%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG011^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:28 AM UTC 2026
% Result : Theorem 8.42s 1.59s
% Output : Refutation 8.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 20
% Syntax : Number of formulae : 212 ( 103 unt; 0 typ; 9 def)
% Number of atoms : 2199 ( 262 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 4924 ( 305 ~; 215 |; 359 &;3196 @)
% ( 9 <=>; 370 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 95 usr; 27 con; 0-4 aty)
% ( 348 !!; 122 ??; 0 @@+; 0 @@-)
% Number of variables : 874 ( 17 sgn 102 !; 6 ?; 874 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vOR: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
sK2: reg ).
thf(func_def_66,type,
sK3: reg ).
thf(func_def_67,type,
sK4: reg > reg ).
thf(func_def_68,type,
sK5: reg > reg ).
thf(func_def_69,type,
sK6: reg ).
thf(func_def_70,type,
sK7: reg > reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg ).
thf(func_def_73,type,
sK10: reg ).
thf(func_def_74,type,
sK11: reg ).
thf(func_def_75,type,
sK12: reg > reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > reg ).
thf(func_def_79,type,
sK16: reg ).
thf(func_def_80,type,
sK17: reg ).
thf(func_def_81,type,
sK18: reg > reg ).
thf(func_def_82,type,
sK19: reg > reg ).
thf(func_def_83,type,
sK20: reg > reg ).
thf(func_def_84,type,
sK21: reg > reg ).
thf(func_def_85,type,
sK22: $i > ( $i > $o ) > $i ).
thf(func_def_86,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_87,type,
sK24: $i > ( $i > $o ) > $i ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f35,axiom,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
! [X1: reg] :
( ( ( ntpp @ spain @ X1 )
& ( ntpp @ france @ X1 ) )
=> ( ( pp @ catalunya @ X1 )
& ( pp @ paris @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
! [X1: reg] :
( ( ( ntpp @ spain @ X1 )
& ( ntpp @ france @ X1 ) )
=> ( ( pp @ catalunya @ X1 )
& ( pp @ paris @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f71,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f72,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f94,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f108,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f109,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f112,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f113,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f116,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f117,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f116]) ).
thf(f118,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f119,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f120,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f121,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f120]) ).
thf(f122,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f123,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f130,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f131,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f134,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f135,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f136,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
! [X1: reg] :
( ( ( ntpp @ spain @ X1 )
& ( ntpp @ france @ X1 ) )
=> ( ( pp @ catalunya @ X1 )
& ( pp @ paris @ X1 ) ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f137,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ntpp @ france @ Y1 )
& ( ntpp @ spain @ Y1 ) )
=> ( ( pp @ paris @ Y1 )
& ( pp @ catalunya @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ntpp @ france @ Y1 )
& ( ntpp @ spain @ Y1 ) )
=> ( ( pp @ paris @ Y1 )
& ( pp @ catalunya @ Y1 ) ) ) ) ) ) ),
inference(flattening,[],[f137]) ).
thf(f155,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f167,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f174,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f176,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f178,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f117]) ).
thf(f179,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f180,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f121]) ).
thf(f181,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f185,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f131]) ).
thf(f187,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f188,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ntpp @ france @ Y1 )
& ( ntpp @ spain @ Y1 ) )
=> ( ( pp @ paris @ Y1 )
& ( pp @ catalunya @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f201,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f176,f174,f174]) ).
thf(f203,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f178,f201]) ).
thf(f204,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f179,f174,f174]) ).
thf(f205,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f180,f204,f203,f203]) ).
thf(f206,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f181,f204,f203,f203]) ).
thf(f210,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ catalunya
@ spain ) ) ) ),
inference(definition_unfolding,[],[f185,f167,f155,f205]) ).
thf(f212,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f187,f167,f155,f206]) ).
thf(f213,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y4
@ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 ) )
@ Y2
@ Y3 )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( ( c @ Y5 @ Y6 )
& ~ ( ^ [Y7: reg,Y8: reg] :
( ?? @ reg
@ ^ [Y9: reg] :
( ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y7 )
& ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y8 ) ) )
@ Y5
@ Y6 ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( ( c @ Y5 @ Y6 )
& ~ ( ^ [Y7: reg,Y8: reg] :
( ?? @ reg
@ ^ [Y9: reg] :
( ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y7 )
& ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y8 ) ) )
@ Y5
@ Y6 ) )
@ Y4
@ Y3 ) ) ) )
@ france
@ Y1 )
& ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y4
@ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 ) )
@ Y2
@ Y3 )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( ( c @ Y5 @ Y6 )
& ~ ( ^ [Y7: reg,Y8: reg] :
( ?? @ reg
@ ^ [Y9: reg] :
( ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y7 )
& ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y8 ) ) )
@ Y5
@ Y6 ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( ( c @ Y5 @ Y6 )
& ~ ( ^ [Y7: reg,Y8: reg] :
( ?? @ reg
@ ^ [Y9: reg] :
( ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y7 )
& ( ^ [Y10: reg,Y11: reg] :
( !! @ reg
@ ^ [Y12: reg] :
( ( c @ Y12 @ Y10 )
=> ( c @ Y12 @ Y11 ) ) )
@ Y9
@ Y8 ) ) )
@ Y5
@ Y6 ) )
@ Y4
@ Y3 ) ) ) )
@ spain
@ Y1 ) )
=> ( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ paris
@ Y1 )
& ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ catalunya
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f188,f167,f155,f206,f206,f204,f204]) ).
thf(f214,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( !! @ reg
@ ^ [Y2: reg] :
( ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ france )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ france )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ france ) ) ) ) )
& ( c @ Y3 @ Y2 )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ spain ) ) ) ) )
& ( c @ Y3 @ Y2 )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ paris )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ catalunya )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( !! @ reg
@ ^ [Y2: reg] :
( ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ france )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ france )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ france ) ) ) ) )
& ( c @ Y3 @ Y2 )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ spain ) ) ) ) )
& ( c @ Y3 @ Y2 )
& ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ paris )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ catalunya )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( !! @ reg
@ ^ [Y1: reg] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) )
& ( c @ Y2 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) )
& ( c @ Y2 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( !! @ reg
@ ^ [Y1: reg] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) )
& ( c @ Y2 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) )
& ( c @ Y2 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 )
| ( !! @ reg
@ ^ [Y0: reg] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( c @ Y1 @ Y0 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ Y0 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( c @ Y1 @ Y0 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ Y0 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( $true
= ( a @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( $false
= ( ^ [Y0: reg] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( c @ Y1 @ Y0 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ Y0 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f223,plain,
( $false
= ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( c @ Y0 @ sK2 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ sK2 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK2 ) ) ) ) ) ) ) )
=> ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( c @ Y0 @ sK2 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ sK2 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK2 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ sK2 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK2 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( c @ Y0 @ sK2 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK2 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f225]) ).
thf(f229,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f229]) ).
thf(f232,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ france )
=> ( c @ X1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X1: reg] :
( ( $true
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X1 @ france ) ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f236,plain,
( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ france ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( $false
= ( ( c @ sK3 @ sK2 )
=> ( c @ sK3 @ france ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
( $false
= ( c @ sK3 @ france ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( $true
= ( c @ sK3 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f276,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) ) ) ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f277,plain,
( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) ) ) ) ),
inference(and_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f276]) ).
thf(f279,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ spain )
=> ( c @ X1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X1: reg] :
( ( $true
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X1 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f280]) ).
thf(f282,plain,
( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f283,plain,
( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ spain ) )
@ sK6 ) ),
inference(sigma_proxy_clausification,[],[f282]) ).
thf(f284,plain,
( $false
= ( ( c @ sK6 @ sK2 )
=> ( c @ sK6 @ spain ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f285,plain,
( $false
= ( c @ sK6 @ spain ) ),
inference(imp_proxy_clausification,[],[f284]) ).
thf(f286,plain,
( $true
= ( c @ sK6 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f284]) ).
thf(f322,plain,
( ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) ) ) ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f323,plain,
( ( $false
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) ) ) ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f322]) ).
thf(f324,plain,
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) ) ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) )
@ X2 ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK2 )
=> ( c @ Y0 @ paris ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK2 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( ( c @ X1 @ sK2 )
=> ( c @ X1 @ catalunya ) ) )
| ( $true
= ( ( c @ X2 @ sK2 )
=> ( c @ X2 @ paris ) ) )
| ( $false
= ( ( c @ sK9 @ catalunya )
=> ( c @ sK9 @ sK2 ) ) )
| ( $false
= ( ( c @ sK10 @ paris )
=> ( c @ sK10 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f332,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $true
= ( ( c @ X2 @ sK2 )
=> ( c @ X2 @ paris ) ) )
| ( $false
= ( ( c @ sK9 @ catalunya )
=> ( c @ sK9 @ sK2 ) ) )
| ( $false
= ( ( c @ sK10 @ paris )
=> ( c @ sK10 @ sK2 ) ) )
| ( $true
= ( c @ X1 @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $false
= ( ( c @ sK9 @ catalunya )
=> ( c @ sK9 @ sK2 ) ) )
| ( $false
= ( ( c @ sK10 @ paris )
=> ( c @ sK10 @ sK2 ) ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $false
= ( c @ sK9 @ sK2 ) )
| ( $false
= ( ( c @ sK10 @ paris )
=> ( c @ sK10 @ sK2 ) ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $true
= ( c @ sK9 @ catalunya ) )
| ( $false
= ( ( c @ sK10 @ paris )
=> ( c @ sK10 @ sK2 ) ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f333]) ).
thf(f336,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $true
= ( c @ sK9 @ catalunya ) )
| ( $false
= ( c @ sK10 @ sK2 ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $true
= ( c @ sK9 @ catalunya ) )
| ( $true
= ( c @ sK10 @ paris ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f338,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $false
= ( c @ sK9 @ sK2 ) )
| ( $false
= ( c @ sK10 @ sK2 ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f339,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $false
= ( c @ X2 @ sK2 ) )
| ( $false
= ( c @ sK9 @ sK2 ) )
| ( $true
= ( c @ sK10 @ paris ) )
| ( $true
= ( c @ X1 @ catalunya ) )
| ( $true
= ( c @ X2 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f340,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f341,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f345]) ).
thf(f349,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f347]) ).
thf(f350,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ X3 @ france ) ) ),
inference(imp_proxy_clausification,[],[f352]) ).
thf(f419,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f420,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f419]) ).
thf(f421,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f420]) ).
thf(f422,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f421]) ).
thf(f423,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f422]) ).
thf(f424,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f423]) ).
thf(f426,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f424]) ).
thf(f428,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f426]) ).
thf(f429,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f428]) ).
thf(f430,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f429]) ).
thf(f431,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f430]) ).
thf(f432,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ X3 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f431]) ).
thf(f526,definition,
( spl25_1
<=> ( $true
= ( c @ sK10 @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).
thf(f527,plain,
( ( $true
= ( c @ sK10 @ paris ) )
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f526]) ).
thf(f529,definition,
( spl25_2
<=> ( $true
= ( c @ sK9 @ catalunya ) ) ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
thf(f530,plain,
( ( $true
= ( c @ sK9 @ catalunya ) )
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f529]) ).
thf(f532,definition,
( spl25_3
<=> ! [X2: reg] :
( ( $false
= ( c @ X2 @ sK2 ) )
| ( $true
= ( c @ X2 @ paris ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_3])],[avatar_definition]) ).
thf(f533,plain,
( ! [X2: reg] :
( ( $false
= ( c @ X2 @ sK2 ) )
| ( $true
= ( c @ X2 @ paris ) ) )
| ~ spl25_3 ),
inference(avatar_component_clause,[],[f532]) ).
thf(f535,definition,
( spl25_4
<=> ! [X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $true
= ( c @ X1 @ catalunya ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_4])],[avatar_definition]) ).
thf(f536,plain,
( ! [X1: reg] :
( ( $false
= ( c @ X1 @ sK2 ) )
| ( $true
= ( c @ X1 @ catalunya ) ) )
| ~ spl25_4 ),
inference(avatar_component_clause,[],[f535]) ).
thf(f537,plain,
( spl25_1
| spl25_2
| spl25_3
| spl25_4 ),
inference(avatar_split_clause,[],[f337,f535,f532,f529,f526]) ).
thf(f539,definition,
( spl25_5
<=> ( $false
= ( c @ sK10 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl25_5])],[avatar_definition]) ).
thf(f540,plain,
( ( $false
= ( c @ sK10 @ sK2 ) )
| ~ spl25_5 ),
inference(avatar_component_clause,[],[f539]) ).
thf(f541,plain,
( spl25_5
| spl25_2
| spl25_3
| spl25_4 ),
inference(avatar_split_clause,[],[f336,f535,f532,f529,f539]) ).
thf(f543,definition,
( spl25_6
<=> ( $false
= ( c @ sK9 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl25_6])],[avatar_definition]) ).
thf(f544,plain,
( ( $false
= ( c @ sK9 @ sK2 ) )
| ~ spl25_6 ),
inference(avatar_component_clause,[],[f543]) ).
thf(f545,plain,
( spl25_1
| spl25_6
| spl25_3
| spl25_4 ),
inference(avatar_split_clause,[],[f339,f535,f532,f543,f526]) ).
thf(f546,plain,
( spl25_5
| spl25_6
| spl25_3
| spl25_4 ),
inference(avatar_split_clause,[],[f338,f535,f532,f543,f539]) ).
thf(f548,definition,
( spl25_7
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
thf(f549,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f548]) ).
thf(f551,definition,
( spl25_8
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $true
= ( c @ X3 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
thf(f552,plain,
( ! [X3: reg] :
( ( $true
= ( c @ X3 @ france ) )
| ( $false
= ( c @ X3 @ paris ) ) )
| ~ spl25_8 ),
inference(avatar_component_clause,[],[f551]) ).
thf(f553,plain,
( spl25_7
| spl25_8 ),
inference(avatar_split_clause,[],[f353,f551,f548]) ).
thf(f602,definition,
( spl25_21
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_21])],[avatar_definition]) ).
thf(f603,plain,
( ! [X3: reg] :
( ( $true
= ( c @ X3 @ spain ) )
| ( $false
= ( c @ X3 @ catalunya ) ) )
| ~ spl25_21 ),
inference(avatar_component_clause,[],[f602]) ).
thf(f604,plain,
( spl25_7
| spl25_21 ),
inference(avatar_split_clause,[],[f432,f602,f548]) ).
thf(f1165,plain,
( ( $true = $false )
| ( $true
= ( c @ sK6 @ catalunya ) )
| ~ spl25_4 ),
inference(constrained_superposition,[],[f286,f536]) ).
thf(f1172,plain,
( ( $true
= ( c @ sK6 @ catalunya ) )
| ~ spl25_4 ),
inference(trivial_inequality_removal,[],[f1165]) ).
thf(f1817,plain,
( ( $true = $false )
| ~ spl25_7 ),
inference(constrained_superposition,[],[f549,f221]) ).
thf(f1843,plain,
( $false
| ~ spl25_7 ),
inference(trivial_inequality_removal,[],[f1817]) ).
thf(f1844,plain,
~ spl25_7,
inference(avatar_contradiction_clause,[],[f1843]) ).
thf(f1892,plain,
( ( $true = $false )
| ( $false
= ( c @ sK3 @ paris ) )
| ~ spl25_8 ),
inference(constrained_superposition,[],[f238,f552]) ).
thf(f1902,plain,
( ( $false
= ( c @ sK3 @ paris ) )
| ~ spl25_8 ),
inference(trivial_inequality_removal,[],[f1892]) ).
thf(f1951,plain,
( ( $true = $false )
| ( $false
= ( c @ sK6 @ catalunya ) )
| ~ spl25_21 ),
inference(constrained_superposition,[],[f285,f603]) ).
thf(f1961,plain,
( ( $false
= ( c @ sK6 @ catalunya ) )
| ~ spl25_21 ),
inference(trivial_inequality_removal,[],[f1951]) ).
thf(f2103,plain,
( ( $true = $false )
| ~ spl25_4
| ~ spl25_21 ),
inference(constrained_superposition,[],[f1961,f1172]) ).
thf(f2138,plain,
( $false
| ~ spl25_4
| ~ spl25_21 ),
inference(trivial_inequality_removal,[],[f2103]) ).
thf(f2139,plain,
( ~ spl25_4
| ~ spl25_21 ),
inference(avatar_contradiction_clause,[],[f2138]) ).
thf(f2855,plain,
( ( $true = $false )
| ( $true
= ( c @ sK3 @ paris ) )
| ~ spl25_3 ),
inference(constrained_superposition,[],[f533,f239]) ).
thf(f2906,plain,
( ( $true
= ( c @ sK3 @ paris ) )
| ~ spl25_3 ),
inference(trivial_inequality_removal,[],[f2855]) ).
thf(f2912,plain,
( ( $true = $false )
| ~ spl25_3
| ~ spl25_8 ),
inference(forward_demodulation,[],[f2906,f1902]) ).
thf(f2913,plain,
( $false
| ~ spl25_3
| ~ spl25_8 ),
inference(trivial_inequality_removal,[],[f2912]) ).
thf(f2914,plain,
( ~ spl25_3
| ~ spl25_8 ),
inference(avatar_contradiction_clause,[],[f2913]) ).
thf(f4140,plain,
( ( $true = $false )
| ( $false
= ( c @ sK10 @ france ) )
| ~ spl25_5 ),
inference(constrained_superposition,[],[f540,f234]) ).
thf(f4171,plain,
( ( $false
= ( c @ sK10 @ france ) )
| ~ spl25_5 ),
inference(trivial_inequality_removal,[],[f4140]) ).
thf(f4197,plain,
( ( $true = $false )
| ( $false
= ( c @ sK10 @ paris ) )
| ~ spl25_5
| ~ spl25_8 ),
inference(constrained_superposition,[],[f552,f4171]) ).
thf(f4231,plain,
( ( $false
= ( c @ sK10 @ paris ) )
| ~ spl25_5
| ~ spl25_8 ),
inference(trivial_inequality_removal,[],[f4197]) ).
thf(f4251,plain,
( ( $true = $false )
| ~ spl25_1
| ~ spl25_5
| ~ spl25_8 ),
inference(constrained_superposition,[],[f4231,f527]) ).
thf(f4311,plain,
( $false
| ~ spl25_1
| ~ spl25_5
| ~ spl25_8 ),
inference(trivial_inequality_removal,[],[f4251]) ).
thf(f4312,plain,
( ~ spl25_1
| ~ spl25_5
| ~ spl25_8 ),
inference(avatar_contradiction_clause,[],[f4311]) ).
thf(f9424,plain,
( ( $true = $false )
| ( $false
= ( c @ sK9 @ spain ) )
| ~ spl25_6 ),
inference(constrained_superposition,[],[f544,f281]) ).
thf(f9469,plain,
( ( $false
= ( c @ sK9 @ spain ) )
| ~ spl25_6 ),
inference(trivial_inequality_removal,[],[f9424]) ).
thf(f9510,plain,
( ( $true = $false )
| ( $false
= ( c @ sK9 @ catalunya ) )
| ~ spl25_6
| ~ spl25_21 ),
inference(constrained_superposition,[],[f603,f9469]) ).
thf(f9562,plain,
( ( $false
= ( c @ sK9 @ catalunya ) )
| ~ spl25_6
| ~ spl25_21 ),
inference(trivial_inequality_removal,[],[f9510]) ).
thf(f10375,plain,
( ( $true = $false )
| ~ spl25_2
| ~ spl25_6
| ~ spl25_21 ),
inference(constrained_superposition,[],[f9562,f530]) ).
thf(f10468,plain,
( $false
| ~ spl25_2
| ~ spl25_6
| ~ spl25_21 ),
inference(trivial_inequality_removal,[],[f10375]) ).
thf(f10469,plain,
( ~ spl25_2
| ~ spl25_6
| ~ spl25_21 ),
inference(avatar_contradiction_clause,[],[f10468]) ).
cnf(s1,plain,
( spl25_1
| spl25_2
| spl25_3
| spl25_4 ),
inference(sat_conversion,[],[f537]) ).
cnf(s2,plain,
( spl25_2
| spl25_3
| spl25_4
| spl25_5 ),
inference(sat_conversion,[],[f541]) ).
cnf(s3,plain,
( spl25_1
| spl25_3
| spl25_4
| spl25_6 ),
inference(sat_conversion,[],[f545]) ).
cnf(s4,plain,
( spl25_3
| spl25_4
| spl25_5
| spl25_6 ),
inference(sat_conversion,[],[f546]) ).
cnf(s5,plain,
( spl25_7
| spl25_8 ),
inference(sat_conversion,[],[f553]) ).
cnf(s17,plain,
( spl25_7
| spl25_21 ),
inference(sat_conversion,[],[f604]) ).
cnf(s34,plain,
~ spl25_7,
inference(sat_conversion,[],[f1844]) ).
cnf(s36,plain,
( ~ spl25_4
| ~ spl25_21 ),
inference(sat_conversion,[],[f2139]) ).
cnf(s38,plain,
( ~ spl25_3
| ~ spl25_8 ),
inference(sat_conversion,[],[f2914]) ).
cnf(s40,plain,
( ~ spl25_1
| ~ spl25_5
| ~ spl25_8 ),
inference(sat_conversion,[],[f4312]) ).
cnf(s42,plain,
( ~ spl25_2
| ~ spl25_6
| ~ spl25_21 ),
inference(sat_conversion,[],[f10469]) ).
cnf(s55,plain,
spl25_21,
inference(rat,[],[s17,s34]) ).
cnf(s56,plain,
~ spl25_4,
inference(rat,[],[s36,s55]) ).
cnf(s68,plain,
spl25_8,
inference(rat,[],[s5,s34]) ).
cnf(s69,plain,
~ spl25_3,
inference(rat,[],[s38,s68]) ).
cnf(s70,plain,
( spl25_5
| spl25_6 ),
inference(rat,[],[s4,s56,s69]) ).
cnf(s71,plain,
( spl25_1
| spl25_6 ),
inference(rat,[],[s3,s56,s69]) ).
cnf(s72,plain,
( spl25_2
| spl25_5 ),
inference(rat,[],[s2,s56,s69]) ).
cnf(s73,plain,
( spl25_1
| spl25_2 ),
inference(rat,[],[s1,s56,s69]) ).
cnf(s74,plain,
spl25_1,
inference(rat,[],[s42,s73,s71,s55]) ).
cnf(s75,plain,
~ spl25_5,
inference(rat,[],[s40,s68,s74]) ).
cnf(s76,plain,
spl25_6,
inference(rat,[],[s70,s75]) ).
cnf(s77,plain,
spl25_2,
inference(rat,[],[s72,s75]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s42,s55,s76,s77]) ).
thf(f10471,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG011^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 18:33:36 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.03/1.05 % (2490087)Will run a generic schedule for satisfiability detection.
% 4.03/1.05 % (2490105)dis+10_1_sil=32000:sp=arity:random_seed=800642339:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.03/1.05 % (2490103)% WARNING: option uhcvi not known.
% 4.03/1.05 % (2490102)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=126466736_2999 on theBenchmark for (2999ds/0Mi)
% 4.03/1.05 % (2490106)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4052275892:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.03/1.05 % (2490104)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=675133735:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.03/1.05 % (2490109)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=421773340:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.03/1.05 % (2490107)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=168004891:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.03/1.05 % (2490103)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3534257456:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.03/1.05 % (2490106)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.03/1.05 % (2490103)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.03/1.05 % Exception at run slice level
% 4.03/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.03/1.05 % (2490103)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.03/1.05 % (2490105)Instruction limit reached!
% 4.03/1.05 % (2490105)------------------------------
% 4.03/1.05 % (2490105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/1.05 % (2490105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.05 % (2490105)CaDiCaL version: 2.1.3
% 4.03/1.05 % (2490105)Termination reason: Instruction limit
% 4.03/1.05 % (2490105)Termination phase: Saturation
% 4.03/1.05 % (2490105)Time elapsed: 0.027 s
% 4.03/1.05 % (2490105)Peak memory usage: 12 MB
% 4.03/1.05 % (2490105)Instructions burned: 105 (million)
% 4.03/1.05 % (2490129)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3819181282:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.03/1.05 % (2490135)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3698717968:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.03/1.05 % Exception at run slice level
% 4.03/1.05 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.03/1.05 % (2490148)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1316492390:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.03/1.05 % (2490106)Instruction limit reached!
% 4.03/1.05 % (2490106)------------------------------
% 4.03/1.05 % (2490106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/1.05 % (2490106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.05 % (2490106)CaDiCaL version: 2.1.3
% 4.03/1.05 % (2490106)Termination reason: Instruction limit
% 4.03/1.05 % (2490106)Termination phase: Saturation
% 4.03/1.05 % (2490106)Time elapsed: 0.056 s
% 4.03/1.05 % (2490106)Peak memory usage: 13 MB
% 4.03/1.05 % (2490106)Instructions burned: 118 (million)
% 4.03/1.05 % (2490148)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.03/1.05 % (2490148)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.03/1.05 % (2490107)Instruction limit reached!
% 4.03/1.05 % (2490107)------------------------------
% 4.03/1.05 % (2490107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/1.05 % (2490107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.05 % (2490107)CaDiCaL version: 2.1.3
% 4.03/1.05 % (2490107)Termination reason: Instruction limit
% 4.03/1.05 % (2490107)Termination phase: Saturation
% 4.03/1.05 % (2490107)Time elapsed: 0.063 s
% 4.03/1.05 % (2490107)Peak memory usage: 13 MB
% 4.03/1.05 % (2490107)Instructions burned: 132 (million)
% 4.03/1.05 % (2490135)Instruction limit reached!
% 4.03/1.05 % (2490135)------------------------------
% 4.03/1.05 % (2490135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490135)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490135)Termination reason: Instruction limit
% 8.42/1.59 % (2490135)Termination phase: Saturation
% 8.42/1.59 % (2490135)Time elapsed: 0.036 s
% 8.42/1.59 % (2490135)Peak memory usage: 13 MB
% 8.42/1.59 % (2490135)Instructions burned: 133 (million)
% 8.42/1.59 % (2490159)ott-21_1_sil=16000:fs=off:random_seed=2765940916:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 8.42/1.59 % (2490109)Instruction limit reached!
% 8.42/1.59 % (2490109)------------------------------
% 8.42/1.59 % (2490109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490109)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490109)Termination reason: Instruction limit
% 8.42/1.59 % (2490109)Termination phase: Saturation
% 8.42/1.59 % (2490109)Time elapsed: 0.076 s
% 8.42/1.59 % (2490109)Peak memory usage: 12 MB
% 8.42/1.59 % (2490109)Instructions burned: 159 (million)
% 8.42/1.59 % (2490163)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1754311912:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490162)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3152874328:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.42/1.59 % (2490167)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1079712220:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490166)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2260955488:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 8.42/1.59 % (2490172)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2488101038:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 8.42/1.59 % (2490172)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.42/1.59 % (2490159)Instruction limit reached!
% 8.42/1.59 % (2490159)------------------------------
% 8.42/1.59 % (2490159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490159)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490159)Termination reason: Instruction limit
% 8.42/1.59 % (2490159)Termination phase: Saturation
% 8.42/1.59 % (2490159)Time elapsed: 0.089 s
% 8.42/1.59 % (2490159)Peak memory usage: 12 MB
% 8.42/1.59 % (2490159)Instructions burned: 180 (million)
% 8.42/1.59 % (2490190)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=9654759:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 8.42/1.59 % (2490190)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.42/1.59 % (2490172)Instruction limit reached!
% 8.42/1.59 % (2490172)------------------------------
% 8.42/1.59 % (2490172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490172)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490172)Termination reason: Instruction limit
% 8.42/1.59 % (2490172)Termination phase: Saturation
% 8.42/1.59 % (2490172)Time elapsed: 0.172 s
% 8.42/1.59 % (2490172)Peak memory usage: 15 MB
% 8.42/1.59 % (2490172)Instructions burned: 694 (million)
% 8.42/1.59 % (2490216)fmb+10_1_sil=64000:random_seed=1983699899:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 8.42/1.59 % (2490216)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490162)Instruction limit reached!
% 8.42/1.59 % (2490162)------------------------------
% 8.42/1.59 % (2490162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490162)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490162)Termination reason: Instruction limit
% 8.42/1.59 % (2490162)Termination phase: Saturation
% 8.42/1.59 % (2490162)Time elapsed: 0.245 s
% 8.42/1.59 % (2490162)Peak memory usage: 13 MB
% 8.42/1.59 % (2490162)Instructions burned: 480 (million)
% 8.42/1.59 % (2490226)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3600446585:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 8.42/1.59 % (2490233)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=832196961:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490236)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=661175530:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 8.42/1.59 % (2490236)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.42/1.59 % (2490237)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2387038656:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 8.42/1.59 % (2490237)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.42/1.59 % (2490237)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.42/1.59 % (2490148)Instruction limit reached!
% 8.42/1.59 % (2490148)------------------------------
% 8.42/1.59 % (2490148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490148)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490148)Termination reason: Instruction limit
% 8.42/1.59 % (2490148)Termination phase: Saturation
% 8.42/1.59 % (2490148)Time elapsed: 0.331 s
% 8.42/1.59 % (2490148)Peak memory usage: 15 MB
% 8.42/1.59 % (2490148)Instructions burned: 684 (million)
% 8.42/1.59 % (2490246)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1044908578:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490260)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2446160190:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490269)ott-2_1_sil=16000:newcnf=on:random_seed=2965250246:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 8.42/1.59 % (2490269)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.42/1.59 % (2490166)Instruction limit reached!
% 8.42/1.59 % (2490166)------------------------------
% 8.42/1.59 % (2490166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490166)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490166)Termination reason: Instruction limit
% 8.42/1.59 % (2490166)Termination phase: Saturation
% 8.42/1.59 % (2490166)Time elapsed: 0.621 s
% 8.42/1.59 % (2490166)Peak memory usage: 22 MB
% 8.42/1.59 % (2490166)Instructions burned: 1181 (million)
% 8.42/1.59 % (2490328)ott+10_1_sil=32000:tgt=ground:random_seed=1911794531:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 8.42/1.59 % (2490190)Instruction limit reached!
% 8.42/1.59 % (2490190)------------------------------
% 8.42/1.59 % (2490190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490190)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490190)Termination reason: Instruction limit
% 8.42/1.59 % (2490190)Termination phase: Saturation
% 8.42/1.59 % (2490190)Time elapsed: 0.597 s
% 8.42/1.59 % (2490190)Peak memory usage: 16 MB
% 8.42/1.59 % (2490190)Instructions burned: 880 (million)
% 8.42/1.59 % (2490342)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2709088765:i=54282_2991 on theBenchmark for (2991ds/54282Mi)
% 8.42/1.59 % Exception at run slice level
% 8.42/1.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.42/1.59 % (2490345)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=732434931:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 8.42/1.59 % (2490345)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.42/1.59 % (2490269)Instruction limit reached!
% 8.42/1.59 % (2490269)------------------------------
% 8.42/1.59 % (2490269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.59 % (2490269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.59 % (2490269)CaDiCaL version: 2.1.3
% 8.42/1.59 % (2490269)Termination reason: Instruction limit
% 8.42/1.59 % (2490269)Termination phase: Saturation
% 8.42/1.59 % (2490269)Time elapsed: 0.539 s
% 8.42/1.59 % (2490269)Peak memory usage: 13 MB
% 8.42/1.59 % (2490269)Instructions burned: 871 (million)
% 8.42/1.59 % (2490371)dis+21_1_sil=32000:sas=cadical:random_seed=2844444095:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 8.42/1.59 % (2490345) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2490087-2490345"...
% 8.42/1.59 % (2490345)...printing done.
% 8.42/1.59 % (2490345)Refutation found. Thanks to Tanya!
% 8.42/1.59 % SZS status Theorem for theBenchmark
% 8.42/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 8.42/1.60 % (2490345)------------------------------
% 8.42/1.60 % (2490345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.42/1.60 % (2490345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.42/1.60 % (2490345)CaDiCaL version: 2.1.3
% 8.42/1.60 % (2490345)Termination reason: Refutation
% 8.42/1.60 % (2490345)Time elapsed: 0.522 s
% 8.42/1.60 % (2490345)Peak memory usage: 16 MB
% 8.42/1.60 % (2490345)Instructions burned: 1236 (million)
% 8.42/1.60 % (2490087)Success in time 1.383 s
% 8.42/1.60 % Vampire exiting
%------------------------------------------------------------------------------