%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG011^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 07:49:26 AM UTC 2026
% Result : Theorem 1.06s 0.56s
% Output : Refutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 20
% Syntax : Number of formulae : 216 ( 103 unt; 0 typ; 9 def)
% Number of atoms : 2255 ( 276 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 4994 ( 307 ~; 231 |; 359 &;3240 @)
% ( 9 <=>; 378 =>; 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 : 879 ( 17 sgn 107 !; 6 ?; 879 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
vAND: $o > $o > $o ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
vIMP: $o > $o > $o ).
thf(func_def_59,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
sK0: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK1: reg > reg ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_67,type,
sK4: reg ).
thf(func_def_68,type,
sK5: reg > reg ).
thf(func_def_69,type,
sK6: reg > 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_75,type,
sK12: reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: reg > reg ).
thf(func_def_81,type,
sK18: reg ).
thf(func_def_82,type,
sK19: reg ).
thf(func_def_83,type,
sK20: reg ).
thf(func_def_84,type,
sK21: reg > reg ).
thf(func_def_85,type,
sK22: reg > reg ).
thf(func_def_86,type,
sK23: reg ).
thf(func_def_87,type,
sK24: $i > ( $i > $o ) > $i ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f37,axiom,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) )
= o ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= tpp ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) )
= ntpp ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox/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/sandbox/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(f56,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f57,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f68,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f69,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f72,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= tpp ),
inference(rectify,[],[f41]) ).
thf(f73,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f78,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
! [X1: reg] :
( ( ( ntpp @ spain @ X1 )
& ( ntpp @ france @ X1 ) )
=> ( ( pp @ catalunya @ X1 )
& ( pp @ paris @ X1 ) ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f79,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ntpp @ france @ Y1 )
& ( ntpp @ spain @ Y1 ) )
=> ( ( pp @ paris @ Y1 )
& ( pp @ catalunya @ Y1 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f86,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f87,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f92,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f93,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f98,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f99,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(fool_elimination,[],[f98]) ).
thf(f102,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f103,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f113,plain,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) )
= o ),
inference(rectify,[],[f37]) ).
thf(f114,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f113]) ).
thf(f117,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f118,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f125,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f126,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f125]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ntpp @ france @ Y1 )
& ( ntpp @ spain @ Y1 ) )
=> ( ( pp @ paris @ Y1 )
& ( pp @ catalunya @ Y1 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f79]) ).
thf(f141,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f143,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(cnf_transformation,[],[f99]) ).
thf(f144,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f145,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f147,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f126]) ).
thf(f148,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ntpp @ france @ Y1 )
& ( ntpp @ spain @ Y1 ) )
=> ( ( pp @ paris @ Y1 )
& ( pp @ catalunya @ Y1 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f153,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f154,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f158,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f160,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f166,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f114]) ).
thf(f171,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,[],[f166,f145,f145]) ).
thf(f172,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,[],[f147,f171]) ).
thf(f175,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f153,f145,f145]) ).
thf(f176,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ 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 ) ) )
& ( ^ [Y2: reg,Y3: reg] :
( ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f144,f172,f172,f175]) ).
thf(f177,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ 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
@ Y1 )
& ( ^ [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 ) ) )
& ( ^ [Y2: reg,Y3: reg] :
( ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f160,f172,f172,f175]) ).
thf(f179,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ?? @ 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
@ Y2 )
& ( ^ [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 ) ) )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y1
@ Y2 ) )
@ catalunya
@ spain ) ) )
= $true ),
inference(definition_unfolding,[],[f143,f141,f154,f177]) ).
thf(f180,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( ^ [Y2: reg,Y3: reg] :
( ~ ( ?? @ 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 ) ) )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ france
@ Y1 )
& ( ^ [Y2: reg,Y3: reg] :
( ~ ( ?? @ 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 ) ) )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) )
@ spain
@ Y1 ) )
=> ( ( ^ [Y2: reg,Y3: reg] :
( ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 ) )
@ paris
@ Y1 )
& ( ^ [Y2: reg,Y3: reg] :
( ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 ) )
@ catalunya
@ Y1 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f148,f141,f154,f176,f176,f175,f175]) ).
thf(f182,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ~ ( ?? @ 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 ) ) )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y1
@ Y2 ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f158,f141,f154,f176]) ).
thf(f236,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ?? @ 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 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f237,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ?? @ 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 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ?? @ 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 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( ?? @ 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 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( ( ( ?? @ 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 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( ( ( ?? @ 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 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f241]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f288,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( ~ ( ?? @ 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 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ france )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( ?? @ 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 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
=> ( c @ Y3 @ Y2 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ paris )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ catalunya )
=> ( c @ Y3 @ Y2 ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f292,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( ~ ( ?? @ 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 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ france )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( ?? @ 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 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
=> ( c @ Y3 @ Y2 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ paris )
=> ( c @ Y3 @ Y2 ) ) )
& ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ catalunya )
=> ( c @ Y3 @ Y2 ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ sK10 )
= $false ),
inference(sigma_proxy_clausification,[],[f291]) ).
thf(f293,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( ~ ( ?? @ 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 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( ?? @ 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 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ Y1 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ Y1 ) ) ) ) ) )
| ~ ( a @ sK10 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f294,plain,
( ( ^ [Y0: $i] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( ~ ( ?? @ 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 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( ?? @ 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 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ Y1 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ Y1 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ Y1 ) ) ) ) ) )
| ~ ( a @ sK10 @ Y0 ) )
@ sK11 )
= $false ),
inference(sigma_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( ~ ( ?? @ 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 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( ?? @ 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 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ Y0 ) ) ) ) ) )
| ~ ( a @ sK10 @ sK11 ) )
= $false ),
inference(beta-eta_normalization,[],[f294]) ).
thf(f296,plain,
( ( ~ ( a @ sK10 @ sK11 ) )
= $false ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f297,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( ~ ( ?? @ 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 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( ?? @ 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 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f298,plain,
( ( ^ [Y0: reg] :
( ( ~ ( ?? @ 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 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( ?? @ 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 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ Y0 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ Y0 ) ) ) ) )
@ sK12 )
= $false ),
inference(sigma_proxy_clausification,[],[f297]) ).
thf(f299,plain,
( ( ( ~ ( ?? @ 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 @ sK12 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK12 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK12 ) ) )
& ~ ( ?? @ 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 @ sK12 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK12 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK12 ) ) ) )
=> ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ( ~ ( ?? @ 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 @ sK12 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK12 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK12 ) ) )
& ~ ( ?? @ 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 @ sK12 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK12 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK12 ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f299]) ).
thf(f302,plain,
( ( ~ ( ?? @ 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 @ sK12 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK12 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK12 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( ~ ( ?? @ 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 @ sK12 )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK12 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK12 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f301]) ).
thf(f304,plain,
( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK12 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f303]) ).
thf(f342,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK12 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f304]) ).
thf(f343,plain,
( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f304]) ).
thf(f344,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) ) )
= $false ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f345,plain,
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ france ) )
@ sK15 )
= $false ),
inference(sigma_proxy_clausification,[],[f344]) ).
thf(f346,plain,
( ( ( c @ sK15 @ sK12 )
=> ( c @ sK15 @ france ) )
= $false ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f347,plain,
( ( c @ sK15 @ france )
= $false ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f348,plain,
( ( c @ sK15 @ sK12 )
= $true ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f349,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ sK12 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f350,plain,
! [X1: reg] :
( ( ( c @ X1 @ france )
=> ( c @ X1 @ sK12 ) )
= $true ),
inference(beta-eta_normalization,[],[f349]) ).
thf(f351,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK12 )
= $true )
| ( ( c @ X1 @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f350]) ).
thf(f352,plain,
( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK12 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f302]) ).
thf(f391,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK12 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f352]) ).
thf(f392,plain,
( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f352]) ).
thf(f393,plain,
( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) ) ) ),
inference(not_proxy_clausification,[],[f392]) ).
thf(f394,plain,
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ spain ) )
@ sK18 )
= $false ),
inference(sigma_proxy_clausification,[],[f393]) ).
thf(f395,plain,
( ( ( c @ sK18 @ sK12 )
=> ( c @ sK18 @ spain ) )
= $false ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f396,plain,
( ( c @ sK18 @ spain )
= $false ),
inference(imp_proxy_clausification,[],[f395]) ).
thf(f397,plain,
( ( c @ sK18 @ sK12 )
= $true ),
inference(imp_proxy_clausification,[],[f395]) ).
thf(f398,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ sK12 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f391]) ).
thf(f399,plain,
! [X1: reg] :
( ( ( c @ X1 @ spain )
=> ( c @ X1 @ sK12 ) )
= $true ),
inference(beta-eta_normalization,[],[f398]) ).
thf(f400,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK12 )
= $true )
| ( ( c @ X1 @ spain )
= $false ) ),
inference(imp_proxy_clausification,[],[f399]) ).
thf(f401,plain,
( ( $false
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) ) ) )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f300]) ).
thf(f402,plain,
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) ) ) )
= $false )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f401]) ).
thf(f403,plain,
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) ) ) )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X1: reg] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f403]) ).
thf(f405,plain,
! [X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f404]) ).
thf(f406,plain,
! [X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) )
@ sK19 ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f405]) ).
thf(f407,plain,
! [X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) )
@ sK19 ) )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(not_proxy_clausification,[],[f406]) ).
thf(f408,plain,
! [X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) )
@ sK19 ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) )
@ sK20 ) ) ),
inference(sigma_proxy_clausification,[],[f407]) ).
thf(f409,plain,
! [X2: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ catalunya ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ sK12 ) )
@ sK19 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ sK12 ) )
@ sK20 ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK12 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f408]) ).
thf(f410,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ sK19 @ paris )
=> ( c @ sK19 @ sK12 ) )
= $false )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true )
| ( ( ( c @ X1 @ sK12 )
=> ( c @ X1 @ paris ) )
= $true )
| ( ( ( c @ sK20 @ catalunya )
=> ( c @ sK20 @ sK12 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f409]) ).
thf(f411,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ X1 @ sK12 )
=> ( c @ X1 @ paris ) )
= $true )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true )
| ( ( ( c @ sK20 @ catalunya )
=> ( c @ sK20 @ sK12 ) )
= $false )
| ( ( c @ sK19 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f410]) ).
thf(f412,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ sK20 @ catalunya )
=> ( c @ sK20 @ sK12 ) )
= $false )
| ( ( ( c @ X1 @ sK12 )
=> ( c @ X1 @ paris ) )
= $true )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true )
| ( $true
= ( c @ sK19 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f410]) ).
thf(f413,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ X1 @ sK12 )
=> ( c @ X1 @ paris ) )
= $true )
| ( ( c @ sK20 @ sK12 )
= $false )
| ( $true
= ( c @ sK19 @ paris ) )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ sK20 @ catalunya ) )
| ( ( ( c @ X1 @ sK12 )
=> ( c @ X1 @ paris ) )
= $true )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true )
| ( $true
= ( c @ sK19 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f412]) ).
thf(f415,plain,
! [X2: reg,X1: reg] :
( ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X1 @ sK12 )
= $false )
| ( $true
= ( c @ sK20 @ catalunya ) )
| ( $true
= ( c @ sK19 @ paris ) )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: reg,X1: reg] :
( ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ X2 @ catalunya )
= $true )
| ( ( c @ X1 @ sK12 )
= $false )
| ( $true
= ( c @ sK20 @ catalunya ) )
| ( $true
= ( c @ sK19 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f415]) ).
thf(f417,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true )
| ( ( c @ X1 @ sK12 )
= $false )
| ( $true
= ( c @ sK19 @ paris ) )
| ( ( c @ X1 @ paris )
= $true )
| ( ( c @ sK20 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f413]) ).
thf(f418,plain,
! [X2: reg,X1: reg] :
( ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ sK20 @ sK12 )
= $false )
| ( ( c @ X2 @ catalunya )
= $true )
| ( $true
= ( c @ sK19 @ paris ) )
| ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X1 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f417]) ).
thf(f419,plain,
! [X2: reg,X1: reg] :
( ( ( c @ sK19 @ sK12 )
= $false )
| ( ( ( c @ X2 @ sK12 )
=> ( c @ X2 @ catalunya ) )
= $true )
| ( ( ( c @ sK20 @ catalunya )
=> ( c @ sK20 @ sK12 ) )
= $false )
| ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X1 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f411]) ).
thf(f420,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ sK20 @ catalunya )
=> ( c @ sK20 @ sK12 ) )
= $false )
| ( ( c @ X1 @ sK12 )
= $false )
| ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X2 @ catalunya )
= $true )
| ( ( c @ sK19 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f419]) ).
thf(f421,plain,
! [X2: reg,X1: reg] :
( ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ X2 @ catalunya )
= $true )
| ( ( c @ sK20 @ sK12 )
= $false )
| ( ( c @ sK19 @ sK12 )
= $false )
| ( ( c @ X1 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X2: reg,X1: reg] :
( ( ( c @ X2 @ catalunya )
= $true )
| ( $true
= ( c @ sK20 @ catalunya ) )
| ( ( c @ sK19 @ sK12 )
= $false )
| ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X1 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f420]) ).
thf(f423,plain,
( ( a @ sK10 @ sK11 )
= $true ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f424,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ 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 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f425,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ 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 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f424]) ).
thf(f426,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ 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 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f425]) ).
thf(f427,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( ?? @ 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 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f426]) ).
thf(f428,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ 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 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f427]) ).
thf(f429,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ 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 ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f428]) ).
thf(f430,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f429]) ).
thf(f468,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f430]) ).
thf(f476,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f468]) ).
thf(f477,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f478]) ).
thf(f529,definition,
( spl25_7
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
thf(f530,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f529]) ).
thf(f584,definition,
( spl25_20
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl25_20])],[avatar_definition]) ).
thf(f585,plain,
( ! [X3: reg] :
( ( $true
= ( c @ X3 @ spain ) )
| ( $false
= ( c @ X3 @ catalunya ) ) )
| ~ spl25_20 ),
inference(avatar_component_clause,[],[f584]) ).
thf(f586,plain,
( spl25_7
| spl25_20 ),
inference(avatar_split_clause,[],[f290,f584,f529]) ).
thf(f588,definition,
( spl25_21
<=> ( $true
= ( c @ sK19 @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl25_21])],[avatar_definition]) ).
thf(f590,plain,
( ( $true
= ( c @ sK19 @ paris ) )
| ~ spl25_21 ),
inference(avatar_component_clause,[],[f588]) ).
thf(f592,definition,
( spl25_22
<=> ! [X1: reg] :
( ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X1 @ sK12 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl25_22])],[avatar_definition]) ).
thf(f593,plain,
( ! [X1: reg] :
( ( ( c @ X1 @ sK12 )
= $false )
| ( ( c @ X1 @ paris )
= $true ) )
| ~ spl25_22 ),
inference(avatar_component_clause,[],[f592]) ).
thf(f595,definition,
( spl25_23
<=> ( $true
= ( c @ sK20 @ catalunya ) ) ),
introduced(definition,[new_symbols(definition,[spl25_23])],[avatar_definition]) ).
thf(f597,plain,
( ( $true
= ( c @ sK20 @ catalunya ) )
| ~ spl25_23 ),
inference(avatar_component_clause,[],[f595]) ).
thf(f599,definition,
( spl25_24
<=> ! [X2: reg] :
( ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ X2 @ catalunya )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl25_24])],[avatar_definition]) ).
thf(f600,plain,
( ! [X2: reg] :
( ( ( c @ X2 @ sK12 )
= $false )
| ( ( c @ X2 @ catalunya )
= $true ) )
| ~ spl25_24 ),
inference(avatar_component_clause,[],[f599]) ).
thf(f601,plain,
( spl25_21
| spl25_22
| spl25_23
| spl25_24 ),
inference(avatar_split_clause,[],[f416,f599,f595,f592,f588]) ).
thf(f603,definition,
( spl25_25
<=> ( ( c @ sK20 @ sK12 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl25_25])],[avatar_definition]) ).
thf(f605,plain,
( ( ( c @ sK20 @ sK12 )
= $false )
| ~ spl25_25 ),
inference(avatar_component_clause,[],[f603]) ).
thf(f606,plain,
( spl25_22
| spl25_24
| spl25_21
| spl25_25 ),
inference(avatar_split_clause,[],[f418,f603,f588,f599,f592]) ).
thf(f608,definition,
( spl25_26
<=> ( ( c @ sK19 @ sK12 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl25_26])],[avatar_definition]) ).
thf(f610,plain,
( ( ( c @ sK19 @ sK12 )
= $false )
| ~ spl25_26 ),
inference(avatar_component_clause,[],[f608]) ).
thf(f611,plain,
( spl25_23
| spl25_26
| spl25_24
| spl25_22 ),
inference(avatar_split_clause,[],[f422,f592,f599,f608,f595]) ).
thf(f612,plain,
( spl25_22
| spl25_25
| spl25_24
| spl25_26 ),
inference(avatar_split_clause,[],[f421,f608,f599,f603,f592]) ).
thf(f640,definition,
( spl25_33
<=> ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl25_33])],[avatar_definition]) ).
thf(f641,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl25_33 ),
inference(avatar_component_clause,[],[f640]) ).
thf(f642,plain,
( spl25_7
| spl25_33 ),
inference(avatar_split_clause,[],[f479,f640,f529]) ).
thf(f684,plain,
( ( $true = $false )
| ( ( c @ sK15 @ paris )
= $true )
| ~ spl25_22 ),
inference(superposition,[],[f593,f348]) ).
thf(f688,plain,
( ( ( c @ sK15 @ paris )
= $true )
| ~ spl25_22 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f997,plain,
( ( $true = $false )
| ~ spl25_7 ),
inference(superposition,[],[f530,f423]) ).
thf(f1011,plain,
( $false
| ~ spl25_7 ),
inference(trivial_inequality_removal,[],[f997]) ).
thf(f1012,plain,
~ spl25_7,
inference(avatar_contradiction_clause,[],[f1011]) ).
thf(f1020,plain,
( ( $true = $false )
| ( ( c @ sK18 @ catalunya )
= $false )
| ~ spl25_20 ),
inference(superposition,[],[f396,f585]) ).
thf(f1022,plain,
( ( ( c @ sK18 @ catalunya )
= $false )
| ~ spl25_20 ),
inference(trivial_inequality_removal,[],[f1020]) ).
thf(f1035,plain,
( ( ( c @ sK15 @ france )
= $true )
| ( $true = $false )
| ~ spl25_22
| ~ spl25_33 ),
inference(superposition,[],[f688,f641]) ).
thf(f1044,plain,
( ( ( c @ sK15 @ france )
= $true )
| ~ spl25_22
| ~ spl25_33 ),
inference(trivial_inequality_removal,[],[f1035]) ).
thf(f1054,plain,
( ( $true = $false )
| ~ spl25_22
| ~ spl25_33 ),
inference(forward_demodulation,[],[f1044,f347]) ).
thf(f1055,plain,
( $false
| ~ spl25_22
| ~ spl25_33 ),
inference(trivial_inequality_removal,[],[f1054]) ).
thf(f1056,plain,
( ~ spl25_22
| ~ spl25_33 ),
inference(avatar_contradiction_clause,[],[f1055]) ).
thf(f1062,plain,
( ( ( c @ sK18 @ catalunya )
= $true )
| ( $true = $false )
| ~ spl25_24 ),
inference(superposition,[],[f600,f397]) ).
thf(f1081,plain,
( ( ( c @ sK18 @ catalunya )
= $true )
| ~ spl25_24 ),
inference(trivial_inequality_removal,[],[f1062]) ).
thf(f1089,plain,
( ( $true = $false )
| ~ spl25_20
| ~ spl25_24 ),
inference(forward_demodulation,[],[f1081,f1022]) ).
thf(f1090,plain,
( $false
| ~ spl25_20
| ~ spl25_24 ),
inference(trivial_inequality_removal,[],[f1089]) ).
thf(f1091,plain,
( ~ spl25_20
| ~ spl25_24 ),
inference(avatar_contradiction_clause,[],[f1090]) ).
thf(f1096,plain,
( ( ( c @ sK20 @ spain )
= $false )
| ( $true = $false )
| ~ spl25_25 ),
inference(superposition,[],[f400,f605]) ).
thf(f1099,plain,
( ( ( c @ sK20 @ spain )
= $false )
| ~ spl25_25 ),
inference(trivial_inequality_removal,[],[f1096]) ).
thf(f1108,plain,
( ( $true = $false )
| ( $false
= ( c @ sK20 @ catalunya ) )
| ~ spl25_20
| ~ spl25_25 ),
inference(superposition,[],[f585,f1099]) ).
thf(f1110,plain,
( ( $false
= ( c @ sK20 @ catalunya ) )
| ~ spl25_20
| ~ spl25_25 ),
inference(trivial_inequality_removal,[],[f1108]) ).
thf(f1124,plain,
( ( $true = $false )
| ~ spl25_20
| ~ spl25_23
| ~ spl25_25 ),
inference(superposition,[],[f1110,f597]) ).
thf(f1129,plain,
( $false
| ~ spl25_20
| ~ spl25_23
| ~ spl25_25 ),
inference(trivial_inequality_removal,[],[f1124]) ).
thf(f1130,plain,
( ~ spl25_20
| ~ spl25_23
| ~ spl25_25 ),
inference(avatar_contradiction_clause,[],[f1129]) ).
thf(f1131,plain,
( ( ( c @ sK19 @ france )
= $true )
| ( $true = $false )
| ~ spl25_21
| ~ spl25_33 ),
inference(superposition,[],[f590,f641]) ).
thf(f1134,plain,
( ( ( c @ sK19 @ france )
= $true )
| ~ spl25_21
| ~ spl25_33 ),
inference(trivial_inequality_removal,[],[f1131]) ).
thf(f1142,plain,
( ( $true = $false )
| ( ( c @ sK19 @ france )
= $false )
| ~ spl25_26 ),
inference(superposition,[],[f351,f610]) ).
thf(f1144,plain,
( ( ( c @ sK19 @ france )
= $false )
| ~ spl25_26 ),
inference(trivial_inequality_removal,[],[f1142]) ).
thf(f1165,plain,
( ( $true = $false )
| ~ spl25_21
| ~ spl25_26
| ~ spl25_33 ),
inference(superposition,[],[f1144,f1134]) ).
thf(f1170,plain,
( $false
| ~ spl25_21
| ~ spl25_26
| ~ spl25_33 ),
inference(trivial_inequality_removal,[],[f1165]) ).
thf(f1171,plain,
( ~ spl25_21
| ~ spl25_26
| ~ spl25_33 ),
inference(avatar_contradiction_clause,[],[f1170]) ).
cnf(s18,plain,
( spl25_7
| spl25_20 ),
inference(sat_conversion,[],[f586]) ).
cnf(s19,plain,
( spl25_21
| spl25_22
| spl25_23
| spl25_24 ),
inference(sat_conversion,[],[f601]) ).
cnf(s20,plain,
( spl25_21
| spl25_22
| spl25_24
| spl25_25 ),
inference(sat_conversion,[],[f606]) ).
cnf(s21,plain,
( spl25_22
| spl25_23
| spl25_24
| spl25_26 ),
inference(sat_conversion,[],[f611]) ).
cnf(s22,plain,
( spl25_22
| spl25_24
| spl25_25
| spl25_26 ),
inference(sat_conversion,[],[f612]) ).
cnf(s29,plain,
( spl25_7
| spl25_33 ),
inference(sat_conversion,[],[f642]) ).
cnf(s35,plain,
~ spl25_7,
inference(sat_conversion,[],[f1012]) ).
cnf(s37,plain,
( ~ spl25_22
| ~ spl25_33 ),
inference(sat_conversion,[],[f1056]) ).
cnf(s39,plain,
( ~ spl25_20
| ~ spl25_24 ),
inference(sat_conversion,[],[f1091]) ).
cnf(s41,plain,
( ~ spl25_20
| ~ spl25_23
| ~ spl25_25 ),
inference(sat_conversion,[],[f1130]) ).
cnf(s43,plain,
( ~ spl25_21
| ~ spl25_26
| ~ spl25_33 ),
inference(sat_conversion,[],[f1171]) ).
cnf(s44,plain,
spl25_33,
inference(rat,[],[s29,s35]) ).
cnf(s45,plain,
~ spl25_22,
inference(rat,[],[s37,s44]) ).
cnf(s52,plain,
( spl25_24
| spl25_25
| spl25_26 ),
inference(rat,[],[s22,s45]) ).
cnf(s53,plain,
( spl25_23
| spl25_24
| spl25_26 ),
inference(rat,[],[s21,s45]) ).
cnf(s54,plain,
( spl25_21
| spl25_24
| spl25_25 ),
inference(rat,[],[s20,s45]) ).
cnf(s55,plain,
( spl25_21
| spl25_23
| spl25_24 ),
inference(rat,[],[s19,s45]) ).
cnf(s56,plain,
spl25_20,
inference(rat,[],[s18,s35]) ).
cnf(s57,plain,
~ spl25_24,
inference(rat,[],[s39,s56]) ).
cnf(s70,plain,
spl25_21,
inference(rat,[],[s41,s55,s54,s56,s57]) ).
cnf(s71,plain,
~ spl25_26,
inference(rat,[],[s43,s44,s70]) ).
cnf(s72,plain,
spl25_25,
inference(rat,[],[s52,s57,s71]) ).
cnf(s73,plain,
spl25_23,
inference(rat,[],[s53,s57,s71]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s41,s56,s72,s73]) ).
thf(f1172,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEG011^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 % Computer : n011.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 18:34:16 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running higher-order theorem proving
% 0.26/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.06/0.51 % (484242)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.06/0.51 % (484247)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=575417339:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.06/0.51 % (484253)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.06/0.51 % (484253)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.06/0.51 % (484248)lrs+10_16_si=on:nwc=1.5:random_seed=131764605:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.06/0.51 % (484249)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1334503128:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.06/0.51 % (484250)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2777727456:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.06/0.51 % (484251)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2363178172:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.06/0.51 % (484253)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4164879841:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.06/0.51 % (484252)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1335459577:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.06/0.51 % (484249)Instruction limit reached!
% 1.06/0.51 % (484249)------------------------------
% 1.06/0.51 % (484249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (484249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (484249)CaDiCaL version: 2.1.3
% 1.06/0.51 % (484249)Termination reason: Instruction limit
% 1.06/0.51 % (484249)Termination phase: shuffling
% 1.06/0.51 % (484249)Time elapsed: 0.003 s
% 1.06/0.51 % (484249)Peak memory usage: 9 MB
% 1.06/0.51 % (484249)Instructions burned: 3 (million)
% 1.06/0.51 % (484248)Instruction limit reached!
% 1.06/0.51 % (484248)------------------------------
% 1.06/0.51 % (484248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (484248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (484248)CaDiCaL version: 2.1.3
% 1.06/0.51 % (484248)Termination reason: Instruction limit
% 1.06/0.51 % (484248)Termination phase: Saturation
% 1.06/0.51 % (484248)Time elapsed: 0.015 s
% 1.06/0.51 % (484248)Peak memory usage: 11 MB
% 1.06/0.51 % (484248)Instructions burned: 19 (million)
% 1.06/0.51 % (484251)Instruction limit reached!
% 1.06/0.51 % (484251)------------------------------
% 1.06/0.51 % (484251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (484251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (484251)CaDiCaL version: 2.1.3
% 1.06/0.51 % (484251)Termination reason: Instruction limit
% 1.06/0.51 % (484251)Termination phase: Saturation
% 1.06/0.51 % (484251)Time elapsed: 0.023 s
% 1.06/0.51 % (484251)Peak memory usage: 11 MB
% 1.06/0.51 % (484251)Instructions burned: 24 (million)
% 1.06/0.51 % (484247)Instruction limit reached!
% 1.06/0.51 % (484247)------------------------------
% 1.06/0.51 % (484247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (484247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.51 % (484247)CaDiCaL version: 2.1.3
% 1.06/0.51 % (484247)Termination reason: Instruction limit
% 1.06/0.51 % (484247)Termination phase: Saturation
% 1.06/0.51 % (484247)Time elapsed: 0.038 s
% 1.06/0.51 % (484247)Peak memory usage: 12 MB
% 1.06/0.51 % (484247)Instructions burned: 88 (million)
% 1.06/0.51 % (484261)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2091533705:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.06/0.51 % (484261)Instruction limit reached!
% 1.06/0.51 % (484261)------------------------------
% 1.06/0.51 % (484261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.51 % (484261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484261)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484261)Termination reason: Instruction limit
% 1.06/0.56 % (484261)Termination phase: shuffling
% 1.06/0.56 % (484261)Time elapsed: 0.002 s
% 1.06/0.56 % (484261)Peak memory usage: 9 MB
% 1.06/0.56 % (484261)Instructions burned: 2 (million)
% 1.06/0.56 % (484262)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=730384863:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.06/0.56 % (484264)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1766555:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.06/0.56 % (484263)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.06/0.56 % (484262)Instruction limit reached!
% 1.06/0.56 % (484262)------------------------------
% 1.06/0.56 % (484262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484262)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484262)Termination reason: Instruction limit
% 1.06/0.56 % (484262)Termination phase: shuffling
% 1.06/0.56 % (484262)Time elapsed: 0.005 s
% 1.06/0.56 % (484262)Peak memory usage: 10 MB
% 1.06/0.56 % (484262)Instructions burned: 6 (million)
% 1.06/0.56 % (484266)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.06/0.56 % (484266)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.06/0.56 % (484263)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2943030942:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.06/0.56 % (484266)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1312348270:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.06/0.56 % (484264)Instruction limit reached!
% 1.06/0.56 % (484264)------------------------------
% 1.06/0.56 % (484264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484264)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484264)Termination reason: Instruction limit
% 1.06/0.56 % (484264)Termination phase: Property scanning
% 1.06/0.56 % (484264)Time elapsed: 0.011 s
% 1.06/0.56 % (484264)Peak memory usage: 10 MB
% 1.06/0.56 % (484264)Instructions burned: 13 (million)
% 1.06/0.56 % (484263)Instruction limit reached!
% 1.06/0.56 % (484263)------------------------------
% 1.06/0.56 % (484263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484263)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484263)Termination reason: Instruction limit
% 1.06/0.56 % (484263)Termination phase: Property scanning
% 1.06/0.56 % (484263)Time elapsed: 0.007 s
% 1.06/0.56 % (484263)Peak memory usage: 10 MB
% 1.06/0.56 % (484263)Instructions burned: 8 (million)
% 1.06/0.56 % (484252)Instruction limit reached!
% 1.06/0.56 % (484252)------------------------------
% 1.06/0.56 % (484252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484252)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484252)Termination reason: Instruction limit
% 1.06/0.56 % (484252)Termination phase: Saturation
% 1.06/0.56 % (484252)Time elapsed: 0.069 s
% 1.06/0.56 % (484252)Peak memory usage: 13 MB
% 1.06/0.56 % (484252)Instructions burned: 78 (million)
% 1.06/0.56 % (484269)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=59201044:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.06/0.56 % (484266)Instruction limit reached!
% 1.06/0.56 % (484266)------------------------------
% 1.06/0.56 % (484266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484266)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484266)Termination reason: Instruction limit
% 1.06/0.56 % (484266)Termination phase: Saturation
% 1.06/0.56 % (484266)Time elapsed: 0.024 s
% 1.06/0.56 % (484266)Peak memory usage: 11 MB
% 1.06/0.56 % (484266)Instructions burned: 29 (million)
% 1.06/0.56 % (484273)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.06/0.56 % (484273)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=736339555:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.06/0.56 % (484272)lrs+10_1_si=on:cs=on:random_seed=2178035601:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.06/0.56 % (484273)Instruction limit reached!
% 1.06/0.56 % (484273)------------------------------
% 1.06/0.56 % (484273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484273)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484273)Termination reason: Instruction limit
% 1.06/0.56 % (484273)Termination phase: shuffling
% 1.06/0.56 % (484273)Time elapsed: 0.002 s
% 1.06/0.56 % (484273)Peak memory usage: 9 MB
% 1.06/0.56 % (484273)Instructions burned: 2 (million)
% 1.06/0.56 % (484274)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3818060170:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.06/0.56 % (484272)Instruction limit reached!
% 1.06/0.56 % (484272)------------------------------
% 1.06/0.56 % (484272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484272)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484272)Termination reason: Instruction limit
% 1.06/0.56 % (484272)Termination phase: Property scanning
% 1.06/0.56 % (484272)Time elapsed: 0.007 s
% 1.06/0.56 % (484272)Peak memory usage: 10 MB
% 1.06/0.56 % (484272)Instructions burned: 8 (million)
% 1.06/0.56 % (484269)Instruction limit reached!
% 1.06/0.56 % (484269)------------------------------
% 1.06/0.56 % (484269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484269)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484269)Termination reason: Instruction limit
% 1.06/0.56 % (484269)Termination phase: Saturation
% 1.06/0.56 % (484269)Time elapsed: 0.041 s
% 1.06/0.56 % (484269)Peak memory usage: 13 MB
% 1.06/0.56 % (484269)Instructions burned: 87 (million)
% 1.06/0.56 % (484276)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=649651806:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.06/0.56 % (484274)Refutation not found, incomplete strategy
% 1.06/0.56 % (484274)------------------------------
% 1.06/0.56 % (484274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484274)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484274)Termination reason: Refutation not found, incomplete strategy
% 1.06/0.56 % (484274)Time elapsed: 0.014 s
% 1.06/0.56 % (484274)Peak memory usage: 12 MB
% 1.06/0.56 % (484274)Instructions burned: 15 (million)
% 1.06/0.56 % (484274)------------------------------
% 1.06/0.56 % (484274)------------------------------
% 1.06/0.56 % (484279)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3813774974:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.06/0.56 % (484253)Instruction limit reached!
% 1.06/0.56 % (484253)------------------------------
% 1.06/0.56 % (484253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484253)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484253)Termination reason: Instruction limit
% 1.06/0.56 % (484253)Termination phase: Saturation
% 1.06/0.56 % (484253)Time elapsed: 0.126 s
% 1.06/0.56 % (484253)Peak memory usage: 13 MB
% 1.06/0.56 % (484253)Instructions burned: 158 (million)
% 1.06/0.56 % (484282)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4005414476:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.06/0.56 % (484276)Refutation not found, incomplete strategy
% 1.06/0.56 % (484276)------------------------------
% 1.06/0.56 % (484276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484276)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484276)Termination reason: Refutation not found, incomplete strategy
% 1.06/0.56 % (484276)Time elapsed: 0.013 s
% 1.06/0.56 % (484276)Peak memory usage: 12 MB
% 1.06/0.56 % (484276)Instructions burned: 14 (million)
% 1.06/0.56 % (484276)------------------------------
% 1.06/0.56 % (484276)------------------------------
% 1.06/0.56 % (484281)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=862132210:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.06/0.56 % (484285)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2084471299:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.06/0.56 % (484279)Instruction limit reached!
% 1.06/0.56 % (484279)------------------------------
% 1.06/0.56 % (484279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484279)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484279)Termination reason: Instruction limit
% 1.06/0.56 % (484279)Termination phase: Saturation
% 1.06/0.56 % (484279)Time elapsed: 0.025 s
% 1.06/0.56 % (484279)Peak memory usage: 12 MB
% 1.06/0.56 % (484279)Instructions burned: 25 (million)
% 1.06/0.56 % (484281)Instruction limit reached!
% 1.06/0.56 % (484281)------------------------------
% 1.06/0.56 % (484281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484281)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484281)Termination reason: Instruction limit
% 1.06/0.56 % (484281)Termination phase: Property scanning
% 1.06/0.56 % (484281)Time elapsed: 0.011 s
% 1.06/0.56 % (484281)Peak memory usage: 10 MB
% 1.06/0.56 % (484281)Instructions burned: 14 (million)
% 1.06/0.56 % (484285)Instruction limit reached!
% 1.06/0.56 % (484285)------------------------------
% 1.06/0.56 % (484285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484285)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484285)Termination reason: Instruction limit
% 1.06/0.56 % (484285)Termination phase: Property scanning
% 1.06/0.56 % (484285)Time elapsed: 0.012 s
% 1.06/0.56 % (484285)Peak memory usage: 10 MB
% 1.06/0.56 % (484285)Instructions burned: 15 (million)
% 1.06/0.56 % (484288)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=761001935:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.06/0.56 % (484286)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3092851630:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.06/0.56 % (484286)Instruction limit reached!
% 1.06/0.56 % (484286)------------------------------
% 1.06/0.56 % (484286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.56 % (484286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.56 % (484286)CaDiCaL version: 2.1.3
% 1.06/0.56 % (484286)Termination reason: Instruction limit
% 1.06/0.56 % (484286)Termination phase: Property scanning
% 1.06/0.56 % (484286)Time elapsed: 0.004 s
% 1.06/0.56 % (484286)Peak memory usage: 10 MB
% 1.06/0.56 % (484286)Instructions burned: 4 (million)
% 1.06/0.56 % (484282) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-484242-484282"...
% 1.06/0.56 % (484282)...printing done.
% 1.06/0.56 % (484291)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=208317575:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.06/0.56 % (484282)Refutation found. Thanks to Tanya!
% 1.06/0.56 % SZS status Theorem for theBenchmark
% 1.06/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.06/0.57 % (484282)------------------------------
% 1.06/0.57 % (484282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.57 % (484282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.57 % (484282)CaDiCaL version: 2.1.3
% 1.06/0.57 % (484282)Termination reason: Refutation
% 1.06/0.57 % (484282)Time elapsed: 0.046 s
% 1.06/0.57 % (484282)Peak memory usage: 13 MB
% 1.06/0.57 % (484282)Instructions burned: 100 (million)
% 1.06/0.57 % (484242)Success in time 0.22 s
% 1.06/0.57 % Vampire exiting
%------------------------------------------------------------------------------