%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM476+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 : n008.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 0.66s 0.50s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 24 unt; 0 def)
% Number of atoms : 168 ( 102 equ)
% Maximal formula atoms : 31 ( 4 avg)
% Number of connectives : 146 ( 20 ~; 28 |; 92 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 5 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',m_AddZero) ).
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(m__1324,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1324) ).
fof(m__1324_04,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1324_04) ).
fof(m__,conjecture,
( ( xl != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1) )
& W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( xl != sz00
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( xn = sdtasdt0(xl,W2)
& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)
& W2 = sdtmndt0(W1,W0)
& sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& sdtlseqdt0(W0,W1)
& ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)
& aNaturalNumber0(W1) )
& W0 = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) )
=> ( doDivides0(xl,xn)
| ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_35,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( sdtasdt0(xl,W0) != xn
| ~ aNaturalNumber0(W0) )
& ( ? [X0] :
( ? [W1] :
( ? [W2] :
( sdtasdt0(xl,W2) = xn
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& sdtmndt0(W1,X0) = W2
& sdtpldt0(X0,W2) = W1
& aNaturalNumber0(W2) )
& sdtlseqdt0(X0,W1)
& ? [X1] :
( sdtpldt0(X0,X1) = W1
& aNaturalNumber0(X1) )
& sdtsldt0(sdtpldt0(xm,xn),xl) = W1
& sdtasdt0(xl,W1) = sdtpldt0(xm,xn)
& aNaturalNumber0(W1) )
& sdtsldt0(xm,xl) = X0
& sdtasdt0(xl,X0) = xm
& aNaturalNumber0(X0) )
| xl = sz00 ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
( ~ doDivides0(xl,xn)
& ! [W0] :
( sdtasdt0(xl,W0) != xn
| ~ aNaturalNumber0(W0) )
& ( ( sdtasdt0(xl,sK0) = xn
& sdtpldt0(sdtasdt0(xl,sK3),sdtasdt0(xl,sK0)) = sdtpldt0(sdtasdt0(xl,sK3),xn)
& sdtmndt0(sK4,sK3) = sK0
& sdtpldt0(sK3,sK0) = sK4
& aNaturalNumber0(sK0)
& sdtlseqdt0(sK3,sK4)
& sdtpldt0(sK3,sK5) = sK4
& aNaturalNumber0(sK5)
& sdtsldt0(sdtpldt0(xm,xn),xl) = sK4
& sdtasdt0(xl,sK4) = sdtpldt0(xm,xn)
& aNaturalNumber0(sK4)
& sdtsldt0(xm,xl) = sK3
& sdtasdt0(xl,sK3) = xm
& aNaturalNumber0(sK3) )
| xl = sz00 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK0]),skolemize(X0,sK3),skolemize(W1,sK4),skolemize(X1,sK5),skolemize(W2,sK0)],[nnf_35]) ).
fof(sk_m___neg,plain,
( ~ doDivides0(xl,xn)
& ! [VAR_0] :
( sdtasdt0(xl,VAR_0) != xn
| ~ aNaturalNumber0(VAR_0) )
& ( sdtasdt0(xl,sK0) = xn
| xl = sz00 )
& ( sdtpldt0(sdtasdt0(xl,sK3),sdtasdt0(xl,sK0)) = sdtpldt0(sdtasdt0(xl,sK3),xn)
| xl = sz00 )
& ( sdtmndt0(sK4,sK3) = sK0
| xl = sz00 )
& ( sdtpldt0(sK3,sK0) = sK4
| xl = sz00 )
& ( aNaturalNumber0(sK0)
| xl = sz00 )
& ( sdtlseqdt0(sK3,sK4)
| xl = sz00 )
& ( sdtpldt0(sK3,sK5) = sK4
| xl = sz00 )
& ( aNaturalNumber0(sK5)
| xl = sz00 )
& ( sdtsldt0(sdtpldt0(xm,xn),xl) = sK4
| xl = sz00 )
& ( sdtasdt0(xl,sK4) = sdtpldt0(xm,xn)
| xl = sz00 )
& ( aNaturalNumber0(sK4)
| xl = sz00 )
& ( sdtsldt0(xm,xl) = sK3
| xl = sz00 )
& ( sdtasdt0(xl,sK3) = xm
| xl = sz00 )
& ( aNaturalNumber0(sK3)
| xl = sz00 ) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_36,negated_conjecture,
~ doDivides0(xl,xn),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_37,negated_conjecture,
( sdtasdt0(xl,A) != xn
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_38,negated_conjecture,
( sdtasdt0(xl,sK0) = xn
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_42,negated_conjecture,
( aNaturalNumber0(sK0)
| xl = sz00 ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
fof(nnf_34,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [W0] :
( sdtasdt0(xl,W0) = sdtpldt0(xm,xn)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [X0] :
( sdtasdt0(xl,X0) = xm
& aNaturalNumber0(X0) ) ),
inference(fof_nnf,[status(thm)],[m__1324_04]) ).
fof(sk_m__1324_04,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
& sdtasdt0(xl,sK1) = sdtpldt0(xm,xn)
& aNaturalNumber0(sK1)
& doDivides0(xl,xm)
& sdtasdt0(xl,sK2) = xm
& aNaturalNumber0(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1]),skolemize(X0,sK2),skolemize(W0,sK1)],[nnf_34]) ).
cnf(c_54,plain,
sdtasdt0(xl,sK1) = sdtpldt0(xm,xn),
inference(split_conjunct,[status(thm)],[sk_m__1324_04]) ).
cnf(c_55,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK1),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_56,plain,
aNaturalNumber0(sK1),
inference(split_conjunct,[status(thm)],[sk_m__1324_04]) ).
cnf(c_57,plain,
doDivides0(xl,xm),
inference(split_conjunct,[status(thm)],[sk_m__1324_04]) ).
cnf(c_58,plain,
sdtasdt0(xl,sK2) = xm,
inference(split_conjunct,[status(thm)],[sk_m__1324_04]) ).
cnf(c_59,plain,
aNaturalNumber0(sK2),
inference(split_conjunct,[status(thm)],[sk_m__1324_04]) ).
cnf(c_60,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_105,plain,
( sdtasdt0(sz00,A) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_111,plain,
( sdtpldt0(sz00,A) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_AddZero]) ).
cnf(c_904,negated_conjecture,
( xl = sz00
| sdtasdt0(xl,sK0) != xn ),
inference(resolve,[status(thm)],[c_37,c_42]) ).
cnf(c_905,negated_conjecture,
( xl = sz00
| xl = sz00 ),
inference(resolve,[status(thm)],[c_904,c_38]) ).
cnf(c_202,negated_conjecture,
xl = sz00,
inference(copy,[status(thm)],[c_905]) ).
cnf(c_204,plain,
sdtasdt0(sz00,sK2) = xm,
inference(paramod,[status(thm)],[c_202,c_58]) ).
cnf(c_205,plain,
doDivides0(sz00,xm),
inference(paramod,[status(thm)],[c_202,c_57]) ).
cnf(c_206,plain,
sdtpldt0(xm,xn) = sdtasdt0(sz00,sK1),
inference(paramod,[status(thm)],[c_202,c_55]) ).
cnf(c_208,negated_conjecture,
~ doDivides0(sz00,xn),
inference(paramod,[status(thm)],[c_202,c_36]) ).
cnf(c_906,plain,
sdtasdt0(sz00,sK2) = sz00,
inference(resolve,[status(thm)],[c_105,c_59]) ).
cnf(c_571,plain,
xm = sz00,
inference(paramod,[status(thm)],[c_204,c_906]) ).
cnf(c_572,plain,
sdtasdt0(sz00,sK1) = sz00,
inference(resolve,[status(thm)],[c_105,c_56]) ).
cnf(c_907,plain,
sdtpldt0(sz00,xn) = sdtasdt0(sz00,sK1),
inference(paramod,[status(thm)],[c_571,c_206]) ).
cnf(c_687,plain,
sdtpldt0(sz00,xn) = sz00,
inference(paramod,[status(thm)],[c_572,c_907]) ).
cnf(c_688,plain,
doDivides0(sz00,sz00),
inference(paramod,[status(thm)],[c_571,c_205]) ).
cnf(c_908,plain,
sdtpldt0(sz00,xn) = xn,
inference(resolve,[status(thm)],[c_111,c_60]) ).
cnf(c_909,plain,
sz00 = xn,
inference(paramod,[status(thm)],[c_687,c_908]) ).
cnf(c_885,plain,
xn = sz00,
inference(copy,[status(thm)],[c_909]) ).
cnf(c_910,negated_conjecture,
~ doDivides0(sz00,sz00),
inference(paramod,[status(thm)],[c_885,c_208]) ).
cnf(c_903,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_688,c_910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 02:55:39 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2636466 was started by sandbox2 on n008,
% 0.10/0.36 % Sat Sep 26 02:55:39 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.66/0.50
% 0.66/0.50 % SZS status Theorem for theBenchmark
% 0.66/0.50
% 0.66/0.50 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.66/0.50 % Length of proof is 29.
% 0.66/0.50 % Level of proof is 7.
% 0.66/0.50 % Maximum clause weight is 18.000.
% 0.66/0.50 % Given clauses 52.
% 0.66/0.50
% 0.66/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------