TSTP Solution File: LCL485+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL485+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 : n015.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 08:24:02 EDT 2023
% Result : Theorem 29.55s 4.56s
% Output : Refutation 29.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 27
% Syntax : Number of formulae : 322 ( 181 unt; 0 def)
% Number of atoms : 493 ( 83 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 317 ( 146 ~; 138 |; 2 &)
% ( 13 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 547 (; 543 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f187493,plain,
$false,
inference(subsumption_resolution,[],[f187490,f15192]) ).
fof(f15192,plain,
! [X1] : is_a_theorem(equiv(X1,X1)),
inference(subsumption_resolution,[],[f7096,f15148]) ).
fof(f15148,plain,
! [X2,X3] : is_a_theorem(or(equiv(X2,X2),X3)),
inference(subsumption_resolution,[],[f4171,f15130]) ).
fof(f15130,plain,
! [X4] : is_a_theorem(implies(X4,X4)),
inference(resolution,[],[f15070,f199]) ).
fof(f199,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f127,f121]) ).
fof(f121,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f107,f89]) ).
fof(f89,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_modus_ponens) ).
fof(f107,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,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.A4q171XXLJ/Vampire---4.8_16134',modus_ponens) ).
fof(f127,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[],[f119,f110]) ).
fof(f110,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(subsumption_resolution,[],[f97,f91]) ).
fof(f91,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_op_implies_or) ).
fof(f97,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',op_implies_or) ).
fof(f119,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(subsumption_resolution,[],[f105,f87]) ).
fof(f87,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_r3) ).
fof(f105,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f56,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',r3) ).
fof(f15070,plain,
! [X17] : is_a_theorem(or(X17,not(X17))),
inference(resolution,[],[f14878,f463]) ).
fof(f463,plain,
! [X24,X23] : is_a_theorem(or(X23,or(X24,not(X23)))),
inference(superposition,[],[f118,f377]) ).
fof(f377,plain,
! [X2,X3] : implies(not(X2),X3) = or(X2,X3),
inference(superposition,[],[f114,f111]) ).
fof(f111,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(subsumption_resolution,[],[f98,f92]) ).
fof(f92,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',hilbert_op_implies_and) ).
fof(f98,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,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.A4q171XXLJ/Vampire---4.8_16134',op_implies_and) ).
fof(f114,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(subsumption_resolution,[],[f100,f93]) ).
fof(f93,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',hilbert_op_or) ).
fof(f100,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,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.A4q171XXLJ/Vampire---4.8_16134',op_or) ).
fof(f118,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(subsumption_resolution,[],[f104,f88]) ).
fof(f88,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_r2) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',r2) ).
fof(f14878,plain,
! [X16,X17] :
( ~ is_a_theorem(or(X16,or(X17,X17)))
| is_a_theorem(or(X16,X17)) ),
inference(resolution,[],[f14434,f121]) ).
fof(f14434,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X1,X1)),or(X0,X1))),
inference(resolution,[],[f13949,f122]) ).
fof(f122,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))),
inference(subsumption_resolution,[],[f108,f84]) ).
fof(f84,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_r5) ).
fof(f108,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f57,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
( r5
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',r5) ).
fof(f13949,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(or(X1,X1),X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f13928,f755]) ).
fof(f755,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f450,f110]) ).
fof(f450,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f121,f377]) ).
fof(f13928,plain,
! [X2] : is_a_theorem(not(not(implies(or(X2,X2),X2)))),
inference(forward_demodulation,[],[f13856,f110]) ).
fof(f13856,plain,
! [X2] : is_a_theorem(not(not(or(not(or(X2,X2)),X2)))),
inference(resolution,[],[f1975,f9622]) ).
fof(f9622,plain,
! [X6,X7] : is_a_theorem(implies(or(X6,X7),not(not(or(X7,X6))))),
inference(resolution,[],[f9608,f753]) ).
fof(f753,plain,
! [X14,X13] :
( ~ is_a_theorem(not(and(X14,X13)))
| is_a_theorem(implies(X13,not(X14))) ),
inference(resolution,[],[f450,f198]) ).
fof(f198,plain,
! [X0,X1] : is_a_theorem(or(and(X1,X0),implies(X0,not(X1)))),
inference(forward_demodulation,[],[f195,f173]) ).
fof(f173,plain,
! [X10,X11,X9] : implies(implies(X9,not(X10)),X11) = or(and(X9,X10),X11),
inference(superposition,[],[f110,f113]) ).
fof(f113,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f112,f110]) ).
fof(f112,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(subsumption_resolution,[],[f99,f94]) ).
fof(f94,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_op_and) ).
fof(f99,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',op_and) ).
fof(f195,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,not(X0)),implies(X0,not(X1)))),
inference(superposition,[],[f126,f110]) ).
fof(f126,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[],[f119,f110]) ).
fof(f9608,plain,
! [X0,X1] : is_a_theorem(not(and(not(or(X0,X1)),or(X1,X0)))),
inference(forward_demodulation,[],[f9599,f375]) ).
fof(f375,plain,
! [X3,X4,X5] : or(X5,and(not(X3),not(X4))) = not(and(not(X5),or(X3,X4))),
inference(superposition,[],[f114,f114]) ).
fof(f9599,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),and(not(X1),not(X0)))),
inference(superposition,[],[f9094,f377]) ).
fof(f9094,plain,
! [X4,X5] : is_a_theorem(or(implies(X4,X5),and(not(X5),X4))),
inference(superposition,[],[f398,f160]) ).
fof(f160,plain,
! [X8,X6,X7] : implies(and(X6,not(X7)),X8) = or(implies(X6,X7),X8),
inference(superposition,[],[f110,f111]) ).
fof(f398,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(backward_demodulation,[],[f214,f397]) ).
fof(f397,plain,
! [X8,X6,X7] : or(implies(X6,not(X7)),X8) = implies(and(X6,X7),X8),
inference(forward_demodulation,[],[f373,f111]) ).
fof(f373,plain,
! [X8,X6,X7] : or(implies(X6,not(X7)),X8) = not(and(and(X6,X7),not(X8))),
inference(superposition,[],[f114,f113]) ).
fof(f214,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,not(X1)),and(X1,X0))),
inference(resolution,[],[f198,f129]) ).
fof(f129,plain,
! [X2,X1] :
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(resolution,[],[f121,f119]) ).
fof(f1975,plain,
! [X6,X5] :
( ~ is_a_theorem(implies(or(X6,not(or(X6,X6))),X5))
| is_a_theorem(X5) ),
inference(forward_demodulation,[],[f1974,f943]) ).
fof(f943,plain,
! [X2,X0,X1] : implies(or(X0,not(X1)),X2) = or(and(not(X0),X1),X2),
inference(superposition,[],[f110,f459]) ).
fof(f459,plain,
! [X18,X19] : and(not(X18),X19) = not(or(X18,not(X19))),
inference(superposition,[],[f113,f377]) ).
fof(f1974,plain,
! [X6,X5] :
( ~ is_a_theorem(or(and(not(X6),or(X6,X6)),X5))
| is_a_theorem(X5) ),
inference(forward_demodulation,[],[f1957,f377]) ).
fof(f1957,plain,
! [X6,X5] :
( is_a_theorem(X5)
| ~ is_a_theorem(implies(not(and(not(X6),or(X6,X6))),X5)) ),
inference(resolution,[],[f999,f755]) ).
fof(f999,plain,
! [X0] : is_a_theorem(not(not(not(and(not(X0),or(X0,X0)))))),
inference(forward_demodulation,[],[f993,f375]) ).
fof(f993,plain,
! [X0] : is_a_theorem(not(not(or(X0,and(not(X0),not(X0)))))),
inference(backward_demodulation,[],[f623,f941]) ).
fof(f941,plain,
! [X10,X11,X9] : and(not(X11),or(X9,not(X10))) = not(or(X11,and(not(X9),X10))),
inference(superposition,[],[f459,f459]) ).
fof(f623,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,not(not(X0)))))),
inference(forward_demodulation,[],[f618,f375]) ).
fof(f618,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(not(not(X0)))))),
inference(superposition,[],[f551,f377]) ).
fof(f551,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f550,f110]) ).
fof(f550,plain,
! [X0] : is_a_theorem(or(not(X0),and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f549,f377]) ).
fof(f549,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f534,f156]) ).
fof(f156,plain,
! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))),
inference(superposition,[],[f111,f111]) ).
fof(f534,plain,
! [X0] : is_a_theorem(not(and(not(not(X0)),implies(X0,not(X0))))),
inference(superposition,[],[f473,f110]) ).
fof(f473,plain,
! [X22] : is_a_theorem(not(and(not(X22),or(X22,X22)))),
inference(forward_demodulation,[],[f462,f375]) ).
fof(f462,plain,
! [X22] : is_a_theorem(or(X22,and(not(X22),not(X22)))),
inference(superposition,[],[f184,f377]) ).
fof(f184,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_demodulation,[],[f181,f110]) ).
fof(f181,plain,
! [X0] : is_a_theorem(or(not(X0),and(X0,X0))),
inference(resolution,[],[f178,f129]) ).
fof(f178,plain,
! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(backward_demodulation,[],[f124,f173]) ).
fof(f124,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[],[f117,f110]) ).
fof(f117,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(subsumption_resolution,[],[f103,f90]) ).
fof(f90,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_r1) ).
fof(f103,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f54,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',r1) ).
fof(f4171,plain,
! [X2,X3] :
( is_a_theorem(or(equiv(X2,X2),X3))
| ~ is_a_theorem(implies(X2,X2)) ),
inference(superposition,[],[f4111,f115]) ).
fof(f115,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(subsumption_resolution,[],[f101,f95]) ).
fof(f95,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_op_equiv) ).
fof(f101,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,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.A4q171XXLJ/Vampire---4.8_16134',op_equiv) ).
fof(f4111,plain,
! [X10,X9] :
( is_a_theorem(or(and(X9,X9),X10))
| ~ is_a_theorem(X9) ),
inference(resolution,[],[f4058,f451]) ).
fof(f451,plain,
! [X2,X3] :
( ~ is_a_theorem(not(not(X2)))
| is_a_theorem(or(X2,X3)) ),
inference(superposition,[],[f143,f377]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f139,f110]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f129,f130]) ).
fof(f130,plain,
! [X3,X4] :
( is_a_theorem(or(X3,X4))
| ~ is_a_theorem(X4) ),
inference(resolution,[],[f121,f118]) ).
fof(f4058,plain,
! [X30] :
( is_a_theorem(not(not(and(X30,X30))))
| ~ is_a_theorem(X30) ),
inference(resolution,[],[f3807,f184]) ).
fof(f3807,plain,
! [X18,X19] :
( ~ is_a_theorem(implies(X18,X19))
| is_a_theorem(not(not(X19)))
| ~ is_a_theorem(X18) ),
inference(resolution,[],[f2622,f121]) ).
fof(f2622,plain,
! [X4,X5] :
( is_a_theorem(implies(X4,not(not(X5))))
| ~ is_a_theorem(implies(X4,X5)) ),
inference(resolution,[],[f1840,f753]) ).
fof(f1840,plain,
! [X0,X1] :
( is_a_theorem(not(and(not(X1),X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1377,f111]) ).
fof(f1377,plain,
! [X21,X20] :
( ~ is_a_theorem(not(and(X20,X21)))
| is_a_theorem(not(and(X21,X20))) ),
inference(resolution,[],[f749,f398]) ).
fof(f749,plain,
! [X6,X7] :
( ~ is_a_theorem(implies(X6,X7))
| ~ is_a_theorem(not(X7))
| is_a_theorem(not(X6)) ),
inference(resolution,[],[f450,f140]) ).
fof(f140,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f129,f110]) ).
fof(f7096,plain,
! [X1] :
( ~ is_a_theorem(or(equiv(X1,X1),implies(X1,X1)))
| is_a_theorem(equiv(X1,X1)) ),
inference(superposition,[],[f6239,f115]) ).
fof(f6239,plain,
! [X3] :
( ~ is_a_theorem(or(and(X3,X3),X3))
| is_a_theorem(and(X3,X3)) ),
inference(resolution,[],[f5570,f128]) ).
fof(f128,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f121,f117]) ).
fof(f5570,plain,
! [X4,X5] :
( is_a_theorem(or(X4,and(X5,X5)))
| ~ is_a_theorem(or(X4,X5)) ),
inference(resolution,[],[f4648,f121]) ).
fof(f4648,plain,
! [X2,X1] : is_a_theorem(implies(or(X1,X2),or(X1,and(X2,X2)))),
inference(resolution,[],[f2048,f122]) ).
fof(f2048,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X1,and(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f2026,f755]) ).
fof(f2026,plain,
! [X0] : is_a_theorem(not(not(implies(X0,and(X0,X0))))),
inference(resolution,[],[f2022,f757]) ).
fof(f757,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(not(X0))) ),
inference(superposition,[],[f752,f114]) ).
fof(f752,plain,
! [X12] :
( ~ is_a_theorem(not(and(X12,X12)))
| is_a_theorem(not(X12)) ),
inference(resolution,[],[f450,f178]) ).
fof(f2022,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,and(X0,X0)),X1)),
inference(forward_demodulation,[],[f2021,f110]) ).
fof(f2021,plain,
! [X0,X1] : is_a_theorem(or(or(not(X0),and(X0,X0)),X1)),
inference(forward_demodulation,[],[f2020,f377]) ).
fof(f2020,plain,
! [X0,X1] : is_a_theorem(or(implies(not(not(X0)),and(X0,X0)),X1)),
inference(forward_demodulation,[],[f2019,f377]) ).
fof(f2019,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(not(not(X0)),and(X0,X0))),X1)),
inference(forward_demodulation,[],[f2010,f168]) ).
fof(f168,plain,
! [X3,X4,X5] : and(X5,implies(X3,not(X4))) = not(implies(X5,and(X3,X4))),
inference(superposition,[],[f113,f113]) ).
fof(f2010,plain,
! [X0,X1] : is_a_theorem(implies(and(not(not(X0)),implies(X0,not(X0))),X1)),
inference(superposition,[],[f1955,f110]) ).
fof(f1955,plain,
! [X2,X3] : is_a_theorem(implies(and(not(X2),or(X2,X2)),X3)),
inference(resolution,[],[f999,f1208]) ).
fof(f1208,plain,
! [X12,X13] :
( ~ is_a_theorem(not(not(not(X12))))
| is_a_theorem(implies(X12,X13)) ),
inference(superposition,[],[f143,f1143]) ).
fof(f1143,plain,
! [X14,X13] : implies(not(not(X13)),X14) = implies(X13,X14),
inference(forward_demodulation,[],[f1087,f111]) ).
fof(f1087,plain,
! [X14,X13] : implies(not(not(X13)),X14) = not(and(X13,not(X14))),
inference(superposition,[],[f111,f1000]) ).
fof(f1000,plain,
! [X0,X1] : and(X0,X1) = and(not(not(X0)),X1),
inference(forward_demodulation,[],[f942,f113]) ).
fof(f942,plain,
! [X0,X1] : not(implies(X0,not(X1))) = and(not(not(X0)),X1),
inference(superposition,[],[f459,f110]) ).
fof(f187490,plain,
~ is_a_theorem(equiv(implies(sK0,sK1),implies(sK0,sK1))),
inference(backward_demodulation,[],[f130033,f187159]) ).
fof(f187159,plain,
! [X65,X64] : implies(X64,X65) = implies(X64,implies(X64,X65)),
inference(superposition,[],[f186908,f186908]) ).
fof(f186908,plain,
! [X10,X11] : implies(implies(X10,X11),X10) = X10,
inference(resolution,[],[f186631,f120]) ).
fof(f120,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(subsumption_resolution,[],[f106,f86]) ).
fof(f86,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',substitution_of_equivalents) ).
fof(f106,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,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.A4q171XXLJ/Vampire---4.8_16134',substitution_of_equivalents) ).
fof(f186631,plain,
! [X470,X469] : is_a_theorem(equiv(X469,implies(implies(X469,X470),X469))),
inference(forward_demodulation,[],[f186630,f129772]) ).
fof(f129772,plain,
! [X0,X1] : equiv(X0,implies(X1,X0)) = implies(implies(X1,X0),X0),
inference(superposition,[],[f113729,f115]) ).
fof(f113729,plain,
! [X2,X3,X1] : and(implies(X1,implies(X2,X1)),X3) = X3,
inference(superposition,[],[f112867,f52066]) ).
fof(f52066,plain,
! [X8,X6,X7] : equiv(X6,X6) = implies(X7,implies(X8,X7)),
inference(resolution,[],[f51935,f125]) ).
fof(f125,plain,
! [X2,X1] : is_a_theorem(implies(X2,implies(X1,X2))),
inference(superposition,[],[f118,f110]) ).
fof(f51935,plain,
! [X259,X258] :
( ~ is_a_theorem(X258)
| equiv(X259,X259) = X258 ),
inference(resolution,[],[f51832,f15192]) ).
fof(f51832,plain,
! [X10,X11] :
( ~ is_a_theorem(X11)
| ~ is_a_theorem(X10)
| X10 = X11 ),
inference(resolution,[],[f51754,f120]) ).
fof(f51754,plain,
! [X2,X3] :
( is_a_theorem(equiv(X2,X3))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X3) ),
inference(resolution,[],[f50775,f131]) ).
fof(f131,plain,
! [X6,X5] :
( is_a_theorem(implies(X5,X6))
| ~ is_a_theorem(X6) ),
inference(resolution,[],[f121,f125]) ).
fof(f50775,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[],[f42005,f115]) ).
fof(f42005,plain,
! [X44,X42,X43] :
( is_a_theorem(and(X42,implies(X43,X44)))
| ~ is_a_theorem(X42)
| ~ is_a_theorem(X44) ),
inference(resolution,[],[f39806,f2999]) ).
fof(f2999,plain,
! [X14,X15,X13] :
( is_a_theorem(or(implies(X14,X13),X15))
| ~ is_a_theorem(X13) ),
inference(resolution,[],[f2848,f451]) ).
fof(f2848,plain,
! [X12,X13] :
( is_a_theorem(not(not(implies(X12,X13))))
| ~ is_a_theorem(X13) ),
inference(resolution,[],[f2802,f121]) ).
fof(f2802,plain,
! [X2,X3] : is_a_theorem(implies(X2,not(not(implies(X3,X2))))),
inference(resolution,[],[f2793,f753]) ).
fof(f2793,plain,
! [X6,X7] : is_a_theorem(not(and(not(implies(X6,X7)),X7))),
inference(forward_demodulation,[],[f2782,f1075]) ).
fof(f1075,plain,
! [X2,X0,X1] : and(and(X0,not(X1)),X2) = and(not(implies(X0,X1)),X2),
inference(superposition,[],[f1000,f111]) ).
fof(f2782,plain,
! [X6,X7] : is_a_theorem(not(and(and(X6,not(X7)),X7))),
inference(resolution,[],[f639,f480]) ).
fof(f480,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_demodulation,[],[f474,f397]) ).
fof(f474,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,not(X1)),X1)),
inference(resolution,[],[f456,f129]) ).
fof(f456,plain,
! [X12,X13] : is_a_theorem(or(X12,implies(X13,not(X12)))),
inference(superposition,[],[f125,f377]) ).
fof(f639,plain,
! [X4,X5] :
( ~ is_a_theorem(implies(X4,not(X5)))
| is_a_theorem(not(and(X4,X5))) ),
inference(superposition,[],[f624,f113]) ).
fof(f624,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f586,f132]) ).
fof(f132,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,not(X0)))
| is_a_theorem(not(X0)) ),
inference(superposition,[],[f128,f110]) ).
fof(f586,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f479,f121]) ).
fof(f479,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,not(not(X0))))),
inference(superposition,[],[f456,f110]) ).
fof(f39806,plain,
! [X28,X27] :
( ~ is_a_theorem(or(X27,not(X28)))
| is_a_theorem(and(X28,X27))
| ~ is_a_theorem(X28) ),
inference(forward_demodulation,[],[f39805,f24902]) ).
fof(f24902,plain,
! [X7] : not(not(X7)) = X7,
inference(resolution,[],[f24893,f120]) ).
fof(f24893,plain,
! [X1] : is_a_theorem(equiv(X1,not(not(X1)))),
inference(forward_demodulation,[],[f24892,f1411]) ).
fof(f1411,plain,
! [X2,X3] : equiv(X3,not(not(X2))) = and(implies(X3,not(not(X2))),implies(X2,X3)),
inference(superposition,[],[f115,f1143]) ).
fof(f24892,plain,
! [X1] : is_a_theorem(and(implies(X1,not(not(X1))),implies(X1,X1))),
inference(forward_demodulation,[],[f24891,f111]) ).
fof(f24891,plain,
! [X1] : is_a_theorem(and(implies(X1,not(not(X1))),not(and(X1,not(X1))))),
inference(forward_demodulation,[],[f24880,f113]) ).
fof(f24880,plain,
! [X1] : is_a_theorem(and(implies(X1,not(not(X1))),not(not(implies(X1,not(not(X1))))))),
inference(superposition,[],[f17743,f1143]) ).
fof(f17743,plain,
! [X95] : is_a_theorem(and(implies(X95,X95),not(not(implies(X95,X95))))),
inference(resolution,[],[f16475,f551]) ).
fof(f16475,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f16364,f755]) ).
fof(f16364,plain,
! [X0] : is_a_theorem(not(not(implies(X0,X0)))),
inference(resolution,[],[f15476,f1423]) ).
fof(f1423,plain,
! [X16,X17] : is_a_theorem(implies(equiv(X16,X17),implies(X17,X16))),
inference(superposition,[],[f480,f115]) ).
fof(f15476,plain,
! [X56,X57] :
( ~ is_a_theorem(implies(equiv(X57,X57),X56))
| is_a_theorem(not(not(X56))) ),
inference(resolution,[],[f15152,f2622]) ).
fof(f15152,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X0,X0),X1))
| is_a_theorem(X1) ),
inference(subsumption_resolution,[],[f4556,f15130]) ).
fof(f4556,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(equiv(X0,X0),X1)) ),
inference(resolution,[],[f4067,f755]) ).
fof(f4067,plain,
! [X46] :
( is_a_theorem(not(not(equiv(X46,X46))))
| ~ is_a_theorem(implies(X46,X46)) ),
inference(resolution,[],[f3807,f1416]) ).
fof(f1416,plain,
! [X4] : is_a_theorem(implies(implies(X4,X4),equiv(X4,X4))),
inference(superposition,[],[f184,f115]) ).
fof(f39805,plain,
! [X28,X27] :
( is_a_theorem(and(not(not(X28)),X27))
| ~ is_a_theorem(or(X27,not(X28)))
| ~ is_a_theorem(X28) ),
inference(forward_demodulation,[],[f39784,f459]) ).
fof(f39784,plain,
! [X28,X27] :
( ~ is_a_theorem(or(X27,not(X28)))
| is_a_theorem(not(or(not(X28),not(X27))))
| ~ is_a_theorem(X28) ),
inference(resolution,[],[f37013,f25424]) ).
fof(f25424,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(not(X0))
| ~ is_a_theorem(X1) ),
inference(backward_demodulation,[],[f12639,f24902]) ).
fof(f12639,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(not(not(not(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f11647,f110]) ).
fof(f11647,plain,
! [X34,X35] :
( ~ is_a_theorem(or(X34,not(X35)))
| is_a_theorem(not(not(X34)))
| ~ is_a_theorem(X35) ),
inference(resolution,[],[f1341,f121]) ).
fof(f1341,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,not(not(X0))))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[],[f210,f377]) ).
fof(f210,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[],[f140,f110]) ).
fof(f37013,plain,
! [X11,X12] :
( is_a_theorem(implies(or(X12,not(X11)),X12))
| ~ is_a_theorem(or(X11,X12)) ),
inference(forward_demodulation,[],[f36998,f943]) ).
fof(f36998,plain,
! [X11,X12] :
( ~ is_a_theorem(or(X11,X12))
| is_a_theorem(or(and(not(X12),X11),X12)) ),
inference(resolution,[],[f36214,f129]) ).
fof(f36214,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(not(X0),X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(forward_demodulation,[],[f36198,f377]) ).
fof(f36198,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(not(X0),X1)))
| ~ is_a_theorem(implies(not(X1),X0)) ),
inference(superposition,[],[f35356,f459]) ).
fof(f35356,plain,
! [X80,X79] :
( is_a_theorem(or(X79,not(or(X79,X80))))
| ~ is_a_theorem(implies(X80,X79)) ),
inference(resolution,[],[f32018,f3361]) ).
fof(f3361,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(or(X3,X4),or(X3,X5)))
| ~ is_a_theorem(implies(X4,X5)) ),
inference(resolution,[],[f122,f121]) ).
fof(f32018,plain,
! [X113,X112] :
( ~ is_a_theorem(implies(X113,or(X112,X112)))
| is_a_theorem(or(X112,not(X113))) ),
inference(resolution,[],[f31965,f140]) ).
fof(f31965,plain,
! [X12,X13] :
( ~ is_a_theorem(or(or(X12,X12),X13))
| is_a_theorem(or(X12,X13)) ),
inference(forward_demodulation,[],[f31952,f377]) ).
fof(f31952,plain,
! [X12,X13] :
( ~ is_a_theorem(implies(not(or(X12,X12)),X13))
| is_a_theorem(or(X12,X13)) ),
inference(resolution,[],[f3361,f1975]) ).
fof(f112867,plain,
! [X463,X464] : and(equiv(X463,X463),X464) = X464,
inference(forward_demodulation,[],[f112709,f24902]) ).
fof(f112709,plain,
! [X464,X463] : not(not(X464)) = and(equiv(X463,X463),X464),
inference(superposition,[],[f113,f111947]) ).
fof(f111947,plain,
! [X10,X11] : implies(equiv(X11,X11),X10) = X10,
inference(resolution,[],[f111878,f120]) ).
fof(f111878,plain,
! [X14,X13] : is_a_theorem(equiv(X14,implies(equiv(X13,X13),X14))),
inference(backward_demodulation,[],[f58939,f111877]) ).
fof(f111877,plain,
! [X126,X127] : implies(implies(equiv(X126,X126),X127),X127) = equiv(X127,implies(equiv(X126,X126),X127)),
inference(forward_demodulation,[],[f111673,f61464]) ).
fof(f61464,plain,
! [X65,X66,X67] : equiv(X65,implies(X66,X65)) = and(equiv(X67,X67),implies(implies(X66,X65),X65)),
inference(superposition,[],[f115,f52066]) ).
fof(f111673,plain,
! [X126,X127,X125] : implies(implies(equiv(X126,X126),X127),X127) = and(equiv(X125,X125),implies(implies(equiv(X126,X126),X127),X127)),
inference(resolution,[],[f111099,f58939]) ).
fof(f111099,plain,
! [X38,X39] :
( ~ is_a_theorem(X39)
| and(equiv(X38,X38),X39) = X39 ),
inference(resolution,[],[f111009,f42423]) ).
fof(f42423,plain,
! [X6,X5] :
( is_a_theorem(and(equiv(X6,X6),X5))
| ~ is_a_theorem(X5) ),
inference(resolution,[],[f42021,f529]) ).
fof(f529,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X1,X0))
| is_a_theorem(and(X0,X1)) ),
inference(resolution,[],[f398,f121]) ).
fof(f42021,plain,
! [X88,X89] :
( is_a_theorem(and(X88,equiv(X89,X89)))
| ~ is_a_theorem(X88) ),
inference(resolution,[],[f39806,f15148]) ).
fof(f111009,plain,
! [X10,X11] :
( ~ is_a_theorem(and(X10,X11))
| and(X10,X11) = X11 ),
inference(resolution,[],[f51799,f120]) ).
fof(f51799,plain,
! [X130,X131] :
( is_a_theorem(equiv(and(X130,X131),X131))
| ~ is_a_theorem(and(X130,X131)) ),
inference(resolution,[],[f50775,f480]) ).
fof(f58939,plain,
! [X14,X13] : is_a_theorem(implies(implies(equiv(X13,X13),X14),X14)),
inference(forward_demodulation,[],[f58913,f48957]) ).
fof(f48957,plain,
! [X14,X13] : implies(equiv(X13,X13),X14) = or(equiv(not(X13),X13),X14),
inference(superposition,[],[f110,f48387]) ).
fof(f48387,plain,
! [X0] : not(equiv(X0,X0)) = equiv(not(X0),X0),
inference(forward_demodulation,[],[f48386,f45070]) ).
fof(f45070,plain,
! [X0] : implies(X0,X0) = equiv(X0,X0),
inference(superposition,[],[f44179,f115]) ).
fof(f44179,plain,
! [X5] : and(X5,X5) = X5,
inference(resolution,[],[f44173,f120]) ).
fof(f44173,plain,
! [X0] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(subsumption_resolution,[],[f44133,f480]) ).
fof(f44133,plain,
! [X0] :
( is_a_theorem(equiv(and(X0,X0),X0))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(superposition,[],[f41998,f115]) ).
fof(f41998,plain,
! [X24,X23] :
( is_a_theorem(and(X23,implies(X24,and(X24,X24))))
| ~ is_a_theorem(X23) ),
inference(resolution,[],[f39806,f2022]) ).
fof(f48386,plain,
! [X0] : not(implies(X0,X0)) = equiv(not(X0),X0),
inference(forward_demodulation,[],[f48385,f110]) ).
fof(f48385,plain,
! [X0] : equiv(not(X0),X0) = not(or(not(X0),X0)),
inference(forward_demodulation,[],[f48165,f24902]) ).
fof(f48165,plain,
! [X0] : not(or(not(X0),X0)) = equiv(not(X0),not(not(X0))),
inference(superposition,[],[f47484,f26771]) ).
fof(f26771,plain,
! [X6,X5] : and(not(X5),not(X6)) = not(or(X5,X6)),
inference(superposition,[],[f24902,f114]) ).
fof(f47484,plain,
! [X35] : and(not(X35),X35) = equiv(X35,not(X35)),
inference(forward_demodulation,[],[f47483,f45869]) ).
fof(f45869,plain,
! [X233] : or(X233,X233) = X233,
inference(forward_demodulation,[],[f45224,f24902]) ).
fof(f45224,plain,
! [X233] : not(not(X233)) = or(X233,not(not(X233))),
inference(superposition,[],[f26772,f44179]) ).
fof(f26772,plain,
! [X8,X7] : not(and(not(X7),X8)) = or(X7,not(X8)),
inference(superposition,[],[f24902,f459]) ).
fof(f47483,plain,
! [X35] : and(not(X35),or(X35,X35)) = equiv(X35,not(X35)),
inference(forward_demodulation,[],[f47186,f377]) ).
fof(f47186,plain,
! [X35] : equiv(X35,not(X35)) = and(not(X35),implies(not(X35),X35)),
inference(superposition,[],[f115,f45135]) ).
fof(f45135,plain,
! [X100] : not(X100) = implies(X100,not(X100)),
inference(superposition,[],[f26769,f44179]) ).
fof(f26769,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and(X0,X1)),
inference(superposition,[],[f24902,f113]) ).
fof(f58913,plain,
! [X14,X13] : is_a_theorem(implies(or(equiv(not(X13),X13),X14),X14)),
inference(resolution,[],[f58876,f29118]) ).
fof(f29118,plain,
! [X3,X4] :
( ~ is_a_theorem(or(X4,equiv(not(X3),X3)))
| is_a_theorem(X4) ),
inference(superposition,[],[f25662,f24902]) ).
fof(f25662,plain,
! [X70,X69] :
( ~ is_a_theorem(or(X69,equiv(X70,not(X70))))
| is_a_theorem(X69) ),
inference(backward_demodulation,[],[f24208,f24902]) ).
fof(f24208,plain,
! [X70,X69] :
( is_a_theorem(not(not(X69)))
| ~ is_a_theorem(or(X69,equiv(X70,not(X70)))) ),
inference(resolution,[],[f23939,f928]) ).
fof(f928,plain,
! [X0,X1] :
( is_a_theorem(or(X0,not(not(X1))))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f454,f121]) ).
fof(f454,plain,
! [X8,X9] : is_a_theorem(implies(or(X8,X9),or(X9,not(not(X8))))),
inference(superposition,[],[f126,f377]) ).
fof(f23939,plain,
! [X16,X15] :
( ~ is_a_theorem(or(equiv(X16,not(X16)),X15))
| is_a_theorem(X15) ),
inference(forward_demodulation,[],[f23912,f377]) ).
fof(f23912,plain,
! [X16,X15] :
( is_a_theorem(X15)
| ~ is_a_theorem(implies(not(equiv(X16,not(X16))),X15)) ),
inference(resolution,[],[f23870,f755]) ).
fof(f23870,plain,
! [X0] : is_a_theorem(not(not(not(equiv(X0,not(X0)))))),
inference(forward_demodulation,[],[f23869,f1410]) ).
fof(f1410,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f115,f377]) ).
fof(f23869,plain,
! [X0] : is_a_theorem(not(not(not(and(implies(X0,not(X0)),or(X0,X0)))))),
inference(forward_demodulation,[],[f23868,f1077]) ).
fof(f1077,plain,
! [X8,X6,X7] : and(implies(X6,not(X7)),X8) = and(not(and(X6,X7)),X8),
inference(superposition,[],[f1000,f113]) ).
fof(f23868,plain,
! [X0] : is_a_theorem(not(not(not(and(not(and(X0,X0)),or(X0,X0)))))),
inference(forward_demodulation,[],[f23867,f375]) ).
fof(f23867,plain,
! [X0] : is_a_theorem(not(not(or(and(X0,X0),and(not(X0),not(X0)))))),
inference(forward_demodulation,[],[f23866,f941]) ).
fof(f23866,plain,
! [X0] : is_a_theorem(not(and(not(and(X0,X0)),or(X0,not(not(X0)))))),
inference(forward_demodulation,[],[f23865,f375]) ).
fof(f23865,plain,
! [X0] : is_a_theorem(or(and(X0,X0),and(not(X0),not(not(not(X0)))))),
inference(forward_demodulation,[],[f23851,f173]) ).
fof(f23851,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),and(not(X0),not(not(not(X0)))))),
inference(superposition,[],[f14530,f110]) ).
fof(f14530,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f14529,f377]) ).
fof(f14529,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f14528,f395]) ).
fof(f395,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f371,f111]) ).
fof(f371,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f114,f111]) ).
fof(f14528,plain,
! [X0] : is_a_theorem(or(and(not(X0),not(X0)),and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f14527,f173]) ).
fof(f14527,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),not(not(X0))),and(X0,not(not(X0))))),
inference(forward_demodulation,[],[f14521,f110]) ).
fof(f14521,plain,
! [X0] : is_a_theorem(implies(or(not(not(X0)),not(not(X0))),and(X0,not(not(X0))))),
inference(superposition,[],[f14435,f1000]) ).
fof(f14435,plain,
! [X2] : is_a_theorem(implies(or(X2,X2),and(X2,X2))),
inference(resolution,[],[f13949,f5575]) ).
fof(f5575,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(X0,and(X1,X1)))),
inference(forward_demodulation,[],[f5571,f110]) ).
fof(f5571,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(not(X0),and(X1,X1)))),
inference(superposition,[],[f4648,f110]) ).
fof(f58876,plain,
! [X2,X1] : is_a_theorem(or(implies(or(X1,X2),X2),X1)),
inference(resolution,[],[f56526,f129]) ).
fof(f56526,plain,
! [X479,X480] : is_a_theorem(or(X479,implies(or(X479,X480),X480))),
inference(forward_demodulation,[],[f56525,f110]) ).
fof(f56525,plain,
! [X479,X480] : is_a_theorem(or(X479,or(not(or(X479,X480)),X480))),
inference(subsumption_resolution,[],[f56163,f15192]) ).
fof(f56163,plain,
! [X481,X479,X480] :
( ~ is_a_theorem(equiv(X481,X481))
| is_a_theorem(or(X479,or(not(or(X479,X480)),X480))) ),
inference(superposition,[],[f5833,f53573]) ).
fof(f53573,plain,
! [X8,X7] : equiv(X8,X8) = or(not(X7),X7),
inference(superposition,[],[f52187,f24902]) ).
fof(f52187,plain,
! [X442,X441] : or(X442,not(X442)) = equiv(X441,X441),
inference(resolution,[],[f51935,f15070]) ).
fof(f5833,plain,
! [X8,X6,X7] :
( ~ is_a_theorem(or(X7,or(X6,X8)))
| is_a_theorem(or(X6,or(X7,X8))) ),
inference(resolution,[],[f123,f121]) ).
fof(f123,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(subsumption_resolution,[],[f109,f85]) ).
fof(f85,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',principia_r4) ).
fof(f109,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f58,plain,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
( r4
<=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',r4) ).
fof(f186630,plain,
! [X470,X469] : is_a_theorem(implies(implies(implies(X469,X470),X469),X469)),
inference(forward_demodulation,[],[f186228,f111947]) ).
fof(f186228,plain,
! [X471,X470,X469] : is_a_theorem(implies(implies(implies(X469,X470),X469),implies(equiv(X471,X471),X469))),
inference(superposition,[],[f46382,f180102]) ).
fof(f180102,plain,
! [X46,X47,X45] : equiv(X45,X45) = or(X46,implies(X46,X47)),
inference(resolution,[],[f179975,f51935]) ).
fof(f179975,plain,
! [X40,X39] : is_a_theorem(or(X40,implies(X40,X39))),
inference(superposition,[],[f179742,f24902]) ).
fof(f179742,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,not(X1)))),
inference(resolution,[],[f147431,f198]) ).
fof(f147431,plain,
! [X163,X166,X164] :
( ~ is_a_theorem(or(and(X164,X163),X166))
| is_a_theorem(or(X163,X166)) ),
inference(forward_demodulation,[],[f147430,f173]) ).
fof(f147430,plain,
! [X163,X166,X164] :
( is_a_theorem(or(X163,X166))
| ~ is_a_theorem(implies(implies(X164,not(X163)),X166)) ),
inference(forward_demodulation,[],[f147024,f111947]) ).
fof(f147024,plain,
! [X163,X166,X164,X165] :
( is_a_theorem(implies(equiv(X165,X165),or(X163,X166)))
| ~ is_a_theorem(implies(implies(X164,not(X163)),X166)) ),
inference(superposition,[],[f3361,f52178]) ).
fof(f52178,plain,
! [X405,X407,X406] : equiv(X405,X405) = or(X406,implies(X407,not(X406))),
inference(resolution,[],[f51935,f456]) ).
fof(f46382,plain,
! [X6,X5] : is_a_theorem(implies(implies(X6,X5),implies(or(X5,X6),X5))),
inference(superposition,[],[f122,f45869]) ).
fof(f130033,plain,
~ is_a_theorem(equiv(implies(sK0,sK1),implies(sK0,implies(sK0,sK1)))),
inference(backward_demodulation,[],[f116,f129772]) ).
fof(f116,plain,
~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))),
inference(subsumption_resolution,[],[f102,f83]) ).
fof(f83,plain,
~ implies_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
~ implies_2,
inference(flattening,[],[f46]) ).
fof(f46,negated_conjecture,
~ implies_2,
inference(negated_conjecture,[],[f45]) ).
fof(f45,conjecture,
implies_2,
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',hilbert_implies_2) ).
fof(f102,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f72,f81]) ).
fof(f81,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
( implies_2
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> implies_2 ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134',implies_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL485+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 18:02:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.A4q171XXLJ/Vampire---4.8_16134
% 0.15/0.36 % (16347)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (16352)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)
% 0.22/0.42 % (16354)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 % (16353)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)
% 0.22/0.42 % (16358)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)
% 0.22/0.42 % (16357)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 % (16355)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 % (16356)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 % (16355)Refutation not found, incomplete strategy% (16355)------------------------------
% 0.22/0.43 % (16355)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (16355)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (16355)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (16355)Memory used [KB]: 9978
% 0.22/0.43 % (16355)Time elapsed: 0.004 s
% 0.22/0.43 % (16355)------------------------------
% 0.22/0.43 % (16355)------------------------------
% 0.22/0.48 % (16354)Refutation not found, incomplete strategy% (16354)------------------------------
% 0.22/0.48 % (16354)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.48 % (16354)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.48 % (16354)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.48
% 0.22/0.48 % (16354)Memory used [KB]: 1023
% 0.22/0.48 % (16354)Time elapsed: 0.057 s
% 0.22/0.48 % (16354)------------------------------
% 0.22/0.48 % (16354)------------------------------
% 0.22/0.48 % (16373)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)
% 0.22/0.48 % (16373)Refutation not found, incomplete strategy% (16373)------------------------------
% 0.22/0.48 % (16373)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.48 % (16373)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.48 % (16373)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.48
% 0.22/0.48 % (16373)Memory used [KB]: 1023
% 0.22/0.48 % (16373)Time elapsed: 0.003 s
% 0.22/0.48 % (16373)------------------------------
% 0.22/0.48 % (16373)------------------------------
% 0.22/0.51 % (16389)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 % (16389)Refutation not found, incomplete strategy% (16389)------------------------------
% 0.22/0.51 % (16389)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.51 % (16389)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.51 % (16389)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.51
% 0.22/0.51 % (16389)Memory used [KB]: 9978
% 0.22/0.51 % (16389)Time elapsed: 0.002 s
% 0.22/0.51 % (16389)------------------------------
% 0.22/0.51 % (16389)------------------------------
% 0.22/0.52 % (16395)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 % (16416)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)
% 29.55/4.55 % (16395)First to succeed.
% 29.55/4.56 % (16395)Refutation found. Thanks to Tanya!
% 29.55/4.56 % SZS status Theorem for Vampire---4
% 29.55/4.56 % SZS output start Proof for Vampire---4
% See solution above
% 29.55/4.56 % (16395)------------------------------
% 29.55/4.56 % (16395)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 29.55/4.56 % (16395)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 29.55/4.56 % (16395)Termination reason: Refutation
% 29.55/4.56
% 29.55/4.56 % (16395)Memory used [KB]: 94667
% 29.55/4.56 % (16395)Time elapsed: 4.036 s
% 29.55/4.56 % (16395)------------------------------
% 29.55/4.56 % (16395)------------------------------
% 29.55/4.56 % (16347)Success in time 4.178 s
% 29.55/4.56 % Vampire---4.8 exiting
%------------------------------------------------------------------------------