%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM524+3 : 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 : n014.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 5.40s 1.17s
% Output : CNFRefutation 5.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 24 unt; 0 def)
% Number of atoms : 144 ( 59 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 153 ( 62 ~; 63 |; 20 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 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 : 33 ( 0 sgn 11 !; 2 ?)
% 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)
& ? [W0] :
( xn = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [W0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__3046) ).
fof(m__3059,axiom,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('theBenchmark.p',m__3059) ).
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_98,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xq,xq)) != sdtasdt0(xm,xm),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_99,plain,
sdtsldt0(xn,xp) = xq,
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_100,plain,
sdtasdt0(xp,xq) = xn,
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_101,plain,
aNaturalNumber0(xq),
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_102,plain,
doDivides0(xp,xn),
inference(clausify,[status(thm)],[m__3046]) ).
cnf(c_105,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_111,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausify,[status(thm)],[m__3014]) ).
cnf(c_124,plain,
xp != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_127,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_128,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_129,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_132,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_138,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_183,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_189,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_3031,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_132,c_127]) ).
cnf(c_3032,plain,
( sdtsldt0(sdtasdt0(A,xn),xp) = sdtasdt0(A,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(A)
| ~ doDivides0(xp,xn)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_3031,c_129]) ).
cnf(c_3033,plain,
( sdtsldt0(sdtasdt0(A,xn),xp) = sdtasdt0(A,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(A)
| sz00 = xp ),
inference(resolve,[status(thm)],[c_3032,c_102]) ).
cnf(c_3034,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,sdtsldt0(xn,xp))
| sz00 = xp ),
inference(resolve,[status(thm)],[c_3033,c_129]) ).
cnf(c_3035,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,xq)
| sz00 = xp ),
inference(paramod,[status(thm)],[c_99,c_3034]) ).
cnf(c_3036,plain,
( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,xq)
| xp = sz00 ),
inference(copy,[status(thm)],[c_3035]) ).
cnf(c_1182,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,xq),
inference(resolve,[status(thm)],[c_124,c_3036]) ).
cnf(c_3037,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_138,c_111]) ).
cnf(c_3038,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,xq) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_1182,c_3037]) ).
cnf(c_3039,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,xq) = sdtasdt0(xm,xm)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_3038]) ).
cnf(c_3040,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_3039]) ).
cnf(c_3041,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_127,c_3040]) ).
cnf(c_3042,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq)
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_124,c_3041]) ).
cnf(c_1357,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_105,c_3042]) ).
cnf(c_3043,plain,
( sdtasdt0(sdtasdt0(xp,A),B) = sdtasdt0(xp,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_183,c_127]) ).
cnf(c_3044,plain,
( sdtasdt0(sdtasdt0(xp,xq),A) = sdtasdt0(xp,sdtasdt0(xq,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_3043,c_101]) ).
cnf(c_3045,plain,
sdtasdt0(sdtasdt0(xp,xq),xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(resolve,[status(thm)],[c_3044,c_101]) ).
cnf(c_3046,plain,
sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(paramod,[status(thm)],[c_100,c_3045]) ).
cnf(c_2303,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xn,xq),
inference(copy,[status(thm)],[c_3046]) ).
cnf(c_3047,negated_conjecture,
sdtasdt0(xn,xq) != sdtasdt0(xm,xm),
inference(paramod,[status(thm)],[c_2303,c_98]) ).
cnf(c_2369,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xn,xq),
inference(copy,[status(thm)],[c_3047]) ).
cnf(c_2370,negated_conjecture,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_2369,c_1357]) ).
cnf(c_3048,plain,
( aNaturalNumber0(sdtasdt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_189,c_129]) ).
cnf(c_3016,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(resolve,[status(thm)],[c_3048,c_129]) ).
cnf(c_3049,plain,
( aNaturalNumber0(sdtasdt0(xm,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_189,c_128]) ).
cnf(c_3021,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolve,[status(thm)],[c_3049,c_128]) ).
cnf(c_3050,negated_conjecture,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolve,[status(thm)],[c_3016,c_2370]) ).
cnf(c_3030,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3021,c_3050]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM524+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:06:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2006650 was started by sandbox2 on n014,
% 0.10/0.38 % Sat Sep 26 03:06:18 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 5.40/1.17
% 5.40/1.17 % SZS status Theorem for theBenchmark
% 5.40/1.17
% 5.40/1.17 % Proof 1 at 0.61 (+ 0.14) seconds.
% 5.40/1.17 % Length of proof is 31.
% 5.40/1.17 % Level of proof is 5.
% 5.40/1.17 % Maximum clause weight is 42.000.
% 5.40/1.17 % Given clauses 94.
% 5.40/1.17
% 5.40/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------