%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : RNG115+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n027.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 03:02:56 PM UTC 2025
% Result : Theorem 14.02s 2.06s
% Output : CNFRefutation 14.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 120 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 123 ( 50 ~; 44 |; 17 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 38 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& xu = sdtpldt0(W0,W1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [W0,W1] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& xu = sdtpldt0(W0,W1) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(110,plain,
( xu != sdtpldt0(X0,X1)
| ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( xu != sdtpldt0(sK3(slsdtgt0(xa),slsdtgt0(xb),xI,xu),sK4(slsdtgt0(xa),slsdtgt0(xb),xI,xu))
| ~ aElementOf0(sK3(slsdtgt0(xa),slsdtgt0(xb),xI,xu),slsdtgt0(xa))
| ~ aElementOf0(sK4(slsdtgt0(xa),slsdtgt0(xb),xI,xu),slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[110]) ).
fof(mDefSSum,plain,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( aElementOf0(W4,W0)
& aElementOf0(W5,W1)
& sdtpldt0(W4,W5) = W3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
cnf(31,plain,
( X0 != sdtpldt1(X1,X2)
| ~ aElementOf0(X3,X0)
| ~ aSet0(X1)
| ~ aSet0(X2)
| sdtpldt0(sK3(X1,X2,X0,X3),sK4(X1,X2,X0,X3)) = X3 ),
inference(cnf,[status(esa)],[mDefSSum]) ).
cnf(l16,plain,
( xI != sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
| ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xb))
| sdtpldt0(sK3(slsdtgt0(xa),slsdtgt0(xb),xI,xu),sK4(slsdtgt0(xa),slsdtgt0(xb),xI,xu)) = xu ),
inference(instantiation,[status(thm)],[31]) ).
fof(m__2273,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [W0] :
( ( aElementOf0(W0,xI)
& W0 != sz00 )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
cnf(106,plain,
aElementOf0(xu,xI),
inference(cnf,[status(esa)],[m__2273]) ).
cnf(l56,plain,
aElementOf0(xu,xI),
inference(instantiation,[status(thm)],[106]) ).
fof(mDefPrIdeal,plain,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& sdtasdt0(W0,W3) = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
cnf(84,plain,
( ~ aElement0(X0)
| X1 != slsdtgt0(X0)
| aSet0(X1) ),
inference(cnf,[status(esa)],[mDefPrIdeal]) ).
cnf(l32,plain,
( ~ aElement0(xa)
| slsdtgt0(xa) != slsdtgt0(xa)
| aSet0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[84]) ).
cnf(l59,plain,
( ~ aElement0(xb)
| slsdtgt0(xb) != slsdtgt0(xb)
| aSet0(slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[84]) ).
fof(m__2174,plain,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
cnf(99,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(cnf,[status(esa)],[m__2174]) ).
cnf(l55,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(instantiation,[status(thm)],[99]) ).
fof(m__2091,plain,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
cnf(94,plain,
aElement0(xa),
inference(cnf,[status(esa)],[m__2091]) ).
cnf(l73,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[94]) ).
cnf(95,plain,
aElement0(xb),
inference(cnf,[status(esa)],[m__2091]) ).
cnf(l71,plain,
aElement0(xb),
inference(instantiation,[status(thm)],[95]) ).
cnf(29,plain,
( X0 != sdtpldt1(X1,X2)
| ~ aElementOf0(X3,X0)
| ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(sK3(X1,X2,X0,X3),X1) ),
inference(cnf,[status(esa)],[mDefSSum]) ).
cnf(l1,plain,
( xI != sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
| ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xb))
| aElementOf0(sK3(slsdtgt0(xa),slsdtgt0(xb),xI,xu),slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[29]) ).
cnf(30,plain,
( X0 != sdtpldt1(X1,X2)
| ~ aElementOf0(X3,X0)
| ~ aSet0(X1)
| ~ aSet0(X2)
| aElementOf0(sK4(X1,X2,X0,X3),X2) ),
inference(cnf,[status(esa)],[mDefSSum]) ).
cnf(l25,plain,
( xI != sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
| ~ aElementOf0(xu,xI)
| ~ aSet0(slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xb))
| aElementOf0(sK4(slsdtgt0(xa),slsdtgt0(xb),xI,xu),slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[30]) ).
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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
cnf(48,plain,
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf,[status(esa)],[mDefIdeal]) ).
cnf(l177,plain,
( ~ aIdeal0(slsdtgt0(xb))
| aSet0(slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l91,plain,
( ~ aIdeal0(slsdtgt0(xb))
| aSet0(slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l90,plain,
aElementOf0(xu,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l45,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(instantiation,[status(thm)],[99]) ).
cnf(l5,plain,
aElementOf0(xu,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l65,plain,
( ~ aIdeal0(slsdtgt0(xa))
| aSet0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[48]) ).
fof(mPrIdeal,plain,
! [W0] :
( aElement0(W0)
=> aIdeal0(slsdtgt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrIdeal) ).
cnf(93,plain,
( ~ aElement0(X0)
| aIdeal0(slsdtgt0(X0)) ),
inference(cnf,[status(esa)],[mPrIdeal]) ).
cnf(l323,plain,
( ~ aElement0(xb)
| aIdeal0(slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[93]) ).
cnf(l106,plain,
( ~ aElement0(xa)
| aIdeal0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[93]) ).
cnf(l3,plain,
( ~ aIdeal0(slsdtgt0(xa))
| aSet0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l31,plain,
( ~ aElement0(xa)
| aIdeal0(slsdtgt0(xa)) ),
inference(instantiation,[status(thm)],[93]) ).
cnf(l8,plain,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(instantiation,[status(thm)],[99]) ).
cnf(l92,plain,
( ~ aElement0(xb)
| aIdeal0(slsdtgt0(xb)) ),
inference(instantiation,[status(thm)],[93]) ).
cnf(l342,plain,
aElement0(xb),
inference(instantiation,[status(thm)],[95]) ).
cnf(l351,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[94]) ).
cnf(l95,plain,
aElement0(xb),
inference(instantiation,[status(thm)],[95]) ).
cnf(l38,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[94]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l16,l56,l32,l59,l55,l73,l71,l1,l25,l177,l91,l90,l45,l5,l65,l323,l106,l3,l31,l8,l92,l342,l351,l95,l38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : RNG115+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.09 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n027.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 18:04:19 EDT 2025
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % launching worker at depth: 1
% 0.09/0.30 % launching worker at depth: 4
% 0.09/0.30 % launching worker at depth: 2
% 0.09/0.30 % launching worker at depth: 3
% 0.09/0.30 % launching worker at depth: 5
% 0.09/0.30 % launching worker at depth: 6
% 0.09/0.30 % launching worker at depth: 7
% 0.09/0.30 % launching worker at depth: 8
% 0.09/0.30 % launching worker at depth: 9
% 0.14/0.33 % launching worker at depth: 10
% 0.14/0.35 % launching worker at depth: 11
% 14.02/2.06 % SZS status Theorem for theBenchmark
% 14.02/2.06 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------