%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : RNG111+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 : n023.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 03:02:55 PM UTC 2025
% Result : Theorem 221.27s 28.15s
% Output : CNFRefutation 221.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 84 ( 45 unt; 0 def)
% Number of atoms : 200 ( 86 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 219 ( 103 ~; 88 |; 16 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 19 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
! [W0] :
( ( aElementOf0(W0,xI)
& W0 != sz00 )
=> ( ! [W1] :
( ( aElementOf0(W1,xI)
& W1 != sz00 )
=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
=> ? [W2] :
( aElementOf0(W2,xI)
& W2 != sz00
& ! [W3] :
( ( aElementOf0(W3,xI)
& W3 != sz00 )
=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) ) ) ) )
=> ? [W1] :
( aElementOf0(W1,xI)
& W1 != sz00
& ! [W2] :
( ( aElementOf0(W2,xI)
& W2 != sz00 )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ! [W0] :
( ( aElementOf0(W0,xI)
& W0 != sz00 )
=> ( ! [W1] :
( ( aElementOf0(W1,xI)
& W1 != sz00 )
=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))
=> ? [W2] :
( aElementOf0(W2,xI)
& W2 != sz00
& ! [W3] :
( ( aElementOf0(W3,xI)
& W3 != sz00 )
=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) ) ) ) )
=> ? [W1] :
( aElementOf0(W1,xI)
& W1 != sz00
& ! [W2] :
( ( aElementOf0(W2,xI)
& W2 != sz00 )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(110,plain,
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK29))
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK30(X0)))
| X0 = sz00
| X1 = sz00 ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aElementOf0(sK31(sK29),xI)
| ~ aElementOf0(sK31(sK30(sK31(sK29))),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| ~ iLess0(sbrdtbr0(sK31(sK30(sK31(sK29)))),sbrdtbr0(sK30(sK31(sK29))))
| sK31(sK29) = sz00
| sK31(sK30(sK31(sK29))) = sz00 ),
inference(instantiation,[status(thm)],[110]) ).
cnf(111,plain,
( ~ aElementOf0(X0,xI)
| X0 = sz00
| aElementOf0(sK31(X0),xI) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l1,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(113,plain,
( ~ aElementOf0(X0,xI)
| X0 = sz00
| iLess0(sbrdtbr0(sK31(X0)),sbrdtbr0(X0)) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l302,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(106,plain,
aElementOf0(sK29,xI),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l368,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l303,plain,
( ~ aElementOf0(sK30(sK31(sK29)),xI)
| sK30(sK31(sK29)) = sz00
| aElementOf0(sK31(sK30(sK31(sK29))),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(108,plain,
( ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK29))
| X0 = sz00
| aElementOf0(sK30(X0),xI) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l306,plain,
( ~ aElementOf0(sK31(sK29),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| sK31(sK29) = sz00
| aElementOf0(sK30(sK31(sK29)),xI) ),
inference(instantiation,[status(thm)],[108]) ).
cnf(107,plain,
sK29 != sz00,
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l304,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(112,plain,
( sK31(X0) != sz00
| ~ aElementOf0(X0,xI)
| X0 = sz00 ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l1070,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(109,plain,
( sK30(X0) != sz00
| ~ aElementOf0(X0,xI)
| ~ iLess0(sbrdtbr0(X0),sbrdtbr0(sK29))
| X0 = sz00 ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l305,plain,
( sK30(sK31(sK29)) != sz00
| ~ aElementOf0(sK31(sK29),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| sK31(sK29) = sz00 ),
inference(instantiation,[status(thm)],[109]) ).
cnf(l307,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l359,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l2,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l345,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l372,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l347,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l1249,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l358,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l334,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l309,plain,
( ~ aElementOf0(sK30(sK31(sK29)),xI)
| sK30(sK31(sK29)) = sz00
| iLess0(sbrdtbr0(sK31(sK30(sK31(sK29)))),sbrdtbr0(sK30(sK31(sK29)))) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l440,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l1248,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l6,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l501,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l442,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l311,plain,
( sK30(sK31(sK29)) != sz00
| ~ aElementOf0(sK31(sK29),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| sK31(sK29) = sz00 ),
inference(instantiation,[status(thm)],[109]) ).
cnf(l441,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l356,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l365,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l386,plain,
( ~ aElementOf0(sK31(sK29),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| sK31(sK29) = sz00
| aElementOf0(sK30(sK31(sK29)),xI) ),
inference(instantiation,[status(thm)],[108]) ).
cnf(l352,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l1071,plain,
( sK31(sK30(sK31(sK29))) != sz00
| ~ aElementOf0(sK30(sK31(sK29)),xI)
| sK30(sK31(sK29)) = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l335,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l315,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l765,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l563,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l360,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l390,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l472,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l460,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l479,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l411,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l363,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l366,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l374,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l699,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l361,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l476,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l481,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1206,plain,
( ~ aElementOf0(sK31(sK29),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| sK31(sK29) = sz00
| aElementOf0(sK30(sK31(sK29)),xI) ),
inference(instantiation,[status(thm)],[108]) ).
cnf(l1227,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l728,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l1232,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l698,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1235,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l450,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l415,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l529,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l1207,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l1366,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l1370,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l1228,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1072,plain,
( sK30(sK31(sK29)) != sz00
| ~ aElementOf0(sK31(sK29),xI)
| ~ iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29))
| sK31(sK29) = sz00 ),
inference(instantiation,[status(thm)],[109]) ).
cnf(l1084,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| aElementOf0(sK31(sK29),xI) ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l1371,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1216,plain,
( sK31(sK29) != sz00
| ~ aElementOf0(sK29,xI)
| sK29 = sz00 ),
inference(instantiation,[status(thm)],[112]) ).
cnf(l1226,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l1233,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1240,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l1113,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1120,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(l1083,plain,
( ~ aElementOf0(sK29,xI)
| sK29 = sz00
| iLess0(sbrdtbr0(sK31(sK29)),sbrdtbr0(sK29)) ),
inference(instantiation,[status(thm)],[113]) ).
cnf(l1088,plain,
aElementOf0(sK29,xI),
inference(instantiation,[status(thm)],[106]) ).
cnf(l1103,plain,
sK29 != sz00,
inference(instantiation,[status(thm)],[107]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l302,l368,l303,l306,l304,l1070,l305,l307,l359,l2,l345,l372,l347,l1249,l358,l334,l309,l440,l1248,l6,l501,l442,l311,l441,l356,l365,l386,l352,l1071,l335,l315,l765,l563,l360,l390,l472,l460,l479,l411,l363,l366,l374,l699,l361,l476,l481,l1206,l1227,l728,l1232,l698,l1235,l450,l415,l529,l1207,l1366,l1370,l1228,l1072,l1084,l1371,l1216,l1226,l1233,l1240,l1113,l1120,l1083,l1088,l1103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG111+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 18:03:04 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.36 % launching worker at depth: 9
% 0.20/0.42 % launching worker at depth: 10
% 8.02/1.37 % launching worker at depth: 11
% 221.27/28.15 % SZS status Theorem for theBenchmark
% 221.27/28.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------