%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG090+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 08:25:50 AM UTC 2026
% Result : Theorem 32.66s 7.77s
% Output : CNFRefutation 32.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 25 unt; 1 def)
% Number of atoms : 127 ( 30 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 124 ( 58 ~; 45 |; 12 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(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(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(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ) ).
fof(m__934,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ) ).
fof(m__967,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ) ).
fof(m__,conjecture,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) ).
fof(negated_conjecture,negated_conjecture,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c3,plain,
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
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(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(c65,plain,
aIdeal0(xI),
inference(clausification,[status(esa)],[m__870]) ).
cnf(c66,plain,
aIdeal0(xJ),
inference(clausification,[status(esa)],[m__870]) ).
cnf(c70,plain,
aElementOf0(xk,xI),
inference(clausification,[status(esa)],[m__934]) ).
cnf(c71,plain,
aElementOf0(xl,xJ),
inference(clausification,[status(esa)],[m__934]) ).
cnf(c72,plain,
xx = sdtpldt0(xk,xl),
inference(clausification,[status(esa)],[m__934]) ).
cnf(c73,plain,
aElementOf0(xm,xI),
inference(clausification,[status(esa)],[m__967]) ).
cnf(c74,plain,
aElementOf0(xn,xJ),
inference(clausification,[status(esa)],[m__967]) ).
cnf(c75,plain,
xy = sdtpldt0(xm,xn),
inference(clausification,[status(esa)],[m__967]) ).
cnf(c77,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(clausification,[status(esa)],[m__994]) ).
cnf(c80,plain,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aElement0(xk)
| ~ aElement0(xm)
| ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) ),
inference(superposition,[status(thm)],[c6,c80]) ).
cnf(d1,plain,
( ~ aSet0(xI)
| aElement0(xm) ),
inference(resolution,[status(thm)],[c23,c73]) ).
cnf(d2,plain,
aSet0(xI),
inference(resolution,[status(thm)],[c55,c65]) ).
cnf(d3,plain,
aElement0(xm),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ aElement0(xk)
| ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ aSet0(xI)
| aElement0(xk) ),
inference(resolution,[status(thm)],[c23,c70]) ).
cnf(d6,plain,
aElement0(xk),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
( ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( ~ aSet0(xJ)
| aElement0(sdtpldt0(xl,xn)) ),
inference(resolution,[status(thm)],[c23,c77]) ).
cnf(d9,plain,
aSet0(xJ),
inference(resolution,[status(thm)],[c55,c66]) ).
cnf(d10,plain,
aElement0(sdtpldt0(xl,xn)),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ aElement0(xm)
| ~ aElement0(xn)
| ~ aElement0(X0)
| sdtpldt0(xy,X0) = sdtpldt0(xm,sdtpldt0(xn,X0)) ),
inference(superposition,[status(thm)],[c75,c6]) ).
cnf(d13,plain,
( ~ aElement0(xn)
| ~ aElement0(X0)
| sdtpldt0(xy,X0) = sdtpldt0(xm,sdtpldt0(xn,X0)) ),
inference(resolution,[status(thm)],[d3,d12]) ).
cnf(d14,plain,
( ~ aSet0(xJ)
| aElement0(xn) ),
inference(resolution,[status(thm)],[c23,c74]) ).
cnf(d15,plain,
aElement0(xn),
inference(resolution,[status(thm)],[d9,d14]) ).
cnf(d16,plain,
( ~ aElement0(X0)
| sdtpldt0(xy,X0) = sdtpldt0(xm,sdtpldt0(xn,X0)) ),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( ~ aElement0(X0)
| ~ aElement0(xn)
| ~ aElement0(X0)
| sdtpldt0(xy,X0) = sdtpldt0(xm,sdtpldt0(X0,xn)) ),
inference(superposition,[status(thm)],[c5,d16]) ).
cnf(d18,plain,
( ~ aElement0(X0)
| sdtpldt0(xy,X0) = sdtpldt0(xm,sdtpldt0(X0,xn)) ),
inference(resolution,[status(thm)],[d15,d17]) ).
cnf(d19,plain,
( ~ aElement0(xl)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xy,xl)) ),
inference(superposition,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
( ~ aSet0(xJ)
| aElement0(xl) ),
inference(resolution,[status(thm)],[c23,c71]) ).
cnf(d21,plain,
aElement0(xl),
inference(resolution,[status(thm)],[d9,d20]) ).
cnf(d22,plain,
sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xy,xl)),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( ~ aElement0(xl)
| ~ aElement0(xy)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,xy)) ),
inference(superposition,[status(thm)],[c5,d22]) ).
cnf(d24,plain,
( ~ aElement0(xy)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,xy)) ),
inference(resolution,[status(thm)],[d21,d23]) ).
cnf(d25,plain,
( ~ aElement0(xm)
| ~ aElement0(xn)
| aElement0(xy) ),
inference(superposition,[status(thm)],[c75,c3]) ).
cnf(d26,plain,
( ~ aElement0(xn)
| aElement0(xy) ),
inference(resolution,[status(thm)],[d3,d25]) ).
cnf(d27,plain,
aElement0(xy),
inference(resolution,[status(thm)],[d15,d26]) ).
cnf(d28,plain,
sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,xy)),
inference(resolution,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
( ~ aElement0(xk)
| ~ aElement0(xl)
| ~ aElement0(X0)
| sdtpldt0(xx,X0) = sdtpldt0(xk,sdtpldt0(xl,X0)) ),
inference(superposition,[status(thm)],[c72,c6]) ).
cnf(d30,plain,
( ~ aElement0(xl)
| ~ aElement0(X0)
| sdtpldt0(xx,X0) = sdtpldt0(xk,sdtpldt0(xl,X0)) ),
inference(resolution,[status(thm)],[d6,d29]) ).
cnf(d31,plain,
( ~ aElement0(X0)
| sdtpldt0(xx,X0) = sdtpldt0(xk,sdtpldt0(xl,X0)) ),
inference(resolution,[status(thm)],[d21,d30]) ).
cnf(d32,plain,
( ~ aElement0(xy)
| sdtpldt0(xx,xy) != sdtpldt0(xx,xy) ),
inference(superposition,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
sdtpldt0(xx,xy) != sdtpldt0(xx,xy),
inference(resolution,[status(thm)],[d27,d32]) ).
cnf(d34,plain,
$false,
inference(equality_resolution,[status(thm)],[d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 06:04:21 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.66/7.77 % SZS status Theorem for theBenchmark.p
% 32.66/7.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------