_4731,plain,
( sdtasdt0(xp,xq) = xn
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_116,c_4730]) ).
cnf(c_4732,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_97,c_4731]) ).
cnf(c_4733,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_4732]) ).
cnf(c_4734,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_104,c_4733]) ).
cnf(c_4735,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| ~ doDivides0(xp,xn)
| xp = sz00 ),
inference(resolve,[status(thm)],[c_106,c_4734]) ).
cnf(c_4736,plain,
( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn
| ~ doDivides0(xp,xn) ),
inference(resolve,[status(thm)],[c_101,c_4735]) ).
cnf(c_730,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = xn,
inference(resolve,[status(thm)],[c_98,c_4736]) ).
cnf(c_4737,plain,
sdtsldt0(xn,xp) = xq,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_4738,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_117,c_4737]) ).
cnf(c_4739,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_97,c_4738]) ).
cnf(c_4740,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_4739]) ).
cnf(c_4741,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_104,c_4740]) ).
cnf(c_4742,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| ~ doDivides0(xp,xn)
| xp = sz00 ),
inference(resolve,[status(thm)],[c_106,c_4741]) ).
cnf(c_4743,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| ~ doDivides0(xp,xn) ),
inference(resolve,[status(thm)],[c_101,c_4742]) ).
cnf(c_742,plain,
aNaturalNumber0(sdtsldt0(xn,xp)),
inference(resolve,[status(thm)],[c_98,c_4743]) ).
cnf(c_4744,plain,
( aNaturalNumber0(sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_166,c_106]) ).
cnf(c_1344,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(resolve,[status(thm)],[c_4744,c_106]) ).
cnf(c_4745,plain,
( aNaturalNumber0(sdtasdt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_166,c_105]) ).
cnf(c_1347,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolve,[status(thm)],[c_4745,c_105]) ).
cnf(c_4746,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm) ),
inference(resolve,[status(thm)],[c_1344,c_708]) ).
cnf(c_1363,plain,
sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm),
inference(resolve,[status(thm)],[c_1347,c_4746]) ).
cnf(c_4747,plain,
( sdtasdt0(sdtasdt0(xp,A),A) = sdtasdt0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_288,c_104]) ).
cnf(c_4748,plain,
sdtasdt0(sdtasdt0(xp,sdtsldt0(xn,xp)),sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(resolve,[status(thm)],[c_4747,c_742]) ).
cnf(c_4749,plain,
sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(paramod,[status(thm)],[c_730,c_4748]) ).
cnf(c_4750,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))),
inference(paramod,[status(thm)],[c_1363,c_4749]) ).
cnf(c_4751,plain,
sdtasdt0(xp,sdtasdt0(sdtsldt0(xn,xp),sdtsldt0(xn,xp))) = sdtasdt0(xm,xm),
inference(copy,[status(thm)],[c_4750]) ).
cnf(c_4718,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_214,c_4751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM524+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % 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 03:06:02 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 1065865 was started by sandbox on n005,
% 0.11/0.39 % Sat Sep 26 03:06:02 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 168.17/21.78
% 168.17/21.78 % given #500 (T,wt=11): 4206 -sdtlseqdt0(xm,sz10) | sdtlseqdt0(xm,xn). [resolve(2557,a,105,a)].
% 168.17/21.78
% 168.17/21.78 % SZS status Theorem for theBenchmark
% 168.17/21.78
% 168.17/21.78 % Proof 1 at 5.01 (+ 0.21) seconds.
% 168.17/21.78 % Length of proof is 32.
% 168.17/21.78 % Level of proof is 5.
% 168.17/21.78 % Maximum clause weight is 42.000.
% 168.17/21.78 % Given clauses 512.
% 168.17/21.78
% 168.17/21.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------