%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM423+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 : n010.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 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 94 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 45 ~; 42 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 28 ( 0 sgn 7 !; 1 ?)
% 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(mEquMod,axiom,
! [W0,W1,W2] :
( ( W2 != sz00
& aInteger0(W2)
& aInteger0(W1)
& aInteger0(W0) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('theBenchmark.p',mEquMod) ).
fof(m__671,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('theBenchmark.p',m__671) ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
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_54,plain,
( ~ aDivisorOf0(C,sdtpldt0(A,smndt0(B)))
| sdteqdtlpzmzozddtrp0(A,B,C)
| C = sz00
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mEquMod]) ).
cnf(c_55,plain,
( ~ aDivisorOf0(C,sdtpldt0(A,smndt0(B)))
| sdteqdtlpzmzozddtrp0(A,B,C)
| sz00 = C
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_54]) ).
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_59,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_76,plain,
( sdtasdt0(B,A) != A
| sz00 = B
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(factor,[status(thm)],[c_51]) ).
cnf(c_244,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(resolve,[status(thm)],[c_56,c_29]) ).
cnf(c_296,plain,
sdtasdt0(xq,sz00) = sz00,
inference(resolve,[status(thm)],[c_57,c_39]) ).
cnf(c_566,plain,
( ~ aDivisorOf0(B,sdtpldt0(xa,smndt0(A)))
| sdteqdtlpzmzozddtrp0(xa,A,B)
| sz00 = B
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_55,c_56]) ).
cnf(c_567,plain,
( ~ aDivisorOf0(A,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,A)
| sz00 = A
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_566,c_56]) ).
cnf(c_568,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq)
| sz00 = xq ),
inference(resolve,[status(thm)],[c_567,c_57]) ).
cnf(c_569,plain,
sz00 != xq,
inference(copy,[status(thm)],[c_58]) ).
cnf(c_570,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(resolve,[status(thm)],[c_568,c_569]) ).
cnf(c_571,negated_conjecture,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))),
inference(resolve,[status(thm)],[c_570,c_59]) ).
cnf(c_345,negated_conjecture,
~ aDivisorOf0(xq,sz00),
inference(paramod,[status(thm)],[c_244,c_571]) ).
cnf(c_572,plain,
( sdtasdt0(A,sz00) != sz00
| sz00 = A
| ~ aInteger0(A)
| aDivisorOf0(A,sz00) ),
inference(resolve,[status(thm)],[c_76,c_20]) ).
cnf(c_573,plain,
( sdtasdt0(xq,sz00) != sz00
| sz00 = xq
| ~ aInteger0(xq) ),
inference(resolve,[status(thm)],[c_572,c_345]) ).
cnf(c_574,plain,
( sdtasdt0(xq,sz00) != sz00
| sz00 = xq ),
inference(resolve,[status(thm)],[c_573,c_57]) ).
cnf(c_575,plain,
sz00 != xq,
inference(copy,[status(thm)],[c_58]) ).
cnf(c_576,plain,
sdtasdt0(xq,sz00) != sz00,
inference(resolve,[status(thm)],[c_574,c_575]) ).
cnf(c_577,plain,
sz00 != sz00,
inference(paramod,[status(thm)],[c_296,c_576]) ).
cnf(c_565,plain,
$false,
inference(copy,[status(thm)],[c_577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 02:41:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2305307 was started by sandbox on n010,
% 0.09/0.36 % Sat Sep 26 02:41:00 2026
% 0.09/0.36 % 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).
% 0.12/0.46
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46
% 0.12/0.46 % Proof 1 at 0.06 (+ 0.03) seconds.
% 0.12/0.46 % Length of proof is 22.
% 0.12/0.46 % Level of proof is 4.
% 0.12/0.46 % Maximum clause weight is 34.000.
% 0.12/0.46 % Given clauses 76.
% 0.12/0.46
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------