%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:25:56 AM UTC 2026
% Result : Theorem 25.89s 10.91s
% Output : CNFRefutation 25.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 18 unt; 2 def)
% Number of atoms : 121 ( 28 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 125 ( 53 ~; 43 |; 16 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aElement0(sz00) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ) ).
fof(mAddComm,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ) ).
fof(mAddZero,axiom,
! [X0] :
( aElement0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
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(mDefDiv,definition,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aElement0(X2) ) ) ) ).
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__2612,hypothesis,
~ doDivides0(xu,xb) ).
fof(m__2666,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ) ).
fof(m__,conjecture,
xr != sz00 ).
fof(negated_conjecture,negated_conjecture,
~ ( xr != sz00 ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aElement0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c4,plain,
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c5,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mAddComm]) ).
cnf(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mAddZero]) ).
cnf(c11,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
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(c81,plain,
( ~ aElement0(X0)
| ~ aElement0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aElement0(X1)
| doDivides0(X0,X1) ),
inference(clausification,[status(esa)],[mDefDiv]) ).
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(c128,plain,
~ doDivides0(xu,xb),
inference(clausification,[status(esa)],[m__2612]) ).
cnf(c129,plain,
aElement0(xq),
inference(clausification,[status(esa)],[m__2666]) ).
cnf(c131,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(clausification,[status(esa)],[m__2666]) ).
cnf(c133,plain,
xr = sz00,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),sz00),
inference(demodulation,[status(thm)],[c131,c133]) ).
cnf(d1,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(sz00)
| xb = sdtpldt0(sz00,sdtasdt0(xq,xu)) ),
inference(superposition,[status(thm)],[c5,d0]) ).
cnf(d2,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| xb = sdtpldt0(sz00,sdtasdt0(xq,xu)) ),
inference(resolution,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(sdtasdt0(xq,xu))
| sdtasdt0(xq,xu) = xb ),
inference(superposition,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( ~ aElement0(xq)
| ~ aElement0(xu)
| ~ aElement0(sdtasdt0(xq,xu))
| sdtasdt0(xu,xq) = xb ),
inference(superposition,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
( ~ aElement0(xu)
| ~ aElement0(sdtasdt0(xq,xu))
| sdtasdt0(xu,xq) = xb ),
inference(resolution,[status(thm)],[c129,d4]) ).
cnf(d6,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(resolution,[status(thm)],[c23,c120]) ).
cnf(d7,plain,
aSet0(xI),
inference(resolution,[status(thm)],[c55,c112]) ).
cnf(d8,plain,
aElement0(xu),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| sdtasdt0(xu,xq) = xb ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| doDivides0(xu,X0)
| ~ aElement0(X0)
| ~ aElement0(xq)
| ~ aElement0(xu)
| xb != X0 ),
inference(superposition,[status(thm)],[d9,c81]) ).
cnf(d11,plain,
( doDivides0(xu,X0)
| ~ aElement0(xu)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(X0)
| xb != X0 ),
inference(resolution,[status(thm)],[c129,d10]) ).
cnf(d12,plain,
( doDivides0(xu,X0)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(X0)
| xb != X0 ),
inference(resolution,[status(thm)],[d8,d11]) ).
cnf(d13,plain,
( doDivides0(xu,xb)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(xb) ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( doDivides0(xu,xb)
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(resolution,[status(thm)],[c109,d13]) ).
cnf(d15,plain,
~ aElement0(sdtasdt0(xq,xu)),
inference(resolution,[status(thm)],[c128,d14]) ).
cnf(d16,plain,
( ~ aElement0(xq)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
~ aElement0(xu),
inference(resolution,[status(thm)],[c129,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d8,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n018.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 06:12:27 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.89/10.91 % SZS status Theorem for theBenchmark.p
% 25.89/10.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------