%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM477+2 : 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 : n004.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 08:17:07 AM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 52 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 14 ~; 10 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 3 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(mMonMul2,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( W0 != sz00
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('theBenchmark.p',mMonMul2) ).
fof(m__1494,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('theBenchmark.p',m__1494) ).
fof(m__1494_04,axiom,
( xn != sz00
& doDivides0(xm,xn)
& ? [W0] :
( xn = sdtasdt0(xm,W0)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1494_04) ).
fof(m__,conjecture,
( sdtlseqdt0(xm,xn)
| ? [W0] :
( sdtpldt0(xm,W0) = xn
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
| ? [W0] :
( sdtpldt0(xm,W0) = xn
& aNaturalNumber0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_37,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_35,plain,
( xn != sz00
& doDivides0(xm,xn)
& ? [W0] :
( sdtasdt0(xm,W0) = xn
& aNaturalNumber0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__1494_04]) ).
fof(sk_m__1494_04,plain,
( xn != sz00
& doDivides0(xm,xn)
& sdtasdt0(xm,sK0) = xn
& aNaturalNumber0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_35]) ).
cnf(c_39,plain,
xn != sz00,
inference(split_conjunct,[status(thm)],[sk_m__1494_04]) ).
cnf(c_41,plain,
sdtasdt0(xm,sK0) = xn,
inference(split_conjunct,[status(thm)],[sk_m__1494_04]) ).
cnf(c_42,plain,
xn = sdtasdt0(xm,sK0),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,plain,
aNaturalNumber0(sK0),
inference(split_conjunct,[status(thm)],[sk_m__1494_04]) ).
cnf(c_46,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1494]) ).
cnf(c_56,plain,
( sdtlseqdt0(B,sdtasdt0(B,A))
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMonMul2]) ).
cnf(c_91,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_106,plain,
sdtasdt0(xm,sK0) != sz00,
inference(paramod,[status(thm)],[c_42,c_39]) ).
cnf(c_108,negated_conjecture,
~ sdtlseqdt0(xm,sdtasdt0(xm,sK0)),
inference(paramod,[status(thm)],[c_42,c_37]) ).
cnf(c_295,plain,
( sdtlseqdt0(A,sdtasdt0(A,sK0))
| sz00 = sK0
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_56,c_43]) ).
cnf(c_296,plain,
( sdtlseqdt0(xm,sdtasdt0(xm,sK0))
| sz00 = sK0 ),
inference(resolve,[status(thm)],[c_295,c_46]) ).
cnf(c_297,plain,
( sdtlseqdt0(xm,sdtasdt0(xm,sK0))
| sK0 = sz00 ),
inference(copy,[status(thm)],[c_296]) ).
cnf(c_219,negated_conjecture,
sK0 = sz00,
inference(resolve,[status(thm)],[c_108,c_297]) ).
cnf(c_242,plain,
sdtasdt0(xm,sz00) != sz00,
inference(paramod,[status(thm)],[c_219,c_106]) ).
cnf(c_298,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolve,[status(thm)],[c_91,c_46]) ).
cnf(c_294,plain,
$false,
inference(resolve,[status(thm)],[c_242,c_298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM477+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:54:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 666923 was started by sandbox on n004,
% 0.09/0.37 % Sat Sep 26 02:54:36 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.41
% 0.09/0.41 % SZS status Theorem for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.41 % Length of proof is 18.
% 0.09/0.41 % Level of proof is 6.
% 0.09/0.41 % Maximum clause weight is 22.000.
% 0.09/0.41 % Given clauses 41.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------