%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG122+4 : 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 : n015.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 188.57s 37.86s
% Output : CNFRefutation 188.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 19 unt; 0 def)
% Number of atoms : 134 ( 38 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 135 ( 50 ~; 40 |; 31 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 18 !; 10 ?)
% 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(mAddAsso,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ).
fof(mAddZero,axiom,
! [X0] :
( aElement0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mAddInvr,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ) ).
fof(mEOfElem,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& ! [X0] :
( aElementOf0(X0,xI)
<=> ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
& ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ) ).
fof(m__2273,hypothesis,
( ! [X0] :
( ( X0 != sz00
& ( aElementOf0(X0,xI)
| ? [X1,X2] :
( sdtpldt0(X1,X2) = X0
& aElementOf0(X2,slsdtgt0(xb))
& aElementOf0(X1,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xu
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ).
fof(m__2666,hypothesis,
( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
| xr = sz00 )
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& aElement0(xr)
& aElement0(xq) ) ).
fof(m__2690,hypothesis,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu))
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ).
fof(m__,conjecture,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ).
fof(negated_conjecture,negated_conjecture,
xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
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(c6,plain,
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mAddAsso]) ).
cnf(c7,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mAddZero]) ).
cnf(c10,plain,
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mAddInvr]) ).
cnf(c23,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c131,plain,
aSet0(xI),
inference(clausification,[status(esa)],[m__2174]) ).
cnf(c172,plain,
aElementOf0(xu,xI),
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c190,plain,
aElement0(xq),
inference(clausification,[status(esa)],[m__2666]) ).
cnf(c191,plain,
aElement0(xr),
inference(clausification,[status(esa)],[m__2666]) ).
cnf(c192,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(clausification,[status(esa)],[m__2666]) ).
cnf(c197,plain,
sdtpldt0(sK154,sK155) = smndt0(sdtasdt0(xq,xu)),
inference(clausification,[status(esa)],[m__2690]) ).
cnf(c198,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(clausification,[status(esa)],[m__2690]) ).
cnf(c206,plain,
xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xr != sdtpldt0(sdtpldt0(sK154,sK155),xb),
inference(demodulation,[status(thm)],[c206,c197]) ).
cnf(d1,plain,
( ~ aElement0(X0)
| ~ aElement0(smndt0(X0))
| ~ aElement0(X0)
| ~ aElement0(X1)
| sdtpldt0(sz00,X1) = sdtpldt0(smndt0(X0),sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c10,c6]) ).
cnf(d2,plain,
( ~ aElement0(smndt0(sdtasdt0(xq,xu)))
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(xr)
| sdtpldt0(sz00,xr) = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ),
inference(superposition,[status(thm)],[c192,d1]) ).
cnf(d3,plain,
( ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(smndt0(sdtasdt0(xq,xu)))
| sdtpldt0(sz00,xr) = sdtpldt0(sdtpldt0(sK154,sK155),xb) ),
inference(demodulation,[status(thm)],[d2,c197]) ).
cnf(d4,plain,
( ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(sdtpldt0(sK154,sK155))
| sdtpldt0(sz00,xr) = sdtpldt0(sdtpldt0(sK154,sK155),xb) ),
inference(demodulation,[status(thm)],[d3,c197]) ).
cnf(d5,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(sdtpldt0(sK154,sK155))
| sdtpldt0(sz00,xr) = sdtpldt0(sdtpldt0(sK154,sK155),xb) ),
inference(resolution,[status(thm)],[c191,d4]) ).
cnf(d6,plain,
( ~ aSet0(xI)
| aElement0(smndt0(sdtasdt0(xq,xu))) ),
inference(resolution,[status(thm)],[c23,c198]) ).
cnf(d7,plain,
aElement0(smndt0(sdtasdt0(xq,xu))),
inference(resolution,[status(thm)],[c131,d6]) ).
cnf(d8,plain,
aElement0(sdtpldt0(sK154,sK155)),
inference(demodulation,[status(thm)],[d7,c197]) ).
cnf(d9,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| sdtpldt0(sz00,xr) = sdtpldt0(sdtpldt0(sK154,sK155),xb) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| xr != sdtpldt0(sz00,xr) ),
inference(superposition,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( ~ aElement0(X0)
| ~ aElement0(sz00)
| ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(superposition,[status(thm)],[c7,c5]) ).
cnf(d12,plain,
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( ~ aElement0(xr)
| ~ aElement0(sdtasdt0(xq,xu))
| xr != xr ),
inference(superposition,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
( ~ aElement0(sdtasdt0(xq,xu))
| xr != xr ),
inference(resolution,[status(thm)],[c191,d13]) ).
cnf(d15,plain,
~ aElement0(sdtasdt0(xq,xu)),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ~ aElement0(xq)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
~ aElement0(xu),
inference(resolution,[status(thm)],[c190,d16]) ).
cnf(d18,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(resolution,[status(thm)],[c23,c172]) ).
cnf(d19,plain,
aElement0(xu),
inference(resolution,[status(thm)],[c131,d18]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG122+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:14:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 188.57/37.86 % SZS status Theorem for theBenchmark.p
% 188.57/37.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------