%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG123+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 : 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 08:25:57 AM UTC 2026
% Result : Theorem 38.48s 8.11s
% Output : CNFRefutation 38.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 55 ( 13 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 46 ( 9 ~; 7 |; 24 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 6 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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__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__2699,hypothesis,
( aElementOf0(xb,xI)
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) )
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xb
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ).
fof(m__2718,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ).
fof(m__,conjecture,
( aElementOf0(xr,xI)
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( aElementOf0(xr,xI)
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xr
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c132,plain,
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(clausification,[status(esa)],[m__2174]) ).
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(c205,plain,
aElementOf0(xb,xI),
inference(clausification,[status(esa)],[m__2699]) ).
cnf(c206,plain,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(clausification,[status(esa)],[m__2718]) ).
cnf(c208,plain,
~ aElementOf0(xr,xI),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xr = sdtpldt0(sdtpldt0(sK154,sK155),xb),
inference(demodulation,[status(thm)],[c206,c197]) ).
cnf(d1,plain,
( ~ aElementOf0(sdtpldt0(sK154,sK155),xI)
| ~ aElementOf0(xb,xI)
| aElementOf0(xr,xI) ),
inference(superposition,[status(thm)],[d0,c132]) ).
cnf(d2,plain,
( ~ aElementOf0(xb,xI)
| ~ aElementOf0(sdtpldt0(sK154,sK155),xI) ),
inference(resolution,[status(thm)],[c208,d1]) ).
cnf(d3,plain,
~ aElementOf0(sdtpldt0(sK154,sK155),xI),
inference(resolution,[status(thm)],[c205,d2]) ).
cnf(d4,plain,
aElementOf0(sdtpldt0(sK154,sK155),xI),
inference(demodulation,[status(thm)],[c198,c197]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+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
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 06:16:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.48/8.11 % SZS status Theorem for theBenchmark.p
% 38.48/8.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------