%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 08:25:57 AM UTC 2026
% Result : Theorem 23.88s 3.57s
% Output : CNFRefutation 23.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 14 unt; 2 def)
% Number of atoms : 62 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 24 ~; 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,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(mDefIdeal,definition,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ) ).
fof(mDefDvs,definition,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( doDivides0(X1,X0)
& aElement0(X1) ) ) ) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ) ).
fof(m__2273,hypothesis,
( ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ) ).
fof(m__2383,hypothesis,
~ ( aDivisorOf0(xu,xb)
& aDivisorOf0(xu,xa) ) ).
fof(m__2479,hypothesis,
~ ~ doDivides0(xu,xa) ).
fof(m__2612,hypothesis,
~ ~ doDivides0(xu,xb) ).
cnf(c23,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c55,plain,
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(clausification,[status(esa)],[mDefIdeal]) ).
cnf(c84,plain,
( ~ doDivides0(X1,X0)
| ~ aElement0(X1)
| aDivisorOf0(X1,X0)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mDefDvs]) ).
cnf(c108,plain,
aElement0(xa),
inference(clausification,[status(esa)],[m__2091]) ).
cnf(c109,plain,
aElement0(xb),
inference(clausification,[status(esa)],[m__2091]) ).
cnf(c112,plain,
aIdeal0(xI),
inference(clausification,[status(esa)],[m__2174]) ).
cnf(c120,plain,
aElementOf0(xu,xI),
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c123,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(clausification,[status(esa)],[m__2383]) ).
cnf(c127,plain,
doDivides0(xu,xa),
inference(clausification,[status(esa)],[m__2479]) ).
cnf(c128,plain,
doDivides0(xu,xb),
inference(clausification,[status(esa)],[m__2612]) ).
cnf(d0,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[c84,c128]) ).
cnf(d1,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[c109,d0]) ).
cnf(d2,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(resolution,[status(thm)],[c23,c120]) ).
cnf(d3,plain,
aSet0(xI),
inference(resolution,[status(thm)],[c55,c112]) ).
cnf(d4,plain,
aElement0(xu),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
aDivisorOf0(xu,xb),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c84,c127]) ).
cnf(d7,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[c108,d6]) ).
cnf(d8,plain,
aDivisorOf0(xu,xa),
inference(resolution,[status(thm)],[d4,d7]) ).
cnf(d9,plain,
~ aDivisorOf0(xu,xb),
inference(resolution,[status(thm)],[d8,c123]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG125+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 06:13:08 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.88/3.57 % SZS status Theorem for theBenchmark.p
% 23.88/3.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------