%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM423+3 : 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 : n004.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 08:16:57 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 66 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 26 |; 9 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 4 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddNeg,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtpldt0(smndt0(W0),W0)
& sdtpldt0(W0,smndt0(W0)) = sz00 ) ),
file('theBenchmark.p',mAddNeg) ).
fof(mMulZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',mMulZero) ).
fof(mDivisor,axiom,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('theBenchmark.p',mDivisor) ).
fof(m__671,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('theBenchmark.p',m__671) ).
fof(m__,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa))
& aInteger0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa))
& aInteger0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('theBenchmark.p',mIntZero) ).
cnf(c_20,plain,
aInteger0(sz00),
inference(clausify,[status(thm)],[mIntZero]) ).
cnf(c_29,plain,
( sdtpldt0(A,smndt0(A)) = sz00
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mAddNeg]) ).
cnf(c_39,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mMulZero]) ).
cnf(c_50,plain,
( sdtasdt0(B,C) != A
| ~ aInteger0(C)
| B = sz00
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mDivisor]) ).
cnf(c_51,plain,
( sdtasdt0(B,C) != A
| ~ aInteger0(C)
| sz00 = B
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_56,plain,
aInteger0(xa),
inference(clausify,[status(thm)],[m__671]) ).
cnf(c_57,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[m__671]) ).
cnf(c_58,plain,
xq != sz00,
inference(clausify,[status(thm)],[m__671]) ).
cnf(c_60,negated_conjecture,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_78,plain,
( sdtasdt0(B,A) != A
| sz00 = B
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(factor,[status(thm)],[c_51]) ).
cnf(c_205,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(resolve,[status(thm)],[c_56,c_29]) ).
cnf(c_230,negated_conjecture,
~ aDivisorOf0(xq,sz00),
inference(paramod,[status(thm)],[c_205,c_60]) ).
cnf(c_242,plain,
sdtasdt0(xq,sz00) = sz00,
inference(resolve,[status(thm)],[c_57,c_39]) ).
cnf(c_446,plain,
( sdtasdt0(A,sz00) != sz00
| sz00 = A
| ~ aInteger0(A)
| aDivisorOf0(A,sz00) ),
inference(resolve,[status(thm)],[c_78,c_20]) ).
cnf(c_447,negated_conjecture,
( sdtasdt0(xq,sz00) != sz00
| sz00 = xq
| ~ aInteger0(xq) ),
inference(resolve,[status(thm)],[c_446,c_230]) ).
cnf(c_448,negated_conjecture,
( sdtasdt0(xq,sz00) != sz00
| sz00 = xq ),
inference(resolve,[status(thm)],[c_447,c_57]) ).
cnf(c_449,plain,
sz00 != xq,
inference(copy,[status(thm)],[c_58]) ).
cnf(c_450,negated_conjecture,
sdtasdt0(xq,sz00) != sz00,
inference(resolve,[status(thm)],[c_448,c_449]) ).
cnf(c_451,negated_conjecture,
sz00 != sz00,
inference(paramod,[status(thm)],[c_242,c_450]) ).
cnf(c_445,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 02:40:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 643232 was started by sandbox on n004,
% 0.08/0.36 % Sat Sep 26 02:40:21 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 19.
% 0.13/0.42 % Level of proof is 4.
% 0.13/0.42 % Maximum clause weight is 17.000.
% 0.13/0.42 % Given clauses 69.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------