%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM478+2 : 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 : n013.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 08:17:08 AM UTC 2026
% Result : Theorem 1.20s 0.59s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 25 unt; 0 def)
% Number of atoms : 106 ( 58 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 34 |; 18 &)
% ( 1 <=>; 6 =>; 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 : 27 ( 0 sgn 8 !; 2 ?)
% 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__1524,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1524) ).
fof(m__1524_04,axiom,
( doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& xl != sz00 ),
file('theBenchmark.p',m__1524_04) ).
fof(m__,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_39,negated_conjecture,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_40,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xn,xm),
inference(copy,[status(thm)],[c_39]) ).
fof(m__1553,axiom,
aNaturalNumber0(xn),
file('theBenchmark.p',m__1553) ).
cnf(c_43,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1553]) ).
fof(nnf_36,plain,
( doDivides0(xl,xm)
& ? [W0] :
( sdtasdt0(xl,W0) = xm
& aNaturalNumber0(W0) )
& xl != sz00 ),
inference(fof_nnf,[status(thm)],[m__1524_04]) ).
fof(sk_m__1524_04,plain,
( doDivides0(xl,xm)
& sdtasdt0(xl,sK0) = xm
& aNaturalNumber0(sK0)
& xl != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_36]) ).
cnf(c_44,plain,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[sk_m__1524_04]) ).
cnf(c_45,plain,
sdtasdt0(xl,sK0) = xm,
inference(split_conjunct,[status(thm)],[sk_m__1524_04]) ).
cnf(c_46,plain,
xm = sdtasdt0(xl,sK0),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_47,plain,
aNaturalNumber0(sK0),
inference(split_conjunct,[status(thm)],[sk_m__1524_04]) ).
cnf(c_48,plain,
xl != sz00,
inference(split_conjunct,[status(thm)],[sk_m__1524_04]) ).
cnf(c_49,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1524]) ).
cnf(c_50,plain,
aNaturalNumber0(sdtasdt0(xl,sK0)),
inference(paramod,[status(thm)],[c_46,c_49]) ).
cnf(c_51,plain,
aNaturalNumber0(xl),
inference(clausify,[status(thm)],[m__1524]) ).
cnf(c_57,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_101,plain,
( sdtasdt0(sdtasdt0(A,B),C) = sdtasdt0(A,sdtasdt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulAsso]) ).
cnf(c_102,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_112,plain,
doDivides0(xl,sdtasdt0(xl,sK0)),
inference(paramod,[status(thm)],[c_46,c_44]) ).
cnf(c_1624,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtasdt0(xn,xm),
inference(paramod,[status(thm)],[c_46,c_40]) ).
cnf(c_115,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtasdt0(xn,sdtasdt0(xl,sK0)),
inference(paramod,[status(thm)],[c_46,c_1624]) ).
cnf(c_1625,plain,
( sdtasdt0(sdtasdt0(xl,A),B) = sdtasdt0(xl,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_101,c_51]) ).
cnf(c_1626,plain,
( sdtasdt0(sdtasdt0(xl,sK0),A) = sdtasdt0(xl,sdtasdt0(sK0,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1625,c_47]) ).
cnf(c_613,plain,
sdtasdt0(sdtasdt0(xl,sK0),xn) = sdtasdt0(xl,sdtasdt0(sK0,xn)),
inference(resolve,[status(thm)],[c_1626,c_43]) ).
cnf(c_1627,plain,
( sdtasdt0(A,sdtasdt0(xl,sK0)) = sdtasdt0(sdtasdt0(xl,sK0),A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_102,c_50]) ).
cnf(c_1628,plain,
sdtasdt0(xn,sdtasdt0(xl,sK0)) = sdtasdt0(sdtasdt0(xl,sK0),xn),
inference(resolve,[status(thm)],[c_1627,c_43]) ).
cnf(c_735,plain,
sdtasdt0(xn,sdtasdt0(xl,sK0)) = sdtasdt0(xl,sdtasdt0(sK0,xn)),
inference(paramod,[status(thm)],[c_613,c_1628]) ).
cnf(c_1629,plain,
( sdtasdt0(A,sK0) = sdtasdt0(sK0,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_102,c_47]) ).
cnf(c_1630,plain,
sdtasdt0(xn,sK0) = sdtasdt0(sK0,xn),
inference(resolve,[status(thm)],[c_1629,c_43]) ).
cnf(c_736,plain,
sdtasdt0(sK0,xn) = sdtasdt0(xn,sK0),
inference(copy,[status(thm)],[c_1630]) ).
cnf(c_1631,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtasdt0(xl,sdtasdt0(sK0,xn)),
inference(paramod,[status(thm)],[c_735,c_115]) ).
cnf(c_841,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(sdtasdt0(xl,sK0),xl))) != sdtasdt0(xl,sdtasdt0(xn,sK0)),
inference(paramod,[status(thm)],[c_736,c_1631]) ).
cnf(c_1632,plain,
( sdtasdt0(xl,B) != A
| ~ aNaturalNumber0(B)
| sdtsldt0(A,xl) = B
| ~ doDivides0(xl,A)
| sz00 = xl
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_57,c_51]) ).
cnf(c_1633,plain,
( sdtasdt0(xl,A) != sdtasdt0(xl,sK0)
| ~ aNaturalNumber0(A)
| sdtsldt0(sdtasdt0(xl,sK0),xl) = A
| ~ doDivides0(xl,sdtasdt0(xl,sK0))
| sz00 = xl ),
inference(resolve,[status(thm)],[c_1632,c_50]) ).
cnf(c_1634,plain,
( sdtasdt0(xl,A) != sdtasdt0(xl,sK0)
| ~ aNaturalNumber0(A)
| sdtsldt0(sdtasdt0(xl,sK0),xl) = A
| sz00 = xl ),
inference(resolve,[status(thm)],[c_1633,c_112]) ).
cnf(c_1635,plain,
( sdtasdt0(xl,sK0) != sdtasdt0(xl,sK0)
| sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0
| sz00 = xl ),
inference(resolve,[status(thm)],[c_1634,c_47]) ).
cnf(c_1636,plain,
( sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0
| sz00 = xl ),
inference(xxres,[status(thm)],[c_1635]) ).
cnf(c_1637,plain,
( sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0
| xl = sz00 ),
inference(copy,[status(thm)],[c_1636]) ).
cnf(c_1618,plain,
sdtsldt0(sdtasdt0(xl,sK0),xl) = sK0,
inference(resolve,[status(thm)],[c_48,c_1637]) ).
cnf(c_1638,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sK0)) != sdtasdt0(xl,sdtasdt0(xn,sK0)),
inference(paramod,[status(thm)],[c_1618,c_841]) ).
cnf(c_1623,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 02:54:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1792700 was started by sandbox2 on n013,
% 0.12/0.38 % Sat Sep 26 02:54:21 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 1.20/0.59
% 1.20/0.59 % SZS status Theorem for theBenchmark
% 1.20/0.59
% 1.20/0.59 % Proof 1 at 0.15 (+ 0.03) seconds.
% 1.20/0.59 % Length of proof is 28.
% 1.20/0.59 % Level of proof is 6.
% 1.20/0.59 % Maximum clause weight is 50.000.
% 1.20/0.59 % Given clauses 58.
% 1.20/0.59
% 1.20/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------