%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM463+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 : n003.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 08:17:04 AM UTC 2026
% Result : Theorem 1.97s 0.69s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 143 ( 67 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 129 ( 40 ~; 62 |; 17 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(m_MulUnit,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',m_MulUnit) ).
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(mLERefl,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('theBenchmark.p',mLERefl) ).
fof(mLETotal,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLETotal) ).
fof(mMonMul,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W2)
& W1 != W2
& W0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) ) ) ),
file('theBenchmark.p',mMonMul) ).
fof(mLENTr,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtlseqdt0(sz10,W0)
& sz10 != W0 )
| W0 = sz10
| W0 = sz00 ) ),
file('theBenchmark.p',mLENTr) ).
fof(m__987,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('theBenchmark.p',m__987) ).
fof(m__,conjecture,
( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [W0] :
( sdtpldt0(xn,W0) = sdtasdt0(xn,xm)
& aNaturalNumber0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [W0] :
( sdtpldt0(xn,W0) = sdtasdt0(xn,xm)
& aNaturalNumber0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_28,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_29,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_37,plain,
( sdtasdt0(B,A) = sdtasdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulComm]) ).
cnf(c_40,plain,
( sdtasdt0(sz10,A) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulUnit]) ).
cnf(c_41,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_62,plain,
( sdtlseqdt0(A,A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLERefl]) ).
cnf(c_65,plain,
( B != A
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLETotal]) ).
cnf(c_70,plain,
( sdtlseqdt0(sdtasdt0(B,A),sdtasdt0(C,A))
| ~ sdtlseqdt0(B,C)
| C = B
| sz00 = A
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMonMul]) ).
cnf(c_71,plain,
( sdtlseqdt0(sz10,A)
| sz10 = A
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLENTr]) ).
cnf(c_72,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__987]) ).
cnf(c_73,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__987]) ).
cnf(c_74,negated_conjecture,
xm != sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_76,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_900,plain,
( sdtlseqdt0(sz10,xm)
| sz10 = xm
| sz00 = xm ),
inference(resolve,[status(thm)],[c_72,c_71]) ).
cnf(c_901,plain,
( sdtlseqdt0(sz10,xm)
| sz10 = xm
| xm = sz00 ),
inference(copy,[status(thm)],[c_900]) ).
cnf(c_902,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz10
| xm = sz00 ),
inference(copy,[status(thm)],[c_901]) ).
cnf(c_282,negated_conjecture,
( sdtlseqdt0(sz10,xm)
| xm = sz10 ),
inference(resolve,[status(thm)],[c_74,c_902]) ).
cnf(c_310,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolve,[status(thm)],[c_72,c_41]) ).
cnf(c_404,plain,
sdtlseqdt0(xn,xn),
inference(resolve,[status(thm)],[c_73,c_62]) ).
cnf(c_430,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolve,[status(thm)],[c_73,c_40]) ).
cnf(c_903,plain,
( sdtasdt0(A,xm) = sdtasdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_37,c_72]) ).
cnf(c_522,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolve,[status(thm)],[c_903,c_73]) ).
cnf(c_593,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xm,xn)),
inference(paramod,[status(thm)],[c_522,c_76]) ).
cnf(c_904,plain,
( sdtlseqdt0(sdtasdt0(A,xn),sdtasdt0(B,xn))
| ~ sdtlseqdt0(A,B)
| B = A
| sz00 = xn
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_70,c_73]) ).
cnf(c_905,plain,
( sdtlseqdt0(sdtasdt0(sz10,xn),sdtasdt0(A,xn))
| ~ sdtlseqdt0(sz10,A)
| A = sz10
| sz00 = xn
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_904,c_29]) ).
cnf(c_906,plain,
( sdtlseqdt0(sdtasdt0(sz10,xn),sdtasdt0(xm,xn))
| ~ sdtlseqdt0(sz10,xm)
| xm = sz10
| sz00 = xn ),
inference(resolve,[status(thm)],[c_905,c_72]) ).
cnf(c_907,plain,
( xm = sz10
| sdtlseqdt0(sdtasdt0(sz10,xn),sdtasdt0(xm,xn))
| xm = sz10
| sz00 = xn ),
inference(resolve,[status(thm)],[c_906,c_282]) ).
cnf(c_908,plain,
( xm = sz10
| sdtlseqdt0(xn,sdtasdt0(xm,xn))
| xm = sz10
| sz00 = xn ),
inference(paramod,[status(thm)],[c_430,c_907]) ).
cnf(c_909,plain,
( xm = sz10
| sdtlseqdt0(xn,sdtasdt0(xm,xn))
| xm = sz10
| xn = sz00 ),
inference(copy,[status(thm)],[c_908]) ).
cnf(c_910,plain,
( sdtlseqdt0(xn,sdtasdt0(xm,xn))
| xm = sz10
| xn = sz00 ),
inference(copy,[status(thm)],[c_909]) ).
cnf(c_750,negated_conjecture,
( xm = sz10
| xn = sz00 ),
inference(resolve,[status(thm)],[c_593,c_910]) ).
cnf(c_911,plain,
( A != xn
| sdtlseqdt0(xn,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_65,c_73]) ).
cnf(c_912,plain,
( sz00 != xn
| sdtlseqdt0(xn,sz00) ),
inference(resolve,[status(thm)],[c_911,c_28]) ).
cnf(c_913,plain,
( xm = sz10
| sz00 = xn ),
inference(copy,[status(thm)],[c_750]) ).
cnf(c_867,plain,
( xm = sz10
| sdtlseqdt0(xn,sz00) ),
inference(resolve,[status(thm)],[c_912,c_913]) ).
cnf(c_914,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xm,sz00))
| xm = sz10 ),
inference(paramod,[status(thm)],[c_750,c_593]) ).
cnf(c_870,plain,
( ~ sdtlseqdt0(xn,sz00)
| xm = sz10 ),
inference(paramod,[status(thm)],[c_310,c_914]) ).
cnf(c_915,plain,
( xm = sz10
| xm = sz10 ),
inference(resolve,[status(thm)],[c_870,c_867]) ).
cnf(c_897,plain,
xm = sz10,
inference(copy,[status(thm)],[c_915]) ).
cnf(c_916,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(sz10,xn)),
inference(paramod,[status(thm)],[c_897,c_593]) ).
cnf(c_917,negated_conjecture,
~ sdtlseqdt0(xn,xn),
inference(paramod,[status(thm)],[c_430,c_916]) ).
cnf(c_899,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_404,c_917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM463+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n003.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 02:52:54 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1864188 was started by sandbox on n003,
% 0.11/0.36 % Sat Sep 26 02:52:54 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 1.97/0.69
% 1.97/0.69 % SZS status Theorem for theBenchmark
% 1.97/0.69
% 1.97/0.69 % Proof 1 at 0.24 (+ 0.04) seconds.
% 1.97/0.69 % Length of proof is 34.
% 1.97/0.69 % Level of proof is 7.
% 1.97/0.69 % Maximum clause weight is 32.000.
% 1.97/0.69 % Given clauses 133.
% 1.97/0.69
% 1.97/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------