%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM464+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 : n017.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 08:17:05 AM UTC 2026
% Result : Theorem 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 44 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 10 ~; 15 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 2 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(mLERefl,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> sdtlseqdt0(W0,W0) ),
file('theBenchmark.p',mLERefl) ).
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(sz10,xm)
| ? [W0] :
( sdtpldt0(sz10,W0) = xm
& aNaturalNumber0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
| ? [W0] :
( sdtpldt0(sz10,W0) = xm
& aNaturalNumber0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_29,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_60,plain,
( sdtlseqdt0(A,A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLERefl]) ).
cnf(c_69,plain,
( sdtlseqdt0(sz10,A)
| sz10 = A
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLENTr]) ).
cnf(c_70,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__987]) ).
cnf(c_72,negated_conjecture,
xm != sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_74,negated_conjecture,
~ sdtlseqdt0(sz10,xm),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_231,plain,
sdtlseqdt0(sz10,sz10),
inference(resolve,[status(thm)],[c_60,c_29]) ).
cnf(c_241,plain,
( sdtlseqdt0(sz10,xm)
| sz10 = xm
| sz00 = xm ),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_242,plain,
( sdtlseqdt0(sz10,xm)
| sz10 = xm
| xm = sz00 ),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_243,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz10
| xm = sz00 ),
inference(copy,[status(thm)],[c_242]) ).
cnf(c_244,negated_conjecture,
( sdtlseqdt0(sz10,xm)
| xm = sz10 ),
inference(resolve,[status(thm)],[c_72,c_243]) ).
cnf(c_239,negated_conjecture,
xm = sz10,
inference(resolve,[status(thm)],[c_74,c_244]) ).
cnf(c_245,negated_conjecture,
~ sdtlseqdt0(sz10,sz10),
inference(paramod,[status(thm)],[c_239,c_74]) ).
cnf(c_240,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_231,c_245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM464+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 02:46:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3822833 was started by sandbox2 on n017,
% 0.08/0.37 % Sat Sep 26 02:46:49 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.41
% 0.08/0.41 % SZS status Theorem for theBenchmark
% 0.08/0.41
% 0.08/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.08/0.41 % Length of proof is 14.
% 0.08/0.41 % Level of proof is 3.
% 0.08/0.41 % Maximum clause weight is 11.000.
% 0.08/0.41 % Given clauses 41.
% 0.08/0.41
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------