%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM427+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 : n005.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 08:16:58 AM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 101 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 51 ~; 44 |; 11 &)
% ( 2 <=>; 4 =>; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mIntMult) ).
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__704,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('theBenchmark.p',m__704) ).
fof(m__747,axiom,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('theBenchmark.p',m__747) ).
fof(m__,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_24,plain,
( aInteger0(smndt0(A))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntNeg]) ).
cnf(c_26,plain,
( aInteger0(sdtasdt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntMult]) ).
cnf(c_52,plain,
( sdtasdt0(B,C) != A
| ~ aInteger0(C)
| B = sz00
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mDivisor]) ).
cnf(c_53,plain,
( sdtasdt0(B,C) != A
| ~ aInteger0(C)
| sz00 = B
| ~ aInteger0(B)
| aDivisorOf0(B,A)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_56,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_57,plain,
( ~ aDivisorOf0(C,sdtpldt0(A,smndt0(B)))
| sdteqdtlpzmzozddtrp0(A,B,C)
| sz00 = C
| ~ aInteger0(C)
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_60,plain,
aInteger0(xa),
inference(clausify,[status(thm)],[m__704]) ).
cnf(c_61,plain,
aInteger0(xb),
inference(clausify,[status(thm)],[m__704]) ).
cnf(c_62,plain,
aInteger0(xq),
inference(clausify,[status(thm)],[m__704]) ).
cnf(c_63,plain,
xq != sz00,
inference(clausify,[status(thm)],[m__704]) ).
cnf(c_65,plain,
aInteger0(xn),
inference(clausify,[status(thm)],[m__747]) ).
fof(m__767,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('theBenchmark.p',m__767) ).
cnf(c_68,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(clausify,[status(thm)],[m__767]) ).
cnf(c_69,plain,
sdtpldt0(xb,smndt0(xa)) = sdtasdt0(xq,smndt0(xn)),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_70,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_387,plain,
aInteger0(smndt0(xn)),
inference(resolve,[status(thm)],[c_65,c_24]) ).
cnf(c_1254,plain,
( ~ aDivisorOf0(B,sdtpldt0(xb,smndt0(A)))
| sdteqdtlpzmzozddtrp0(xb,A,B)
| sz00 = B
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_57,c_61]) ).
cnf(c_1255,plain,
( ~ aDivisorOf0(A,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,A)
| sz00 = A
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_1254,c_60]) ).
cnf(c_1256,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| sz00 = xq ),
inference(resolve,[status(thm)],[c_1255,c_62]) ).
cnf(c_1257,plain,
sz00 != xq,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_1258,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(resolve,[status(thm)],[c_1256,c_1257]) ).
cnf(c_406,negated_conjecture,
~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))),
inference(resolve,[status(thm)],[c_1258,c_70]) ).
cnf(c_734,plain,
~ aDivisorOf0(xq,sdtasdt0(xq,smndt0(xn))),
inference(paramod,[status(thm)],[c_69,c_406]) ).
cnf(c_1259,plain,
( sdtasdt0(xq,A) != sdtasdt0(xq,smndt0(xn))
| ~ aInteger0(A)
| sz00 = xq
| ~ aInteger0(xq)
| ~ aInteger0(sdtasdt0(xq,smndt0(xn))) ),
inference(resolve,[status(thm)],[c_53,c_734]) ).
cnf(c_1260,plain,
( sdtasdt0(xq,A) != sdtasdt0(xq,smndt0(xn))
| ~ aInteger0(A)
| sz00 = xq
| ~ aInteger0(sdtasdt0(xq,smndt0(xn))) ),
inference(resolve,[status(thm)],[c_1259,c_62]) ).
cnf(c_1261,plain,
sz00 != xq,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_1262,plain,
( sdtasdt0(xq,A) != sdtasdt0(xq,smndt0(xn))
| ~ aInteger0(A)
| ~ aInteger0(sdtasdt0(xq,smndt0(xn))) ),
inference(resolve,[status(thm)],[c_1260,c_1261]) ).
cnf(c_1263,plain,
( sdtasdt0(xq,smndt0(xn)) != sdtasdt0(xq,smndt0(xn))
| ~ aInteger0(sdtasdt0(xq,smndt0(xn))) ),
inference(resolve,[status(thm)],[c_1262,c_387]) ).
cnf(c_1099,plain,
~ aInteger0(sdtasdt0(xq,smndt0(xn))),
inference(xxres,[status(thm)],[c_1263]) ).
cnf(c_1264,plain,
( aInteger0(sdtasdt0(A,smndt0(xn)))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_26,c_387]) ).
cnf(c_1265,plain,
~ aInteger0(xq),
inference(resolve,[status(thm)],[c_1264,c_1099]) ).
cnf(c_1253,plain,
$false,
inference(resolve,[status(thm)],[c_62,c_1265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.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 02:41:17 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 1039035 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 02:41:17 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.13/0.46 % Length of proof is 26.
% 0.13/0.46 % Level of proof is 6.
% 0.13/0.46 % Maximum clause weight is 34.000.
% 0.13/0.46 % Given clauses 122.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------