%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM457+1 : 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 : n006.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 08:17:03 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 67 ( 41 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 30 ~; 26 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(mMulCanc,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('theBenchmark.p',mMulCanc) ).
fof(m__624,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('theBenchmark.p',m__624) ).
fof(m__,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
cnf(c_18,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[mSortsC]) ).
cnf(c_31,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_39,plain,
( C = B
| sdtasdt0(A,C) != sdtasdt0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| sz00 = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mMulCanc]) ).
cnf(c_44,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__624]) ).
cnf(c_45,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__624]) ).
cnf(c_46,negated_conjecture,
sdtasdt0(xm,xn) = sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_47,negated_conjecture,
sz00 = sdtasdt0(xm,xn),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,negated_conjecture,
xm != sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_364,negated_conjecture,
xm != sdtasdt0(xm,xn),
inference(paramod,[status(thm)],[c_47,c_48]) ).
cnf(c_49,negated_conjecture,
sdtasdt0(xm,xn) != xm,
inference(copy,[status(thm)],[c_364]) ).
cnf(c_50,negated_conjecture,
xn != sz00,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_365,negated_conjecture,
xn != sdtasdt0(xm,xn),
inference(paramod,[status(thm)],[c_47,c_50]) ).
cnf(c_51,negated_conjecture,
sdtasdt0(xm,xn) != xn,
inference(copy,[status(thm)],[c_365]) ).
cnf(c_80,plain,
( C = B
| sdtasdt0(A,C) != sdtasdt0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| sdtasdt0(xm,xn) = A
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_47,c_39]) ).
cnf(c_366,plain,
( sdtasdt0(A,sdtasdt0(xm,xn)) = sz00
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_47,c_31]) ).
cnf(c_82,plain,
( sdtasdt0(A,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(A) ),
inference(paramod,[status(thm)],[c_47,c_366]) ).
cnf(c_86,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(paramod,[status(thm)],[c_47,c_18]) ).
cnf(c_299,plain,
sdtasdt0(xm,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn),
inference(resolve,[status(thm)],[c_82,c_44]) ).
cnf(c_367,plain,
( B = A
| sdtasdt0(xm,B) != sdtasdt0(xm,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A)
| sdtasdt0(xm,xn) = xm ),
inference(resolve,[status(thm)],[c_80,c_44]) ).
cnf(c_368,negated_conjecture,
( B = A
| sdtasdt0(xm,B) != sdtasdt0(xm,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_367,c_49]) ).
cnf(c_369,negated_conjecture,
( A = xn
| sdtasdt0(xm,A) != sdtasdt0(xm,xn)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_368,c_45]) ).
cnf(c_370,negated_conjecture,
( sdtasdt0(xm,xn) = xn
| sdtasdt0(xm,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) ),
inference(resolve,[status(thm)],[c_369,c_86]) ).
cnf(c_371,negated_conjecture,
sdtasdt0(xm,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn),
inference(resolve,[status(thm)],[c_370,c_51]) ).
cnf(c_372,negated_conjecture,
sdtasdt0(xm,xn) != sdtasdt0(xm,xn),
inference(paramod,[status(thm)],[c_299,c_371]) ).
cnf(c_363,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:48:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 213816 was started by sandbox on n006,
% 0.09/0.37 % Sat Sep 26 02:48:55 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.14/0.41 % Length of proof is 20.
% 0.14/0.41 % Level of proof is 5.
% 0.14/0.41 % Maximum clause weight is 31.000.
% 0.14/0.41 % Given clauses 51.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------