%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM472+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 : n016.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 08:17:06 AM UTC 2026
% Result : Theorem 0.13s 5.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 38 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 40 ( 19 ~; 13 |; 5 &)
% ( 1 <=>; 2 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 4 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mDefLE,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefLE) ).
fof(m__1324,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1324) ).
fof(m__,conjecture,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_36,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_44,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_45,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_73,plain,
( sdtpldt0(A,C) != B
| ~ aNaturalNumber0(C)
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefLE]) ).
cnf(c_100,plain,
( aNaturalNumber0(sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_752,plain,
( sdtpldt0(xm,B) != A
| ~ aNaturalNumber0(B)
| sdtlseqdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_73,c_45]) ).
cnf(c_753,negated_conjecture,
( sdtpldt0(xm,A) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolve,[status(thm)],[c_752,c_36]) ).
cnf(c_754,negated_conjecture,
( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolve,[status(thm)],[c_753,c_44]) ).
cnf(c_251,plain,
~ aNaturalNumber0(sdtpldt0(xm,xn)),
inference(xxres,[status(thm)],[c_754]) ).
cnf(c_755,plain,
( aNaturalNumber0(sdtpldt0(A,xn))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_100,c_44]) ).
cnf(c_756,plain,
~ aNaturalNumber0(xm),
inference(resolve,[status(thm)],[c_755,c_251]) ).
cnf(c_751,plain,
$false,
inference(resolve,[status(thm)],[c_45,c_756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM472+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 02:58:05 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 4049132 was started by sandbox2 on n016,
% 0.08/5.37 % Sat Sep 26 02:58:05 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/5.45
% 0.13/5.45 % SZS status Theorem for theBenchmark
% 0.13/5.45
% 0.13/5.45 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.13/5.45 % Length of proof is 11.
% 0.13/5.45 % Level of proof is 3.
% 0.13/5.45 % Maximum clause weight is 24.000.
% 0.13/5.45 % Given clauses 129.
% 0.13/5.45
% 0.13/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------