%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG090+2 : 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 : n012.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 15.79s 2.37s
% Output : CNFRefutation 15.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 23 unt; 0 def)
% Number of atoms : 134 ( 30 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 144 ( 67 ~; 50 |; 16 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 30 ( 0 sgn 15 !; 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(m__870,hypothesis,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& 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__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(c65,plain,
aSet0(xI),
inference(clausification,[status(esa)],[m__870]) ).
cnf(c69,plain,
aSet0(xJ),
inference(clausification,[status(esa)],[m__870]) ).
cnf(c82,plain,
aElementOf0(xk,xI),
inference(clausification,[status(esa)],[m__934]) ).
cnf(c83,plain,
aElementOf0(xl,xJ),
inference(clausification,[status(esa)],[m__934]) ).
cnf(c84,plain,
xx = sdtpldt0(xk,xl),
inference(clausification,[status(esa)],[m__934]) ).
cnf(c85,plain,
aElementOf0(xm,xI),
inference(clausification,[status(esa)],[m__967]) ).
cnf(c86,plain,
aElementOf0(xn,xJ),
inference(clausification,[status(esa)],[m__967]) ).
cnf(c87,plain,
xy = sdtpldt0(xm,xn),
inference(clausification,[status(esa)],[m__967]) ).
cnf(c89,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(clausification,[status(esa)],[m__994]) ).
cnf(c92,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,c92]) ).
cnf(d1,plain,
( ~ aSet0(xI)
| aElement0(xk) ),
inference(resolution,[status(thm)],[c23,c82]) ).
cnf(d2,plain,
aElement0(xk),
inference(resolution,[status(thm)],[c65,d1]) ).
cnf(d3,plain,
( ~ aElement0(xm)
| ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ aSet0(xI)
| aElement0(xm) ),
inference(resolution,[status(thm)],[c23,c85]) ).
cnf(d5,plain,
aElement0(xm),
inference(resolution,[status(thm)],[c65,d4]) ).
cnf(d6,plain,
( ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ aSet0(xJ)
| aElement0(sdtpldt0(xl,xn)) ),
inference(resolution,[status(thm)],[c23,c89]) ).
cnf(d8,plain,
aElement0(sdtpldt0(xl,xn)),
inference(resolution,[status(thm)],[c69,d7]) ).
cnf(d9,plain,
sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X2)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(X2,sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c5]) ).
cnf(d11,plain,
( ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xn,xm))) ),
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ aElement0(xn)
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xn,xm))) ),
inference(resolution,[status(thm)],[d5,d11]) ).
cnf(d13,plain,
( ~ aSet0(xJ)
| aElement0(xn) ),
inference(resolution,[status(thm)],[c23,c86]) ).
cnf(d14,plain,
aElement0(xn),
inference(resolution,[status(thm)],[c69,d13]) ).
cnf(d15,plain,
( ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xn,xm))) ),
inference(resolution,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
( ~ aSet0(xJ)
| aElement0(xl) ),
inference(resolution,[status(thm)],[c23,c83]) ).
cnf(d17,plain,
aElement0(xl),
inference(resolution,[status(thm)],[c69,d16]) ).
cnf(d18,plain,
( ~ aElement0(sdtpldt0(xl,xn))
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xn,xm))) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xn,xm))),
inference(resolution,[status(thm)],[d8,d18]) ).
cnf(d20,plain,
( ~ aElement0(xn)
| ~ aElement0(xm)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) ),
inference(superposition,[status(thm)],[c5,d19]) ).
cnf(d21,plain,
( ~ aElement0(xn)
| ~ aElement0(xm)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,xy)) ),
inference(demodulation,[status(thm)],[d20,c87]) ).
cnf(d22,plain,
( ~ aElement0(xn)
| sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,xy)) ),
inference(resolution,[status(thm)],[d5,d21]) ).
cnf(d23,plain,
sdtpldt0(xx,xy) != sdtpldt0(xk,sdtpldt0(xl,xy)),
inference(resolution,[status(thm)],[d14,d22]) ).
cnf(d24,plain,
( ~ aElement0(xk)
| ~ aElement0(xl)
| ~ aElement0(X0)
| sdtpldt0(xx,X0) = sdtpldt0(xk,sdtpldt0(xl,X0)) ),
inference(superposition,[status(thm)],[c84,c6]) ).
cnf(d25,plain,
( ~ aElement0(xl)
| ~ aElement0(X0)
| sdtpldt0(xx,X0) = sdtpldt0(xk,sdtpldt0(xl,X0)) ),
inference(resolution,[status(thm)],[d2,d24]) ).
cnf(d26,plain,
( ~ aElement0(X0)
| sdtpldt0(xx,X0) = sdtpldt0(xk,sdtpldt0(xl,X0)) ),
inference(resolution,[status(thm)],[d17,d25]) ).
cnf(d27,plain,
( ~ aElement0(xy)
| sdtpldt0(xx,xy) != sdtpldt0(xx,xy) ),
inference(superposition,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
( ~ aElement0(xm)
| ~ aElement0(xn)
| aElement0(xy) ),
inference(superposition,[status(thm)],[c87,c3]) ).
cnf(d29,plain,
( ~ aElement0(xn)
| aElement0(xy) ),
inference(resolution,[status(thm)],[d5,d28]) ).
cnf(d30,plain,
aElement0(xy),
inference(resolution,[status(thm)],[d14,d29]) ).
cnf(d31,plain,
sdtpldt0(xx,xy) != sdtpldt0(xx,xy),
inference(resolution,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
$false,
inference(equality_resolution,[status(thm)],[d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG090+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 06:02:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.79/2.37 % SZS status Theorem for theBenchmark.p
% 15.79/2.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------