TSTP Solution File: LCL463+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL463+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n004.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 : Thu Aug 31 08:23:55 EDT 2023
% Result : Theorem 65.09s 9.72s
% Output : Refutation 65.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 19
% Syntax : Number of formulae : 182 ( 79 unt; 0 def)
% Number of atoms : 316 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 249 ( 115 ~; 109 |; 2 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 346 (; 342 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f171779,plain,
$false,
inference(subsumption_resolution,[],[f101,f171739]) ).
fof(f171739,plain,
! [X852,X851] : is_a_theorem(implies(X851,implies(X852,X851))),
inference(forward_demodulation,[],[f169081,f168820]) ).
fof(f168820,plain,
! [X2,X3] : or(not(X2),X3) = implies(X2,X3),
inference(superposition,[],[f124,f167559]) ).
fof(f167559,plain,
! [X58] : not(not(X58)) = X58,
inference(subsumption_resolution,[],[f167558,f146075]) ).
fof(f146075,plain,
! [X597] : is_a_theorem(or(not(X597),X597)),
inference(backward_demodulation,[],[f128487,f146070]) ).
fof(f146070,plain,
! [X1399,X1400,X1401] : implies(implies(equiv(X1399,X1399),not(X1400)),X1401) = or(X1400,X1401),
inference(subsumption_resolution,[],[f122196,f146045]) ).
fof(f146045,plain,
! [X21,X19,X20] : is_a_theorem(implies(implies(implies(X19,not(X20)),X21),or(X20,X21))),
inference(resolution,[],[f145890,f221]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X2))
| is_a_theorem(implies(implies(X2,X1),or(X0,X1))) ),
inference(forward_demodulation,[],[f220,f124]) ).
fof(f220,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f185,f124]) ).
fof(f185,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f106,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f96,f83]) ).
fof(f83,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',luka_modus_ponens) ).
fof(f96,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',modus_ponens) ).
fof(f106,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(subsumption_resolution,[],[f97,f79]) ).
fof(f79,plain,
cn1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
cn1,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',luka_cn1) ).
fof(f97,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
( cn1
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f56,plain,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
( cn1
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',cn1) ).
fof(f145890,plain,
! [X133,X131] : is_a_theorem(or(X133,implies(X131,not(X133)))),
inference(forward_demodulation,[],[f145329,f145068]) ).
fof(f145068,plain,
! [X856,X857] : or(X856,and(X857,not(X857))) = X856,
inference(resolution,[],[f125488,f56694]) ).
fof(f56694,plain,
! [X8,X9] : is_a_theorem(implies(and(X8,not(X8)),X9)),
inference(resolution,[],[f56690,f19386]) ).
fof(f19386,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(resolution,[],[f5077,f1068]) ).
fof(f1068,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X2),X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f604,f769]) ).
fof(f769,plain,
! [X10,X9] :
( ~ is_a_theorem(implies(X9,or(X10,X10)))
| is_a_theorem(X10)
| ~ is_a_theorem(X9) ),
inference(resolution,[],[f683,f105]) ).
fof(f683,plain,
! [X8,X9] :
( is_a_theorem(implies(implies(X8,or(X9,X9)),X9))
| ~ is_a_theorem(X8) ),
inference(resolution,[],[f671,f242]) ).
fof(f242,plain,
! [X19,X20] :
( ~ is_a_theorem(implies(X19,or(X20,X20)))
| is_a_theorem(implies(X19,X20)) ),
inference(resolution,[],[f218,f136]) ).
fof(f136,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(backward_demodulation,[],[f102,f124]) ).
fof(f102,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(subsumption_resolution,[],[f93,f82]) ).
fof(f82,plain,
cn3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
cn3,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',luka_cn3) ).
fof(f93,plain,
! [X0] :
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
( cn3
=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f54,plain,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
( cn3
<=> ! [X3] : is_a_theorem(implies(implies(not(X3),X3),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',cn3) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f185,f105]) ).
fof(f671,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f595,f242]) ).
fof(f595,plain,
! [X6,X7,X5] :
( is_a_theorem(implies(implies(X5,X6),or(X7,X6)))
| ~ is_a_theorem(X5) ),
inference(resolution,[],[f580,f221]) ).
fof(f580,plain,
! [X2,X1] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f450,f428]) ).
fof(f428,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),X1))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f416,f124]) ).
fof(f416,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f408,f242]) ).
fof(f408,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),or(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f221,f137]) ).
fof(f137,plain,
! [X2,X1] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X1) ),
inference(backward_demodulation,[],[f108,f124]) ).
fof(f108,plain,
! [X2,X1] :
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f105,f103]) ).
fof(f103,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(subsumption_resolution,[],[f94,f80]) ).
fof(f80,plain,
cn2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',luka_cn2) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
( cn2
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,plain,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
( cn2
<=> ! [X3,X4] : is_a_theorem(implies(X3,implies(not(X3),X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',cn2) ).
fof(f450,plain,
! [X10,X11,X12] :
( ~ is_a_theorem(implies(or(not(X10),X12),X11))
| is_a_theorem(or(X10,X11)) ),
inference(resolution,[],[f409,f105]) ).
fof(f409,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(or(not(X3),X4),X5),or(X3,X5))),
inference(resolution,[],[f221,f151]) ).
fof(f151,plain,
! [X2,X3] : is_a_theorem(or(X2,or(not(X2),X3))),
inference(superposition,[],[f138,f124]) ).
fof(f138,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(backward_demodulation,[],[f103,f124]) ).
fof(f604,plain,
! [X10,X8,X9,X7] :
( is_a_theorem(implies(implies(or(X7,X8),X9),or(X10,X9)))
| ~ is_a_theorem(X7) ),
inference(resolution,[],[f582,f221]) ).
fof(f582,plain,
! [X8,X6,X7] :
( is_a_theorem(or(X6,or(X7,X8)))
| ~ is_a_theorem(X7) ),
inference(resolution,[],[f450,f420]) ).
fof(f420,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f408,f124]) ).
fof(f5077,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(equiv(X0,X1),X2),implies(and(X0,not(X1)),X2))),
inference(resolution,[],[f5062,f219]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,not(X0)))
| is_a_theorem(implies(or(X0,X1),implies(X2,X1))) ),
inference(superposition,[],[f185,f124]) ).
fof(f5062,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(equiv(X0,X1)))),
inference(superposition,[],[f318,f100]) ).
fof(f100,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(subsumption_resolution,[],[f91,f85]) ).
fof(f85,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',luka_op_equiv) ).
fof(f91,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',op_equiv) ).
fof(f318,plain,
! [X50,X48,X49,X47] : is_a_theorem(implies(and(X47,not(X48)),not(and(implies(X47,X48),implies(X49,X50))))),
inference(superposition,[],[f114,f111]) ).
fof(f111,plain,
! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))),
inference(superposition,[],[f98,f98]) ).
fof(f98,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(subsumption_resolution,[],[f89,f84]) ).
fof(f84,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',hilbert_op_implies_and) ).
fof(f89,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',op_implies_and) ).
fof(f114,plain,
! [X6,X7,X5] : is_a_theorem(implies(and(X5,not(X6)),implies(implies(X5,X6),X7))),
inference(superposition,[],[f103,f98]) ).
fof(f56690,plain,
! [X1] : is_a_theorem(equiv(X1,X1)),
inference(subsumption_resolution,[],[f56673,f254]) ).
fof(f254,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f242,f138]) ).
fof(f56673,plain,
! [X1] :
( is_a_theorem(equiv(X1,X1))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f3564,f2649]) ).
fof(f2649,plain,
! [X46,X44,X45] :
( is_a_theorem(implies(and(X44,not(X45)),X46))
| ~ is_a_theorem(implies(X44,X45)) ),
inference(resolution,[],[f681,f114]) ).
fof(f681,plain,
! [X3,X4,X5] :
( ~ is_a_theorem(implies(X4,implies(X3,X5)))
| is_a_theorem(implies(X4,X5))
| ~ is_a_theorem(X3) ),
inference(resolution,[],[f671,f218]) ).
fof(f3564,plain,
! [X83] :
( ~ is_a_theorem(implies(and(X83,not(X83)),equiv(X83,X83)))
| is_a_theorem(equiv(X83,X83)) ),
inference(resolution,[],[f3488,f701]) ).
fof(f701,plain,
! [X0] : is_a_theorem(or(equiv(X0,X0),and(X0,not(X0)))),
inference(superposition,[],[f134,f100]) ).
fof(f134,plain,
! [X8,X9] : is_a_theorem(or(and(implies(X8,X9),implies(X8,X9)),and(X8,not(X9)))),
inference(backward_demodulation,[],[f118,f122]) ).
fof(f122,plain,
! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1))),
inference(superposition,[],[f99,f98]) ).
fof(f99,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(subsumption_resolution,[],[f90,f86]) ).
fof(f86,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',luka_op_or) ).
fof(f90,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',op_or) ).
fof(f118,plain,
! [X8,X9] : is_a_theorem(not(and(not(and(implies(X8,X9),implies(X8,X9))),implies(X8,X9)))),
inference(forward_demodulation,[],[f117,f111]) ).
fof(f117,plain,
! [X8,X9] : is_a_theorem(not(and(implies(implies(X8,X9),and(X8,not(X9))),implies(X8,X9)))),
inference(forward_demodulation,[],[f115,f111]) ).
fof(f115,plain,
! [X8,X9] : is_a_theorem(implies(implies(implies(X8,X9),and(X8,not(X9))),and(X8,not(X9)))),
inference(superposition,[],[f102,f98]) ).
fof(f3488,plain,
! [X24,X23] :
( ~ is_a_theorem(or(X24,X23))
| is_a_theorem(X24)
| ~ is_a_theorem(implies(X23,X24)) ),
inference(resolution,[],[f2651,f769]) ).
fof(f2651,plain,
! [X50,X51,X52] :
( is_a_theorem(implies(or(X50,X51),or(X50,X52)))
| ~ is_a_theorem(implies(X51,X52)) ),
inference(resolution,[],[f681,f189]) ).
fof(f189,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(forward_demodulation,[],[f186,f124]) ).
fof(f186,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X0),X2)))),
inference(superposition,[],[f106,f124]) ).
fof(f125488,plain,
! [X1386,X1387] :
( ~ is_a_theorem(implies(X1387,X1386))
| or(X1386,X1387) = X1386 ),
inference(subsumption_resolution,[],[f122190,f138]) ).
fof(f122190,plain,
! [X1386,X1387] :
( ~ is_a_theorem(implies(X1386,or(X1386,X1387)))
| or(X1386,X1387) = X1386
| ~ is_a_theorem(implies(X1387,X1386)) ),
inference(resolution,[],[f121725,f3489]) ).
fof(f3489,plain,
! [X26,X25] :
( is_a_theorem(implies(or(X26,X25),X26))
| ~ is_a_theorem(implies(X25,X26)) ),
inference(resolution,[],[f2651,f242]) ).
fof(f121725,plain,
! [X18,X19] :
( ~ is_a_theorem(implies(X19,X18))
| ~ is_a_theorem(implies(X18,X19))
| X18 = X19 ),
inference(resolution,[],[f121570,f104]) ).
fof(f104,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(subsumption_resolution,[],[f95,f81]) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',substitution_of_equivalents) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',substitution_of_equivalents) ).
fof(f121570,plain,
! [X326,X325] :
( is_a_theorem(equiv(X326,X325))
| ~ is_a_theorem(implies(X325,X326))
| ~ is_a_theorem(implies(X326,X325)) ),
inference(resolution,[],[f18302,f39482]) ).
fof(f39482,plain,
! [X0,X1] :
( is_a_theorem(or(equiv(X0,X1),and(X1,not(X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f688,f100]) ).
fof(f688,plain,
! [X2,X3,X4] :
( is_a_theorem(or(and(X2,implies(X3,X4)),and(X3,not(X4))))
| ~ is_a_theorem(X2) ),
inference(forward_demodulation,[],[f687,f122]) ).
fof(f687,plain,
! [X2,X3,X4] :
( is_a_theorem(not(and(not(and(X2,implies(X3,X4))),implies(X3,X4))))
| ~ is_a_theorem(X2) ),
inference(forward_demodulation,[],[f685,f111]) ).
fof(f685,plain,
! [X2,X3,X4] :
( is_a_theorem(implies(not(and(X2,implies(X3,X4))),and(X3,not(X4))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f671,f111]) ).
fof(f18302,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,and(X0,not(X1))))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X2) ),
inference(superposition,[],[f18235,f98]) ).
fof(f18235,plain,
! [X8,X9] :
( ~ is_a_theorem(not(X9))
| ~ is_a_theorem(or(X8,X9))
| is_a_theorem(X8) ),
inference(resolution,[],[f17339,f580]) ).
fof(f17339,plain,
! [X31,X32] :
( ~ is_a_theorem(or(X31,not(X32)))
| is_a_theorem(X31)
| ~ is_a_theorem(or(X31,X32)) ),
inference(resolution,[],[f17284,f3552]) ).
fof(f3552,plain,
! [X36,X34,X35] :
( ~ is_a_theorem(implies(or(X35,X36),X34))
| is_a_theorem(X34)
| ~ is_a_theorem(or(X34,X35)) ),
inference(resolution,[],[f3488,f253]) ).
fof(f253,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f251,f124]) ).
fof(f251,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f237,f124]) ).
fof(f237,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f218,f138]) ).
fof(f17284,plain,
! [X90,X89] :
( is_a_theorem(implies(or(X90,X89),X89))
| ~ is_a_theorem(or(X89,not(X90))) ),
inference(resolution,[],[f3539,f242]) ).
fof(f3539,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X1,X2),or(X0,X2)))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(forward_demodulation,[],[f3533,f124]) ).
fof(f3533,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(or(X1,X2),implies(not(X0),X2))) ),
inference(superposition,[],[f219,f124]) ).
fof(f145329,plain,
! [X132,X133,X131] : is_a_theorem(or(X133,implies(X131,or(not(X133),and(X132,not(X132)))))),
inference(superposition,[],[f819,f145068]) ).
fof(f819,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,implies(or(X0,X1),or(not(X2),X1)))),
inference(superposition,[],[f581,f124]) ).
fof(f581,plain,
! [X3,X4,X5] : is_a_theorem(or(X3,implies(implies(X4,X5),or(not(X3),X5)))),
inference(resolution,[],[f450,f189]) ).
fof(f122196,plain,
! [X1399,X1400,X1401] :
( ~ is_a_theorem(implies(implies(implies(equiv(X1399,X1399),not(X1400)),X1401),or(X1400,X1401)))
| implies(implies(equiv(X1399,X1399),not(X1400)),X1401) = or(X1400,X1401) ),
inference(resolution,[],[f121725,f57353]) ).
fof(f57353,plain,
! [X98,X99,X100] : is_a_theorem(implies(or(X98,X99),implies(implies(equiv(X100,X100),not(X98)),X99))),
inference(resolution,[],[f56718,f219]) ).
fof(f56718,plain,
! [X28,X29] : is_a_theorem(implies(implies(equiv(X28,X28),X29),X29)),
inference(subsumption_resolution,[],[f20001,f56694]) ).
fof(f20001,plain,
! [X28,X29] :
( ~ is_a_theorem(implies(and(X28,not(X28)),equiv(X28,X28)))
| is_a_theorem(implies(implies(equiv(X28,X28),X29),X29)) ),
inference(resolution,[],[f8882,f2642]) ).
fof(f2642,plain,
! [X21,X22,X20] :
( ~ is_a_theorem(implies(X22,X20))
| ~ is_a_theorem(X22)
| is_a_theorem(implies(implies(X20,X21),X21)) ),
inference(resolution,[],[f681,f185]) ).
fof(f8882,plain,
! [X7] : is_a_theorem(implies(implies(and(X7,not(X7)),equiv(X7,X7)),equiv(X7,X7))),
inference(resolution,[],[f717,f242]) ).
fof(f717,plain,
! [X0,X1] : is_a_theorem(implies(implies(and(X0,not(X0)),X1),or(equiv(X0,X0),X1))),
inference(resolution,[],[f701,f221]) ).
fof(f128487,plain,
! [X598,X597] : is_a_theorem(implies(implies(equiv(X598,X598),not(not(X597))),X597)),
inference(superposition,[],[f56891,f125490]) ).
fof(f125490,plain,
! [X1388] : or(X1388,not(not(X1388))) = X1388,
inference(forward_demodulation,[],[f125489,f122566]) ).
fof(f122566,plain,
! [X1385] : or(X1385,X1385) = X1385,
inference(subsumption_resolution,[],[f122189,f138]) ).
fof(f122189,plain,
! [X1385] :
( ~ is_a_theorem(implies(X1385,or(X1385,X1385)))
| or(X1385,X1385) = X1385 ),
inference(resolution,[],[f121725,f136]) ).
fof(f125489,plain,
! [X1388] : or(X1388,not(not(or(X1388,X1388)))) = X1388,
inference(subsumption_resolution,[],[f122191,f138]) ).
fof(f122191,plain,
! [X1388] :
( ~ is_a_theorem(implies(X1388,or(X1388,not(not(or(X1388,X1388))))))
| or(X1388,not(not(or(X1388,X1388)))) = X1388 ),
inference(resolution,[],[f121725,f32330]) ).
fof(f32330,plain,
! [X49] : is_a_theorem(implies(or(X49,not(not(or(X49,X49)))),X49)),
inference(resolution,[],[f31469,f242]) ).
fof(f31469,plain,
! [X232,X231] : is_a_theorem(implies(or(X231,not(not(or(X231,X232)))),or(X231,X232))),
inference(resolution,[],[f549,f233]) ).
fof(f233,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(X0)),implies(or(X0,X1),or(X2,X1)))),
inference(superposition,[],[f189,f124]) ).
fof(f549,plain,
! [X3,X4,X5] :
( ~ is_a_theorem(implies(X3,implies(or(not(X4),X5),X4)))
| is_a_theorem(implies(X3,X4)) ),
inference(resolution,[],[f447,f218]) ).
fof(f447,plain,
! [X0,X1] : is_a_theorem(implies(implies(or(not(X0),X1),X0),X0)),
inference(resolution,[],[f409,f242]) ).
fof(f56891,plain,
! [X54,X52,X53] : is_a_theorem(implies(implies(equiv(X52,X52),X53),or(X54,X53))),
inference(resolution,[],[f56712,f221]) ).
fof(f56712,plain,
! [X136,X137] : is_a_theorem(or(X136,equiv(X137,X137))),
inference(subsumption_resolution,[],[f5134,f56694]) ).
fof(f5134,plain,
! [X136,X137] :
( is_a_theorem(or(X136,equiv(X137,X137)))
| ~ is_a_theorem(implies(and(X137,not(X137)),equiv(X137,X137))) ),
inference(resolution,[],[f3487,f701]) ).
fof(f3487,plain,
! [X21,X22,X20] :
( ~ is_a_theorem(or(X21,X20))
| is_a_theorem(or(X22,X21))
| ~ is_a_theorem(implies(X20,X21)) ),
inference(resolution,[],[f2651,f766]) ).
fof(f766,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X2,X2)))
| is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f683,f674]) ).
fof(f674,plain,
! [X10,X11,X12] :
( ~ is_a_theorem(implies(X10,X12))
| is_a_theorem(or(X11,X12))
| ~ is_a_theorem(X10) ),
inference(resolution,[],[f595,f105]) ).
fof(f167558,plain,
! [X58] :
( ~ is_a_theorem(or(not(X58),X58))
| not(not(X58)) = X58 ),
inference(forward_demodulation,[],[f167431,f124]) ).
fof(f167431,plain,
! [X58] :
( ~ is_a_theorem(implies(not(not(X58)),X58))
| not(not(X58)) = X58 ),
inference(resolution,[],[f166766,f121725]) ).
fof(f166766,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(forward_demodulation,[],[f151854,f125490]) ).
fof(f151854,plain,
! [X0] : is_a_theorem(implies(or(X0,not(not(X0))),not(not(X0)))),
inference(superposition,[],[f146718,f124]) ).
fof(f146718,plain,
! [X1] : is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(resolution,[],[f146359,f37077]) ).
fof(f37077,plain,
! [X10,X11] :
( ~ is_a_theorem(or(X10,not(not(X11))))
| is_a_theorem(implies(implies(X10,X11),X11)) ),
inference(resolution,[],[f31428,f17284]) ).
fof(f31428,plain,
! [X80,X81,X79] :
( ~ is_a_theorem(implies(or(not(X80),X81),X79))
| is_a_theorem(implies(implies(X79,X80),X80)) ),
inference(resolution,[],[f549,f185]) ).
fof(f146359,plain,
! [X79] : is_a_theorem(or(X79,not(not(not(X79))))),
inference(resolution,[],[f146075,f17330]) ).
fof(f17330,plain,
! [X8,X7] :
( ~ is_a_theorem(or(X7,not(not(X8))))
| is_a_theorem(or(X8,X7)) ),
inference(resolution,[],[f17284,f450]) ).
fof(f124,plain,
! [X2,X3] : implies(not(X2),X3) = or(X2,X3),
inference(superposition,[],[f99,f98]) ).
fof(f169081,plain,
! [X852,X851] : is_a_theorem(or(not(X851),implies(X852,X851))),
inference(superposition,[],[f145890,f167559]) ).
fof(f101,plain,
~ is_a_theorem(implies(sK0,implies(sK1,sK0))),
inference(subsumption_resolution,[],[f92,f78]) ).
fof(f78,plain,
~ implies_1,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
~ implies_1,
inference(flattening,[],[f44]) ).
fof(f44,negated_conjecture,
~ implies_1,
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
implies_1,
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',hilbert_implies_1) ).
fof(f92,plain,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f69,f76]) ).
fof(f76,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0)))
=> ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( implies_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
=> implies_1 ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402',implies_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL463+1 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Aug 25 06:25:23 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.2m8ecUrebo/Vampire---4.8_13402
% 0.16/0.38 % (13511)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44 % (13512)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.24/0.44 % (13513)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.24/0.44 % (13514)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.24/0.44 % (13515)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.24/0.44 % (13516)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.24/0.44 % (13517)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.24/0.44 % (13518)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.24/0.44 % (13515)Refutation not found, incomplete strategy% (13515)------------------------------
% 0.24/0.44 % (13515)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.44 % (13515)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.44 % (13515)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.44
% 0.24/0.44 % (13515)Memory used [KB]: 9978
% 0.24/0.44 % (13515)Time elapsed: 0.004 s
% 0.24/0.44 % (13515)------------------------------
% 0.24/0.44 % (13515)------------------------------
% 0.24/0.49 % (13514)Refutation not found, incomplete strategy% (13514)------------------------------
% 0.24/0.49 % (13514)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.49 % (13514)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.49 % (13514)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.49
% 0.24/0.49 % (13514)Memory used [KB]: 1023
% 0.24/0.49 % (13514)Time elapsed: 0.058 s
% 0.24/0.49 % (13514)------------------------------
% 0.24/0.49 % (13514)------------------------------
% 0.24/0.49 % (13519)ott+10_5_av=off:bsr=on:br=off:drc=off:fsd=off:fsr=off:fde=unused:gsp=on:lcm=predicate:lma=on:nwc=2.5:sos=all:sp=occurrence:tgt=full:urr=on_375 on Vampire---4 for (375ds/0Mi)
% 0.24/0.49 % (13519)Refutation not found, incomplete strategy% (13519)------------------------------
% 0.24/0.49 % (13519)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.49 % (13519)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.49 % (13519)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.49
% 0.24/0.49 % (13519)Memory used [KB]: 1023
% 0.24/0.49 % (13519)Time elapsed: 0.002 s
% 0.24/0.49 % (13519)------------------------------
% 0.24/0.49 % (13519)------------------------------
% 0.24/0.53 % (13521)ott+10_128_aac=none:add=large:afr=on:anc=all_dependent:bsr=on:bce=on:fsd=off:irw=on:nm=2:nwc=1.5:sp=scramble:tgt=full_251 on Vampire---4 for (251ds/0Mi)
% 0.24/0.53 % (13520)lrs-1010_3_aac=none:anc=none:er=known:fsd=off:fde=unused:gs=on:lcm=predicate:sos=on:sp=weighted_frequency:tgt=ground:stl=62_365 on Vampire---4 for (365ds/0Mi)
% 0.24/0.53 % (13520)Refutation not found, incomplete strategy% (13520)------------------------------
% 0.24/0.53 % (13520)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.53 % (13520)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.53 % (13520)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.53
% 0.24/0.53 % (13520)Memory used [KB]: 9978
% 0.24/0.53 % (13520)Time elapsed: 0.002 s
% 0.24/0.53 % (13520)------------------------------
% 0.24/0.53 % (13520)------------------------------
% 0.24/0.56 % (13522)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_224 on Vampire---4 for (224ds/0Mi)
% 65.09/9.71 % (13518)First to succeed.
% 65.09/9.72 % (13518)Refutation found. Thanks to Tanya!
% 65.09/9.72 % SZS status Theorem for Vampire---4
% 65.09/9.72 % SZS output start Proof for Vampire---4
% See solution above
% 65.09/9.72 % (13518)------------------------------
% 65.09/9.72 % (13518)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 65.09/9.72 % (13518)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 65.09/9.72 % (13518)Termination reason: Refutation
% 65.09/9.72
% 65.09/9.72 % (13518)Memory used [KB]: 103750
% 65.09/9.72 % (13518)Time elapsed: 9.273 s
% 65.09/9.72 % (13518)------------------------------
% 65.09/9.72 % (13518)------------------------------
% 65.09/9.72 % (13511)Success in time 9.326 s
% 65.09/9.72 % Vampire---4.8 exiting
%------------------------------------------------------------------------------