%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : RNG087+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 : n031.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 03:02:51 PM UTC 2025
% Result : Theorem 4.92s 0.95s
% Output : CNFRefutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 89 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 38 ~; 35 |; 13 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 5 con; 0-4 aty)
% Number of variables : 29 ( 0 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& xy = sdtpldt0(W0,W1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [W0,W1] :
( aElementOf0(W0,xI)
& aElementOf0(W1,xJ)
& xy = sdtpldt0(W0,W1) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(64,plain,
( xy != sdtpldt0(X0,X1)
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( xy != sdtpldt0(sK3(xI,xJ,sdtpldt1(xI,xJ),xy),sK4(xI,xJ,sdtpldt1(xI,xJ),xy))
| ~ aElementOf0(sK3(xI,xJ,sdtpldt1(xI,xJ),xy),xI)
| ~ aElementOf0(sK4(xI,xJ,sdtpldt1(xI,xJ),xy),xJ) ),
inference(instantiation,[status(thm)],[64]) ).
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(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(l3,plain,
( sdtpldt1(xI,xJ) != sdtpldt1(xI,xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| ~ aSet0(xI)
| ~ aSet0(xJ)
| aElementOf0(sK4(xI,xJ,sdtpldt1(xI,xJ),xy),xJ) ),
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(l164,plain,
( ~ aIdeal0(xJ)
| aSet0(xJ) ),
inference(instantiation,[status(thm)],[48]) ).
fof(m__870,plain,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
cnf(57,plain,
aIdeal0(xJ),
inference(cnf,[status(esa)],[m__870]) ).
cnf(l219,plain,
aIdeal0(xJ),
inference(instantiation,[status(thm)],[57]) ).
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(l8,plain,
( sdtpldt1(xI,xJ) != sdtpldt1(xI,xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| ~ aSet0(xI)
| ~ aSet0(xJ)
| sdtpldt0(sK3(xI,xJ,sdtpldt1(xI,xJ),xy),sK4(xI,xJ,sdtpldt1(xI,xJ),xy)) = xy ),
inference(instantiation,[status(thm)],[31]) ).
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,
( sdtpldt1(xI,xJ) != sdtpldt1(xI,xJ)
| ~ aElementOf0(xy,sdtpldt1(xI,xJ))
| ~ aSet0(xI)
| ~ aSet0(xJ)
| aElementOf0(sK3(xI,xJ,sdtpldt1(xI,xJ),xy),xI) ),
inference(instantiation,[status(thm)],[29]) ).
cnf(l33,plain,
( ~ aIdeal0(xJ)
| aSet0(xJ) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l163,plain,
( ~ aIdeal0(xI)
| aSet0(xI) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l120,plain,
aIdeal0(xJ),
inference(instantiation,[status(thm)],[57]) ).
fof(m__901,plain,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__901) ).
cnf(59,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(cnf,[status(esa)],[m__901]) ).
cnf(l18,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(instantiation,[status(thm)],[59]) ).
cnf(l191,plain,
( ~ aIdeal0(xI)
| aSet0(xI) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l61,plain,
( ~ aIdeal0(xI)
| aSet0(xI) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l6,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(instantiation,[status(thm)],[59]) ).
cnf(56,plain,
aIdeal0(xI),
inference(cnf,[status(esa)],[m__870]) ).
cnf(l196,plain,
aIdeal0(xI),
inference(instantiation,[status(thm)],[56]) ).
cnf(l166,plain,
aIdeal0(xI),
inference(instantiation,[status(thm)],[56]) ).
cnf(l69,plain,
aIdeal0(xI),
inference(instantiation,[status(thm)],[56]) ).
cnf(l172,plain,
( ~ aIdeal0(xJ)
| aSet0(xJ) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l296,plain,
aIdeal0(xJ),
inference(instantiation,[status(thm)],[57]) ).
cnf(l9,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(instantiation,[status(thm)],[59]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l164,l219,l8,l1,l33,l163,l120,l18,l191,l61,l6,l196,l166,l69,l172,l296,l9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : RNG087+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n031.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 17:54:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.34 % launching worker at depth: 1
% 0.19/0.34 % launching worker at depth: 2
% 0.19/0.34 % launching worker at depth: 4
% 0.19/0.34 % launching worker at depth: 6
% 0.19/0.34 % launching worker at depth: 5
% 0.19/0.34 % launching worker at depth: 8
% 0.19/0.34 % launching worker at depth: 7
% 0.19/0.34 % launching worker at depth: 3
% 0.19/0.34 % launching worker at depth: 9
% 0.19/0.35 % launching worker at depth: 10
% 0.19/0.39 % launching worker at depth: 11
% 4.92/0.95 % SZS status Theorem for theBenchmark
% 4.92/0.95 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------