TSTP Solution File: LCL502+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL502+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 : n028.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 08:24:17 EDT 2023
% Result : Theorem 9.62s 1.74s
% Output : Refutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 19
% Syntax : Number of formulae : 163 ( 74 unt; 0 def)
% Number of atoms : 277 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 210 ( 96 ~; 89 |; 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 : 298 (; 294 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32504,plain,
$false,
inference(subsumption_resolution,[],[f120,f32453]) ).
fof(f32453,plain,
! [X6,X7] : is_a_theorem(implies(or(X6,not(X7)),implies(X7,X6))),
inference(backward_demodulation,[],[f3777,f26639]) ).
fof(f26639,plain,
! [X34,X32,X33] : implies(or(X33,not(X32)),X34) = or(and(not(X33),X32),X34),
inference(superposition,[],[f119,f26024]) ).
fof(f26024,plain,
! [X1] : not(not(X1)) = X1,
inference(resolution,[],[f26022,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.k3AGS1t94e/Vampire---4.8_19769',substitution_of_equivalents) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,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.k3AGS1t94e/Vampire---4.8_19769',substitution_of_equivalents) ).
fof(f26022,plain,
! [X0] : is_a_theorem(equiv(X0,not(not(X0)))),
inference(subsumption_resolution,[],[f26021,f739]) ).
fof(f739,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f639,f102]) ).
fof(f102,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(subsumption_resolution,[],[f93,f78]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',rosser_kn1) ).
fof(f93,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f54,plain,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
( kn1
<=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',kn1) ).
fof(f639,plain,
! [X31,X29,X30] :
( ~ is_a_theorem(implies(X30,and(X29,X31)))
| is_a_theorem(not(and(not(X29),X30))) ),
inference(resolution,[],[f543,f103]) ).
fof(f103,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(subsumption_resolution,[],[f94,f79]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',rosser_kn2) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,plain,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
( kn2
<=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',kn2) ).
fof(f543,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(and(not(X2),X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f311,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f96,f82]) ).
fof(f82,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',rosser_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,[],[f73]) ).
fof(f73,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f72]) ).
fof(f72,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.k3AGS1t94e/Vampire---4.8_19769',modus_ponens) ).
fof(f311,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),not(and(not(X1),X2))))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(superposition,[],[f172,f118]) ).
fof(f118,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f111,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.k3AGS1t94e/Vampire---4.8_19769',hilbert_op_implies_and) ).
fof(f89,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,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.k3AGS1t94e/Vampire---4.8_19769',op_implies_and) ).
fof(f111,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f99,f98]) ).
fof(f99,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(subsumption_resolution,[],[f90,f83]) ).
fof(f83,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',hilbert_op_or) ).
fof(f90,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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.k3AGS1t94e/Vampire---4.8_19769',op_or) ).
fof(f172,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),not(and(X1,X2))))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f121,f105]) ).
fof(f121,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(backward_demodulation,[],[f106,f115]) ).
fof(f115,plain,
! [X2,X3] : implies(not(X2),X3) = or(X2,X3),
inference(superposition,[],[f99,f98]) ).
fof(f106,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(subsumption_resolution,[],[f97,f80]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',rosser_kn3) ).
fof(f97,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f56,plain,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( kn3
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))) ),
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',kn3) ).
fof(f26021,plain,
! [X0] :
( ~ is_a_theorem(not(and(not(X0),X0)))
| is_a_theorem(equiv(X0,not(not(X0)))) ),
inference(forward_literal_rewriting,[],[f26012,f884]) ).
fof(f884,plain,
! [X8,X9] :
( is_a_theorem(implies(X8,not(X9)))
| ~ is_a_theorem(not(and(X9,X8))) ),
inference(resolution,[],[f760,f125]) ).
fof(f125,plain,
! [X2,X1] :
( ~ is_a_theorem(or(X1,X2))
| is_a_theorem(X2)
| ~ is_a_theorem(not(X1)) ),
inference(superposition,[],[f105,f115]) ).
fof(f760,plain,
! [X2,X1] : is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(resolution,[],[f755,f209]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(and(X0,X1),implies(X1,X2))) ),
inference(resolution,[],[f178,f105]) ).
fof(f178,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(forward_demodulation,[],[f173,f98]) ).
fof(f173,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))),
inference(superposition,[],[f121,f115]) ).
fof(f755,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[],[f739,f99]) ).
fof(f26012,plain,
! [X0] :
( is_a_theorem(equiv(X0,not(not(X0))))
| ~ is_a_theorem(implies(X0,not(not(X0)))) ),
inference(superposition,[],[f25877,f137]) ).
fof(f137,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f100,f115]) ).
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.k3AGS1t94e/Vampire---4.8_19769',rosser_op_equiv) ).
fof(f91,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,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.k3AGS1t94e/Vampire---4.8_19769',op_equiv) ).
fof(f25877,plain,
! [X12,X13] :
( is_a_theorem(and(X12,or(not(X13),X13)))
| ~ is_a_theorem(X12) ),
inference(resolution,[],[f19794,f2162]) ).
fof(f2162,plain,
! [X2] : is_a_theorem(and(or(not(X2),X2),or(not(X2),X2))),
inference(resolution,[],[f2146,f825]) ).
fof(f825,plain,
! [X3] :
( ~ is_a_theorem(or(X3,X3))
| is_a_theorem(and(X3,X3)) ),
inference(resolution,[],[f786,f105]) ).
fof(f786,plain,
! [X2] : is_a_theorem(implies(or(X2,X2),and(X2,X2))),
inference(forward_demodulation,[],[f785,f115]) ).
fof(f785,plain,
! [X2] : is_a_theorem(implies(implies(not(X2),X2),and(X2,X2))),
inference(forward_demodulation,[],[f775,f118]) ).
fof(f775,plain,
! [X2] : is_a_theorem(or(and(not(X2),not(X2)),and(X2,X2))),
inference(resolution,[],[f759,f660]) ).
fof(f660,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X0))
| is_a_theorem(or(and(X0,X0),X1)) ),
inference(forward_demodulation,[],[f656,f115]) ).
fof(f656,plain,
! [X0,X1] :
( is_a_theorem(or(and(X0,X0),X1))
| ~ is_a_theorem(implies(not(X1),X0)) ),
inference(superposition,[],[f630,f99]) ).
fof(f630,plain,
! [X0,X1] :
( is_a_theorem(not(and(not(and(X0,X0)),X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f543,f102]) ).
fof(f759,plain,
! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(resolution,[],[f755,f660]) ).
fof(f2146,plain,
! [X0,X1] : is_a_theorem(or(or(not(X0),X0),X1)),
inference(superposition,[],[f2058,f99]) ).
fof(f2058,plain,
! [X18,X19] : is_a_theorem(or(not(and(not(X18),X18)),X19)),
inference(resolution,[],[f2042,f1914]) ).
fof(f1914,plain,
! [X12,X13] :
( ~ is_a_theorem(or(X12,and(not(X13),X13)))
| is_a_theorem(X12) ),
inference(resolution,[],[f1749,f739]) ).
fof(f1749,plain,
! [X2,X3] :
( ~ is_a_theorem(not(X3))
| ~ is_a_theorem(or(X2,X3))
| is_a_theorem(X2) ),
inference(forward_literal_rewriting,[],[f1743,f762]) ).
fof(f762,plain,
! [X5] :
( ~ is_a_theorem(not(not(X5)))
| is_a_theorem(X5) ),
inference(resolution,[],[f755,f125]) ).
fof(f1743,plain,
! [X2,X3] :
( ~ is_a_theorem(or(X2,X3))
| is_a_theorem(not(not(X2)))
| ~ is_a_theorem(not(X3)) ),
inference(superposition,[],[f1330,f99]) ).
fof(f1330,plain,
! [X6,X5] :
( ~ is_a_theorem(not(and(X5,X6)))
| is_a_theorem(not(X5))
| ~ is_a_theorem(X6) ),
inference(resolution,[],[f884,f105]) ).
fof(f2042,plain,
! [X0,X1] : is_a_theorem(or(or(not(X0),X1),X0)),
inference(superposition,[],[f2019,f99]) ).
fof(f2019,plain,
! [X0,X1] : is_a_theorem(not(and(not(or(X0,X1)),X0))),
inference(resolution,[],[f1350,f639]) ).
fof(f1350,plain,
! [X10,X11] : is_a_theorem(implies(X10,and(or(X10,X11),or(X10,X11)))),
inference(forward_demodulation,[],[f1342,f115]) ).
fof(f1342,plain,
! [X10,X11] : is_a_theorem(implies(X10,and(implies(not(X10),X11),implies(not(X10),X11)))),
inference(resolution,[],[f983,f1177]) ).
fof(f1177,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1176,f98]) ).
fof(f1176,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f751,f115]) ).
fof(f751,plain,
! [X2,X3] :
( ~ is_a_theorem(implies(X3,not(X2)))
| is_a_theorem(not(and(X2,X3))) ),
inference(resolution,[],[f739,f306]) ).
fof(f306,plain,
! [X10,X11,X9] :
( ~ is_a_theorem(not(and(X10,X11)))
| is_a_theorem(not(and(X11,X9)))
| ~ is_a_theorem(implies(X9,X10)) ),
inference(resolution,[],[f172,f125]) ).
fof(f983,plain,
! [X0,X1] : is_a_theorem(or(and(implies(X0,X1),implies(X0,X1)),X0)),
inference(resolution,[],[f974,f660]) ).
fof(f974,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[],[f749,f757]) ).
fof(f757,plain,
! [X2,X3] : is_a_theorem(or(implies(X2,X3),and(X2,not(X3)))),
inference(superposition,[],[f739,f113]) ).
fof(f113,plain,
! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1))),
inference(superposition,[],[f99,f98]) ).
fof(f749,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(forward_demodulation,[],[f748,f115]) ).
fof(f748,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(forward_demodulation,[],[f745,f98]) ).
fof(f745,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),not(X0)))) ),
inference(superposition,[],[f639,f115]) ).
fof(f19794,plain,
! [X21,X22,X23] :
( ~ is_a_theorem(and(X22,X23))
| is_a_theorem(and(X21,X22))
| ~ is_a_theorem(X21) ),
inference(resolution,[],[f13983,f105]) ).
fof(f13983,plain,
! [X10,X11,X9] :
( is_a_theorem(implies(and(X10,X11),and(X9,X10)))
| ~ is_a_theorem(X9) ),
inference(forward_literal_rewriting,[],[f13917,f1177]) ).
fof(f13917,plain,
! [X10,X11,X9] :
( ~ is_a_theorem(X9)
| is_a_theorem(or(and(X9,X10),not(and(X10,X11)))) ),
inference(resolution,[],[f8867,f121]) ).
fof(f8867,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X2,X0),X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_literal_rewriting,[],[f8846,f898]) ).
fof(f898,plain,
! [X3,X4] :
( is_a_theorem(or(X3,not(X4)))
| ~ is_a_theorem(implies(X4,X3)) ),
inference(resolution,[],[f761,f105]) ).
fof(f761,plain,
! [X3,X4] : is_a_theorem(implies(implies(X3,X4),or(X4,not(X3)))),
inference(resolution,[],[f755,f203]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,X0))
| is_a_theorem(implies(implies(X0,X1),or(X1,X2))) ),
inference(resolution,[],[f181,f105]) ).
fof(f181,plain,
! [X3,X4,X5] : is_a_theorem(implies(or(X4,X5),implies(implies(X5,X3),or(X3,X4)))),
inference(forward_demodulation,[],[f180,f115]) ).
fof(f180,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(not(X4),X5),implies(implies(X5,X3),or(X3,X4)))),
inference(forward_demodulation,[],[f177,f118]) ).
fof(f177,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(not(X4),X5),or(and(X5,not(X3)),or(X3,X4)))),
inference(superposition,[],[f121,f99]) ).
fof(f8846,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(X1)
| ~ is_a_theorem(or(X1,not(implies(X2,X0)))) ),
inference(resolution,[],[f8819,f588]) ).
fof(f588,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(resolution,[],[f587,f105]) ).
fof(f587,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(or(X1,not(X0))) ),
inference(forward_demodulation,[],[f580,f115]) ).
fof(f580,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(not(X1),not(X0))) ),
inference(superposition,[],[f566,f98]) ).
fof(f566,plain,
! [X0,X1] :
( is_a_theorem(not(and(or(X0,X0),X1)))
| ~ is_a_theorem(implies(X1,not(X0))) ),
inference(resolution,[],[f306,f126]) ).
fof(f126,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(forward_demodulation,[],[f124,f114]) ).
fof(f114,plain,
! [X3,X4,X5] : or(X5,and(not(X3),not(X4))) = not(and(not(X5),or(X3,X4))),
inference(superposition,[],[f99,f99]) ).
fof(f124,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f102,f115]) ).
fof(f8819,plain,
! [X2,X3,X4] :
( is_a_theorem(or(implies(X3,X2),X4))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f1799,f1487]) ).
fof(f1487,plain,
! [X6,X4,X5] :
( ~ is_a_theorem(or(and(X5,X6),X4))
| is_a_theorem(or(X4,X5)) ),
inference(resolution,[],[f992,f105]) ).
fof(f992,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X0))),
inference(resolution,[],[f975,f353]) ).
fof(f353,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(X0)))
| is_a_theorem(implies(or(X0,X1),or(X1,X2))) ),
inference(resolution,[],[f205,f105]) ).
fof(f205,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(X0)),implies(or(X0,X1),or(X1,X2)))),
inference(superposition,[],[f181,f115]) ).
fof(f975,plain,
! [X2,X3] : is_a_theorem(or(X2,not(and(X2,X3)))),
inference(resolution,[],[f749,f755]) ).
fof(f1799,plain,
! [X8,X6,X7] :
( is_a_theorem(or(and(X7,X8),implies(X8,X6)))
| ~ is_a_theorem(X6) ),
inference(resolution,[],[f1753,f209]) ).
fof(f1753,plain,
! [X4,X5] :
( is_a_theorem(or(X4,X5))
| ~ is_a_theorem(X4) ),
inference(resolution,[],[f1729,f1014]) ).
fof(f1014,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f986,f115]) ).
fof(f986,plain,
! [X8,X9] :
( is_a_theorem(implies(X8,X9))
| ~ is_a_theorem(not(X8)) ),
inference(resolution,[],[f974,f125]) ).
fof(f1729,plain,
! [X8] :
( is_a_theorem(not(not(X8)))
| ~ is_a_theorem(X8) ),
inference(resolution,[],[f1330,f739]) ).
fof(f119,plain,
! [X3,X4,X5] : or(and(not(X3),not(X4)),X5) = implies(or(X3,X4),X5),
inference(forward_demodulation,[],[f112,f98]) ).
fof(f112,plain,
! [X3,X4,X5] : or(and(not(X3),not(X4)),X5) = not(and(or(X3,X4),not(X5))),
inference(superposition,[],[f99,f99]) ).
fof(f3777,plain,
! [X6,X7] : is_a_theorem(or(and(not(X6),X7),implies(X7,X6))),
inference(resolution,[],[f3121,f178]) ).
fof(f3121,plain,
! [X4,X5] :
( ~ is_a_theorem(implies(or(X5,not(X5)),X4))
| is_a_theorem(X4) ),
inference(forward_literal_rewriting,[],[f3095,f898]) ).
fof(f3095,plain,
! [X4,X5] :
( is_a_theorem(X4)
| ~ is_a_theorem(or(X4,not(or(X5,not(X5))))) ),
inference(resolution,[],[f2923,f588]) ).
fof(f2923,plain,
! [X2,X0,X1] : is_a_theorem(or(or(X2,not(X0)),or(X0,X1))),
inference(superposition,[],[f2871,f115]) ).
fof(f2871,plain,
! [X21,X22,X23] : is_a_theorem(or(or(X21,X22),implies(X22,X23))),
inference(resolution,[],[f1464,f985]) ).
fof(f985,plain,
! [X6,X7,X5] : is_a_theorem(implies(implies(implies(X5,X6),X7),or(X7,X5))),
inference(resolution,[],[f974,f203]) ).
fof(f1464,plain,
! [X6,X4,X5] :
( ~ is_a_theorem(implies(implies(X5,X6),X4))
| is_a_theorem(or(X4,X5)) ),
inference(resolution,[],[f985,f105]) ).
fof(f120,plain,
~ is_a_theorem(implies(or(sK1,not(sK0)),implies(sK0,sK1))),
inference(backward_demodulation,[],[f101,f115]) ).
fof(f101,plain,
~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))),
inference(subsumption_resolution,[],[f92,f77]) ).
fof(f77,plain,
~ modus_tollens,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
~ modus_tollens,
inference(flattening,[],[f44]) ).
fof(f44,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
modus_tollens,
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',hilbert_modus_tollens) ).
fof(f92,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f75]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
=> ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( modus_tollens
| ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
=> modus_tollens ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769',modus_tollens) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL502+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 06:35:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.22/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.k3AGS1t94e/Vampire---4.8_19769
% 0.22/0.36 % (19895)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (19901)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.42 % (19899)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)
% 0.22/0.42 % (19898)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)
% 0.22/0.42 % (19897)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)
% 0.22/0.43 % (19902)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)
% 0.22/0.43 % (19900)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)
% 0.22/0.43 % (19896)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)
% 0.22/0.43 % (19899)Refutation not found, incomplete strategy% (19899)------------------------------
% 0.22/0.43 % (19899)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (19899)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (19899)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (19899)Memory used [KB]: 9978
% 0.22/0.43 % (19899)Time elapsed: 0.005 s
% 0.22/0.43 % (19899)------------------------------
% 0.22/0.43 % (19899)------------------------------
% 0.22/0.48 % (19898)Refutation not found, incomplete strategy% (19898)------------------------------
% 0.22/0.48 % (19898)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.48 % (19898)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.48 % (19898)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.48
% 0.22/0.48 % (19898)Memory used [KB]: 1023
% 0.22/0.48 % (19898)Time elapsed: 0.054 s
% 0.22/0.48 % (19898)------------------------------
% 0.22/0.48 % (19898)------------------------------
% 0.22/0.48 % (19903)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)
% 0.22/0.49 % (19903)Refutation not found, incomplete strategy% (19903)------------------------------
% 0.22/0.49 % (19903)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.49 % (19903)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.49 % (19903)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.49
% 0.22/0.49 % (19903)Memory used [KB]: 1023
% 0.22/0.49 % (19903)Time elapsed: 0.002 s
% 0.22/0.49 % (19903)------------------------------
% 0.22/0.49 % (19903)------------------------------
% 0.22/0.51 % (19904)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)
% 0.22/0.51 % (19904)Refutation not found, incomplete strategy% (19904)------------------------------
% 0.22/0.51 % (19904)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.51 % (19904)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.51 % (19904)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.51
% 0.22/0.51 % (19904)Memory used [KB]: 9978
% 0.22/0.51 % (19904)Time elapsed: 0.003 s
% 0.22/0.51 % (19904)------------------------------
% 0.22/0.51 % (19904)------------------------------
% 0.22/0.52 % (19905)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)
% 0.22/0.55 % (19906)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)
% 9.62/1.74 % (19902)First to succeed.
% 9.62/1.74 % (19902)Refutation found. Thanks to Tanya!
% 9.62/1.74 % SZS status Theorem for Vampire---4
% 9.62/1.74 % SZS output start Proof for Vampire---4
% See solution above
% 9.62/1.75 % (19902)------------------------------
% 9.62/1.75 % (19902)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 9.62/1.75 % (19902)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 9.62/1.75 % (19902)Termination reason: Refutation
% 9.62/1.75
% 9.62/1.75 % (19902)Memory used [KB]: 26609
% 9.62/1.75 % (19902)Time elapsed: 1.319 s
% 9.62/1.75 % (19902)------------------------------
% 9.62/1.75 % (19902)------------------------------
% 9.62/1.75 % (19895)Success in time 1.378 s
% 9.62/1.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------