%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG126+4 : 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 : n008.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 08:25:58 AM UTC 2026
% Result : Theorem 28.14s 20.97s
% Output : CNFRefutation 28.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 22 unt; 0 def)
% Number of atoms : 126 ( 27 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 111 ( 33 ~; 28 |; 32 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 17 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ) ).
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__2744,hypothesis,
? [X0] :
( sdtasdt0(xu,X0) = xc
& aElement0(X0) ) ).
fof(m__,conjecture,
( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
=> ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xc
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xa))
<=> ? [X1] :
( sdtasdt0(xa,X1) = X0
& aElement0(X1) ) )
=> ( ! [X0] :
( aElementOf0(X0,slsdtgt0(xb))
<=> ? [X1] :
( sdtasdt0(xb,X1) = X0
& aElement0(X1) ) )
=> ( aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X0,X1] :
( sdtpldt0(X0,X1) = xc
& aElementOf0(X1,slsdtgt0(xb))
& aElementOf0(X0,slsdtgt0(xa)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c3,plain,
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c4,plain,
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c11,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c108,plain,
aElement0(xa),
inference(clausification,[status(esa)],[m__2091]) ).
cnf(c109,plain,
aElement0(xb),
inference(clausification,[status(esa)],[m__2091]) ).
cnf(c133,plain,
( aElementOf0(sdtasdt0(X1,X0),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xI) ),
inference(clausification,[status(esa)],[m__2174]) ).
cnf(c145,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(clausification,[status(esa)],[m__2174]) ).
cnf(c169,plain,
aElementOf0(sK142,slsdtgt0(xa)),
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c170,plain,
aElementOf0(sK143,slsdtgt0(xb)),
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c171,plain,
sdtpldt0(sK142,sK143) = xu,
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c172,plain,
aElementOf0(xu,xI),
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c184,plain,
aElement0(sK149),
inference(clausification,[status(esa)],[m__2744]) ).
cnf(c185,plain,
sdtasdt0(xu,sK149) = xc,
inference(clausification,[status(esa)],[m__2744]) ).
cnf(c186,plain,
( aElement0(sK151(X0))
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c187,plain,
( sdtasdt0(xa,sK151(X0)) = X0
| ~ aElementOf0(X0,slsdtgt0(xa)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c189,plain,
( aElement0(sK154(X0))
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c190,plain,
( sdtasdt0(xb,sK154(X0)) = X0
| ~ aElementOf0(X0,slsdtgt0(xb)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c193,plain,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aElement0(sK142)
| ~ aElement0(sK143)
| aElement0(xu) ),
inference(superposition,[status(thm)],[c171,c3]) ).
cnf(d1,plain,
sdtasdt0(xa,sK151(sK142)) = sK142,
inference(resolution,[status(thm)],[c169,c187]) ).
cnf(d2,plain,
( ~ aElement0(xa)
| ~ aElement0(sK151(sK142))
| aElement0(sK142) ),
inference(superposition,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( ~ aElement0(sK151(sK142))
| aElement0(sK142) ),
inference(resolution,[status(thm)],[c108,d2]) ).
cnf(d4,plain,
aElement0(sK151(sK142)),
inference(resolution,[status(thm)],[c169,c186]) ).
cnf(d5,plain,
aElement0(sK142),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( aElement0(xu)
| ~ aElement0(sK143) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
sdtasdt0(xb,sK154(sK143)) = sK143,
inference(resolution,[status(thm)],[c170,c190]) ).
cnf(d8,plain,
( ~ aElement0(xb)
| ~ aElement0(sK154(sK143))
| aElement0(sK143) ),
inference(superposition,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( ~ aElement0(sK154(sK143))
| aElement0(sK143) ),
inference(resolution,[status(thm)],[c109,d8]) ).
cnf(d10,plain,
aElement0(sK154(sK143)),
inference(resolution,[status(thm)],[c170,c189]) ).
cnf(d11,plain,
aElement0(sK143),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
aElement0(xu),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( ~ aElement0(X0)
| sdtasdt0(sK149,X0) = sdtasdt0(X0,sK149) ),
inference(resolution,[status(thm)],[c184,c11]) ).
cnf(d14,plain,
sdtasdt0(sK149,xu) = sdtasdt0(xu,sK149),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
sdtasdt0(sK149,xu) = xc,
inference(demodulation,[status(thm)],[d14,c185]) ).
cnf(d16,plain,
( ~ aElementOf0(xu,xI)
| ~ aElement0(sK149)
| aElementOf0(xc,xI) ),
inference(superposition,[status(thm)],[d15,c133]) ).
cnf(d17,plain,
~ aElementOf0(xc,xI),
inference(demodulation,[status(thm)],[c193,c145]) ).
cnf(d18,plain,
( ~ aElementOf0(xu,xI)
| ~ aElement0(sK149) ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
~ aElement0(sK149),
inference(resolution,[status(thm)],[c172,d18]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[c184,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG126+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:12:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.14/20.97 % SZS status Theorem for theBenchmark.p
% 28.14/20.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------