%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM508+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 : n011.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 08:17:13 AM UTC 2026
% Result : Theorem 35.35s 5.02s
% Output : CNFRefutation 35.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 108 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 113 ( 46 ~; 49 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mIH_03,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(W0,W1) ) ),
file('theBenchmark.p',mIH_03) ).
fof(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__1799,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W2,sdtasdt0(W0,W1))
& isPrime0(W2) )
=> ( iLess0(sdtpldt0(sdtpldt0(W0,W1),W2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) ) ),
file('theBenchmark.p',m__1799) ).
fof(m__2342,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('theBenchmark.p',m__2342) ).
fof(m__2362,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('theBenchmark.p',m__2362) ).
fof(m__2478,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('theBenchmark.p',m__2478) ).
fof(m__,conjecture,
( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_57,plain,
( doDivides0(C,B)
| doDivides0(C,A)
| ~ iLess0(sdtpldt0(sdtpldt0(A,B),C),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(C,sdtasdt0(A,B))
| ~ isPrime0(C)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m__1799]) ).
cnf(c_59,plain,
isPrime0(xr),
inference(clausify,[status(thm)],[m__2342]) ).
cnf(c_66,plain,
( doDivides0(xr,B)
| doDivides0(xr,A)
| ~ iLess0(sdtpldt0(sdtpldt0(A,B),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xr,sdtasdt0(A,B))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_59,c_57]) ).
cnf(c_97,negated_conjecture,
~ doDivides0(xr,xm),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_98,negated_conjecture,
~ doDivides0(xr,xn),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_99,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(clausify,[status(thm)],[m__2478]) ).
cnf(c_100,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(clausify,[status(thm)],[m__2478]) ).
cnf(c_103,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(clausify,[status(thm)],[m__2362]) ).
cnf(c_106,plain,
aNaturalNumber0(xr),
inference(clausify,[status(thm)],[m__2342]) ).
cnf(c_119,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_120,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_121,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_136,plain,
( iLess0(A,B)
| ~ sdtlseqdt0(A,B)
| B = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mIH_03]) ).
cnf(c_182,plain,
( aNaturalNumber0(sdtpldt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB]) ).
cnf(c_212,plain,
( doDivides0(xr,B)
| doDivides0(xr,A)
| ~ iLess0(sdtpldt0(sdtpldt0(A,B),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(xr,sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_106,c_66]) ).
cnf(c_22687,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(resolve,[status(thm)],[c_136,c_99]) ).
cnf(c_22688,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(copy,[status(thm)],[c_22687]) ).
cnf(c_781,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(resolve,[status(thm)],[c_100,c_22688]) ).
cnf(c_1252,plain,
( aNaturalNumber0(sdtpldt0(xn,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_182,c_121]) ).
cnf(c_1258,plain,
( aNaturalNumber0(sdtpldt0(A,xp))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_182,c_119]) ).
cnf(c_1259,plain,
( aNaturalNumber0(sdtpldt0(A,xr))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_182,c_106]) ).
cnf(c_22689,plain,
( doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_212,c_103]) ).
cnf(c_22690,plain,
( doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_121,c_22689]) ).
cnf(c_22691,plain,
( doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolve,[status(thm)],[c_120,c_22690]) ).
cnf(c_22692,negated_conjecture,
( doDivides0(xr,xm)
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolve,[status(thm)],[c_98,c_22691]) ).
cnf(c_1628,negated_conjecture,
~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(resolve,[status(thm)],[c_97,c_22692]) ).
cnf(c_1629,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)) ),
inference(resolve,[status(thm)],[c_1628,c_781]) ).
cnf(c_19875,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(resolve,[status(thm)],[c_1252,c_120]) ).
cnf(c_22506,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(resolve,[status(thm)],[c_1258,c_19875]) ).
cnf(c_22549,plain,
~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)),
inference(resolve,[status(thm)],[c_22506,c_1629]) ).
cnf(c_22693,plain,
aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr)),
inference(resolve,[status(thm)],[c_1259,c_19875]) ).
cnf(c_22686,plain,
$false,
inference(resolve,[status(thm)],[c_22549,c_22693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM508+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:02:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3650949 was started by sandbox2 on n011,
% 0.10/0.37 % Sat Sep 26 03:02:00 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 35.35/5.02
% 35.35/5.02 % given #500 (W,wt=11): 10984 -doDivides0(sz00,xm) | doDivides0(xn,xm). [resolve(10933,a,120,a)].
% 35.35/5.02
% 35.35/5.02 % given #1000 (F,wt=15): 16955 -sdtlseqdt0(sdtpldt0(xr,xr),xr). [resolve(15595,a,150,d),flip(d),unit_del(a,2066),unit_del(b,106),unit_del(d,15807)].
% 35.35/5.02
% 35.35/5.02 % SZS status Theorem for theBenchmark
% 35.35/5.02
% 35.35/5.02 % Proof 1 at 3.46 (+ 1.11) seconds.
% 35.35/5.02 % Length of proof is 33.
% 35.35/5.02 % Level of proof is 7.
% 35.35/5.02 % Maximum clause weight is 47.000.
% 35.35/5.02 % Given clauses 1234.
% 35.35/5.02
% 35.35/5.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------