%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG125+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 : n016.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 08:26:43 AM UTC 2026
% Result : Theorem 0.14s 16.07s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 62 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 14 |; 9 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefIdeal,axiom,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(mDefDvs,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( doDivides0(W1,W0)
& aElement0(W1) ) ) ),
file('theBenchmark.p',mDefDvs) ).
fof(m__2091,axiom,
( aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__2091) ).
fof(m__2174,axiom,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('theBenchmark.p',m__2174) ).
fof(m__2273,axiom,
( ! [W0] :
( ( W0 != sz00
& aElementOf0(W0,xI) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ),
file('theBenchmark.p',m__2273) ).
fof(m__2383,axiom,
~ ( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ),
file('theBenchmark.p',m__2383) ).
fof(m__2479,axiom,
~ ~ doDivides0(xu,xa),
file('theBenchmark.p',m__2479) ).
fof(m__2612,axiom,
~ ~ doDivides0(xu,xb),
file('theBenchmark.p',m__2612) ).
cnf(c_96,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_118,plain,
( aSet0(A)
| ~ aIdeal0(A) ),
inference(clausify,[status(thm)],[mDefIdeal]) ).
cnf(c_143,plain,
( ~ doDivides0(B,A)
| ~ aElement0(B)
| aDivisorOf0(B,A)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mDefDvs]) ).
cnf(c_153,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_154,plain,
aElement0(xb),
inference(clausify,[status(thm)],[m__2091]) ).
cnf(c_156,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[m__2174]) ).
cnf(c_164,plain,
aElementOf0(xu,xI),
inference(clausify,[status(thm)],[m__2273]) ).
cnf(c_167,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(clausify,[status(thm)],[m__2383]) ).
cnf(c_172,plain,
doDivides0(xu,xa),
inference(clausify,[status(thm)],[m__2479]) ).
cnf(c_173,plain,
doDivides0(xu,xb),
inference(clausify,[status(thm)],[m__2612]) ).
cnf(c_523,plain,
aSet0(xI),
inference(resolve,[status(thm)],[c_156,c_118]) ).
cnf(c_858,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolve,[status(thm)],[c_164,c_96]) ).
cnf(c_717,plain,
aElement0(xu),
inference(resolve,[status(thm)],[c_523,c_858]) ).
cnf(c_859,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xa)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_172,c_143]) ).
cnf(c_860,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xa) ),
inference(resolve,[status(thm)],[c_153,c_859]) ).
cnf(c_852,plain,
aDivisorOf0(xu,xa),
inference(resolve,[status(thm)],[c_717,c_860]) ).
cnf(c_856,plain,
~ aDivisorOf0(xu,xb),
inference(resolve,[status(thm)],[c_852,c_167]) ).
cnf(c_861,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xb)
| ~ aElement0(xb) ),
inference(resolve,[status(thm)],[c_173,c_143]) ).
cnf(c_862,plain,
( ~ aElement0(xu)
| aDivisorOf0(xu,xb) ),
inference(resolve,[status(thm)],[c_154,c_861]) ).
cnf(c_863,plain,
~ aElement0(xu),
inference(resolve,[status(thm)],[c_856,c_862]) ).
cnf(c_857,plain,
$false,
inference(resolve,[status(thm)],[c_717,c_863]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.14/15.90 % CPULimit : 300
% 0.14/15.90 % WCLimit : 300
% 0.14/15.90 % DateTime : Sat Sep 26 06:12:17 UTC 2026
% 0.14/15.91 % CPUTime :
% 0.14/15.91 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/15.91 % Process 2655462 was started by sandbox2 on n010,
% 0.14/15.91 % Sat Sep 26 06:12:17 2026
% 0.14/15.91 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/15.92
% 0.14/15.92 % From the command line: assign(max_seconds, 300).
% 0.14/16.07
% 0.14/16.07 % SZS status Theorem for theBenchmark
% 0.14/16.07
% 0.14/16.07 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.14/16.07 % Length of proof is 24.
% 0.14/16.07 % Level of proof is 6.
% 0.14/16.07 % Maximum clause weight is 15.000.
% 0.14/16.07 % Given clauses 97.
% 0.14/16.07
% 0.14/16.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------