%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM477+1 : 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 : n019.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 3.29s 0.88s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 26 unt; 0 def)
% Number of atoms : 145 ( 56 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 149 ( 62 ~; 60 |; 18 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 24 !; 2 ?)
% 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(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mZeroAdd,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W1 = sz00
& W0 = sz00 ) ) ),
file('theBenchmark.p',mZeroAdd) ).
fof(mMonMul2,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( W0 != sz00
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('theBenchmark.p',mMonMul2) ).
fof(mDefDiv,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(m__1494,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('theBenchmark.p',m__1494) ).
fof(m__1494_04,axiom,
( xn != sz00
& doDivides0(xm,xn) ),
file('theBenchmark.p',m__1494_04) ).
fof(m__,conjecture,
sdtlseqdt0(xm,xn),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_37,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_38,plain,
xn != sz00,
inference(clausify,[status(thm)],[m__1494_04]) ).
cnf(c_39,plain,
doDivides0(xm,xn),
inference(clausify,[status(thm)],[m__1494_04]) ).
cnf(c_40,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1494]) ).
cnf(c_41,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1494]) ).
fof(nnf_29,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [X0] :
( sdtasdt0(W0,X0) = W1
& aNaturalNumber0(X0) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mDefDiv]) ).
fof(sk_mDefDiv_sk,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtasdt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ( sdtasdt0(W0,sK0(W0,W1)) = W1
& aNaturalNumber0(sK0(W0,W1)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(W0,W1))],[nnf_29]) ).
fof(sk_mDefDiv,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sdtasdt0(VAR_0,VAR_2) != VAR_1
| ~ aNaturalNumber0(VAR_2)
| doDivides0(VAR_0,VAR_1)
| ~ aNaturalNumber0(VAR_1)
| ~ aNaturalNumber0(VAR_0) )
& ! [VAR_0,VAR_1] :
( sdtasdt0(VAR_0,sK0(VAR_0,VAR_1)) = VAR_1
| ~ doDivides0(VAR_0,VAR_1)
| ~ aNaturalNumber0(VAR_1)
| ~ aNaturalNumber0(VAR_0) )
& ! [VAR_0,VAR_1] :
( aNaturalNumber0(sK0(VAR_0,VAR_1))
| ~ doDivides0(VAR_0,VAR_1)
| ~ aNaturalNumber0(VAR_1)
| ~ aNaturalNumber0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefDiv_sk]) ).
cnf(c_49,plain,
( sdtasdt0(A,sK0(A,B)) = B
| ~ doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefDiv]) ).
cnf(c_50,plain,
( aNaturalNumber0(sK0(A,B))
| ~ doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(split_conjunct,[status(thm)],[sk_mDefDiv]) ).
cnf(c_51,plain,
( sdtlseqdt0(B,sdtasdt0(B,A))
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMonMul2]) ).
cnf(c_74,plain,
( B = sz00
| sdtpldt0(A,B) != sz00
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mZeroAdd]) ).
cnf(c_75,plain,
( sz00 = B
| sdtpldt0(A,B) != sz00
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_83,plain,
( sdtasdt0(A,sdtpldt0(B,C)) = sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mAMDistr]) ).
cnf(c_84,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,C)) = sdtasdt0(A,sdtpldt0(B,C))
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_86,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_92,plain,
( sdtpldt0(A,sz00) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_AddZero]) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_99,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_163,plain,
( sdtpldt0(sdtasdt0(A,B),sdtasdt0(A,B)) = sdtasdt0(A,sdtpldt0(B,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_84]) ).
cnf(c_1341,plain,
( sdtasdt0(xm,sK0(xm,xn)) = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_49,c_39]) ).
cnf(c_1342,plain,
( sdtasdt0(xm,sK0(xm,xn)) = xn
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_41,c_1341]) ).
cnf(c_202,plain,
sdtasdt0(xm,sK0(xm,xn)) = xn,
inference(resolve,[status(thm)],[c_40,c_1342]) ).
cnf(c_1343,plain,
( aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_50,c_39]) ).
cnf(c_1344,plain,
( aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_41,c_1343]) ).
cnf(c_203,plain,
aNaturalNumber0(sK0(xm,xn)),
inference(resolve,[status(thm)],[c_40,c_1344]) ).
cnf(c_1345,plain,
( sz00 = A
| sdtpldt0(xn,A) != sz00
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_75,c_40]) ).
cnf(c_1346,plain,
( sz00 = xn
| sdtpldt0(xn,xn) != sz00 ),
inference(resolve,[status(thm)],[c_1345,c_40]) ).
cnf(c_1347,plain,
sz00 != xn,
inference(copy,[status(thm)],[c_38]) ).
cnf(c_246,plain,
sdtpldt0(xn,xn) != sz00,
inference(resolve,[status(thm)],[c_1346,c_1347]) ).
cnf(c_324,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolve,[status(thm)],[c_86,c_41]) ).
cnf(c_567,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(resolve,[status(thm)],[c_99,c_92]) ).
cnf(c_1348,plain,
( sdtpldt0(sdtasdt0(xm,A),sdtasdt0(xm,A)) = sdtasdt0(xm,sdtpldt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_163,c_41]) ).
cnf(c_1349,plain,
sdtpldt0(sdtasdt0(xm,sK0(xm,xn)),sdtasdt0(xm,sK0(xm,xn))) = sdtasdt0(xm,sdtpldt0(sK0(xm,xn),sK0(xm,xn))),
inference(resolve,[status(thm)],[c_1348,c_203]) ).
cnf(c_1350,plain,
sdtpldt0(xn,sdtasdt0(xm,sK0(xm,xn))) = sdtasdt0(xm,sdtpldt0(sK0(xm,xn),sK0(xm,xn))),
inference(paramod,[status(thm)],[c_202,c_1349]) ).
cnf(c_1351,plain,
sdtpldt0(xn,xn) = sdtasdt0(xm,sdtpldt0(sK0(xm,xn),sK0(xm,xn))),
inference(paramod,[status(thm)],[c_202,c_1350]) ).
cnf(c_1175,plain,
sdtasdt0(xm,sdtpldt0(sK0(xm,xn),sK0(xm,xn))) = sdtpldt0(xn,xn),
inference(copy,[status(thm)],[c_1351]) ).
cnf(c_1352,plain,
( sdtlseqdt0(A,sdtasdt0(A,sK0(xm,xn)))
| sz00 = sK0(xm,xn)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_51,c_203]) ).
cnf(c_1353,plain,
( sdtlseqdt0(xm,sdtasdt0(xm,sK0(xm,xn)))
| sz00 = sK0(xm,xn) ),
inference(resolve,[status(thm)],[c_1352,c_41]) ).
cnf(c_1354,plain,
( sdtlseqdt0(xm,xn)
| sz00 = sK0(xm,xn) ),
inference(paramod,[status(thm)],[c_202,c_1353]) ).
cnf(c_1355,plain,
( sdtlseqdt0(xm,xn)
| sK0(xm,xn) = sz00 ),
inference(copy,[status(thm)],[c_1354]) ).
cnf(c_1339,negated_conjecture,
sK0(xm,xn) = sz00,
inference(resolve,[status(thm)],[c_37,c_1355]) ).
cnf(c_1356,plain,
sdtasdt0(xm,sdtpldt0(sz00,sK0(xm,xn))) = sdtpldt0(xn,xn),
inference(paramod,[status(thm)],[c_1339,c_1175]) ).
cnf(c_1357,plain,
sdtasdt0(xm,sdtpldt0(sz00,sz00)) = sdtpldt0(xn,xn),
inference(paramod,[status(thm)],[c_1339,c_1356]) ).
cnf(c_1358,plain,
sdtasdt0(xm,sz00) = sdtpldt0(xn,xn),
inference(paramod,[status(thm)],[c_567,c_1357]) ).
cnf(c_1359,plain,
sz00 = sdtpldt0(xn,xn),
inference(paramod,[status(thm)],[c_324,c_1358]) ).
cnf(c_1360,plain,
sdtpldt0(xn,xn) = sz00,
inference(copy,[status(thm)],[c_1359]) ).
cnf(c_1340,plain,
$false,
inference(resolve,[status(thm)],[c_246,c_1360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM477+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 02:55:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 245786 was started by sandbox2 on n019,
% 0.09/0.36 % Sat Sep 26 02:55:03 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 3.29/0.88
% 3.29/0.88 % SZS status Theorem for theBenchmark
% 3.29/0.88
% 3.29/0.88 % Proof 1 at 0.44 (+ 0.07) seconds.
% 3.29/0.88 % Length of proof is 33.
% 3.29/0.88 % Level of proof is 5.
% 3.29/0.88 % Maximum clause weight is 34.000.
% 3.29/0.88 % Given clauses 221.
% 3.29/0.88
% 3.29/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------