%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : RNG091+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:02:52 PM UTC 2025
% Result : Theorem 5.49s 1.04s
% Output : CNFRefutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 22 unt; 0 def)
% Number of atoms : 112 ( 18 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 101 ( 29 ~; 30 |; 32 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 35 ( 2 sgn 10 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( ( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& sdtpldt0(W0,W1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& sdtpldt0(W0,W1) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( ( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& sdtpldt0(W0,W1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& sdtpldt0(W0,W1) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(85,plain,
( sdtpldt0(X0,X1) != sdtpldt0(xx,xy)
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sP4(X2,X3) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(xx,xy)
| ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| sP4(sdtasdt0(xz,xl),sdtasdt0(xz,xk)) ),
inference(instantiation,[status(thm)],[85]) ).
cnf(88,plain,
( sdtpldt0(X0,X1) != sdtasdt0(xz,xx)
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| ~ sP4(X1,X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l21,plain,
( sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) != sdtasdt0(xz,xx)
| ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ sP4(sdtasdt0(xz,xl),sdtasdt0(xz,xk)) ),
inference(instantiation,[status(thm)],[88]) ).
fof(m__1021,plain,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1021) ).
cnf(82,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(cnf,[status(esa)],[m__1021]) ).
cnf(l39,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(instantiation,[status(thm)],[82]) ).
fof(mDefIdeal,plain,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
cnf(50,plain,
( ~ aElement0(X0)
| ~ aIdeal0(X1)
| ~ aElementOf0(X2,X1)
| aElementOf0(sdtasdt0(X0,X2),X1) ),
inference(cnf,[status(esa)],[mDefIdeal]) ).
cnf(l40,plain,
( ~ aElement0(xz)
| ~ aIdeal0(xI)
| ~ aElementOf0(xk,xI)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(instantiation,[status(thm)],[50]) ).
fof(m__870,plain,
( aSet0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
cnf(61,plain,
( ~ aElementOf0(X0,xJ)
| ~ aElementOf0(X1,xJ)
| aElementOf0(sdtpldt0(X0,X1),xJ) ),
inference(cnf,[status(esa)],[m__870]) ).
cnf(l4,plain,
( ~ aElementOf0(xl,xJ)
| ~ aElementOf0(xn,xJ)
| aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(instantiation,[status(thm)],[61]) ).
fof(m__1098,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1098) ).
cnf(84,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(cnf,[status(esa)],[m__1098]) ).
cnf(l48,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(instantiation,[status(thm)],[84]) ).
cnf(59,plain,
aIdeal0(xI),
inference(cnf,[status(esa)],[m__870]) ).
cnf(l67,plain,
aIdeal0(xI),
inference(instantiation,[status(thm)],[59]) ).
fof(m__901,plain,
( ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& sdtpldt0(W0,W1) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& sdtpldt0(W0,W1) = xy )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
cnf(72,plain,
aElement0(xz),
inference(cnf,[status(esa)],[m__901]) ).
cnf(l60,plain,
aElement0(xz),
inference(instantiation,[status(thm)],[72]) ).
fof(m__1061,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1061) ).
cnf(83,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(cnf,[status(esa)],[m__1061]) ).
cnf(l9,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(instantiation,[status(thm)],[83]) ).
cnf(57,plain,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X0,X1),xI) ),
inference(cnf,[status(esa)],[m__870]) ).
cnf(l1,plain,
( ~ aElementOf0(xk,xI)
| ~ aElementOf0(xm,xI)
| aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(instantiation,[status(thm)],[57]) ).
fof(m__967,plain,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
cnf(76,plain,
aElementOf0(xm,xI),
inference(cnf,[status(esa)],[m__967]) ).
cnf(l20,plain,
aElementOf0(xm,xI),
inference(instantiation,[status(thm)],[76]) ).
fof(m__934,plain,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
cnf(74,plain,
aElementOf0(xl,xJ),
inference(cnf,[status(esa)],[m__934]) ).
cnf(l8,plain,
aElementOf0(xl,xJ),
inference(instantiation,[status(thm)],[74]) ).
cnf(73,plain,
aElementOf0(xk,xI),
inference(cnf,[status(esa)],[m__934]) ).
cnf(l5,plain,
aElementOf0(xk,xI),
inference(instantiation,[status(thm)],[73]) ).
cnf(77,plain,
aElementOf0(xn,xJ),
inference(cnf,[status(esa)],[m__967]) ).
cnf(l10,plain,
aElementOf0(xn,xJ),
inference(instantiation,[status(thm)],[77]) ).
cnf(l63,plain,
aElementOf0(xk,xI),
inference(instantiation,[status(thm)],[73]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l21,l39,l40,l4,l48,l67,l60,l9,l1,l20,l8,l5,l10,l63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG091+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 17:55:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 5.49/1.04 % SZS status Theorem for theBenchmark
% 5.49/1.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------