%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG008^1 : 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 : n002.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 07:49:25 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 20
% Syntax : Number of formulae : 185 ( 90 unt; 0 typ; 7 def)
% Number of atoms : 1381 ( 201 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2831 ( 167 ~; 129 |; 176 &;1910 @)
% ( 7 <=>; 193 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 91 ( 86 usr; 20 con; 0-4 aty)
% ( 182 !!; 67 ??; 0 @@+; 0 @@-)
% Number of variables : 596 ( 17 sgn 92 !; 6 ?; 596 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_54,type,
vOR: $o > $o > $o ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vAND: $o > $o > $o ).
thf(func_def_58,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_59,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_63,type,
sK0: reg ).
thf(func_def_64,type,
sK1: reg > reg ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_67,type,
sK4: reg > reg ).
thf(func_def_68,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_69,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_70,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_71,type,
sK8: reg ).
thf(func_def_72,type,
sK9: reg ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_75,type,
sK12: reg > reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: reg > reg ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
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(f33,axiom,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).
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(f36,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
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,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) )
= 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] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f51,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f52,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f62,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f63,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f68,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f69,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f71,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f70]) ).
thf(f76,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f77,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(fool_elimination,[],[f76]) ).
thf(f105,plain,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f106,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f107,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f108,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
=> ( ( c @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
inference(rectify,[],[f36]) ).
thf(f110,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f117,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f118,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) )
!= $true ),
inference(fool_elimination,[],[f117]) ).
thf(f125,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f126,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f125]) ).
thf(f131,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f132,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f131]) ).
thf(f136,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f137,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) )
!= $true ),
inference(flattening,[],[f118]) ).
thf(f139,plain,
! [X1: reg,X0: reg] :
( ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f108]) ).
thf(f140,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
| ( ( c @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f139]) ).
thf(f148,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f151,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(cnf_transformation,[],[f77]) ).
thf(f152,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f153,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f156,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f158,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f140]) ).
thf(f163,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f167,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f71]) ).
thf(f176,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f177,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f186,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f187,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f126]) ).
thf(f188,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f201,plain,
( eq
= ( ^ [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,f156,f156]) ).
thf(f202,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,[],[f163,f156,f156]) ).
thf(f204,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ^ [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 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f152,f202]) ).
thf(f205,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,[],[f187,f156,f156]) ).
thf(f206,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [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 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [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 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [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 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f176,f205,f204,f204]) ).
thf(f207,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [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 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [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 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [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 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f188,f205,f204,f204]) ).
thf(f209,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] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y1
@ Y2 ) )
@ catalunya
@ paris )
=> ( ^ [Y1: reg,Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) ) )
@ france
@ spain ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f148,f186,f177,f201,f202]) ).
thf(f210,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] :
( ( ^ [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 )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [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 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [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 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 ) ) ) )
@ catalunya
@ spain ) ) )
= $true ),
inference(definition_unfolding,[],[f151,f186,f177,f206]) ).
thf(f213,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] :
( ( ^ [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 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [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 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [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 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 ) ) ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f167,f186,f177,f207]) ).
thf(f215,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f216,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ paris ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ paris ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ paris ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f231,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f232,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) )
= $true ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f346,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ catalunya ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f347,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ catalunya ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ catalunya ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ catalunya ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ catalunya ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f349]) ).
thf(f351,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ catalunya ) ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f350]) ).
thf(f353,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f351]) ).
thf(f354,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f353]) ).
thf(f362,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f354]) ).
thf(f363,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ X3 @ spain )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f364]) ).
thf(f401,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ paris ) ) ) )
=> ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f402,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ paris ) ) ) )
=> ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ sK14 ) ),
inference(sigma_proxy_clausification,[],[f401]) ).
thf(f403,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ paris ) ) ) )
=> ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) )
| ~ ( a @ sK14 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f402]) ).
thf(f404,plain,
( ( ^ [Y0: $i] :
( ( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ paris ) ) ) )
=> ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) )
| ~ ( a @ sK14 @ Y0 ) )
@ sK15 )
= $false ),
inference(sigma_proxy_clausification,[],[f403]) ).
thf(f405,plain,
( $false
= ( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) )
=> ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
| ~ ( a @ sK14 @ sK15 ) ) ),
inference(beta-eta_normalization,[],[f404]) ).
thf(f406,plain,
( $false
= ( ~ ( a @ sK14 @ sK15 ) ) ),
inference(or_proxy_clausification,[],[f405]) ).
thf(f407,plain,
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) )
=> ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f405]) ).
thf(f408,plain,
( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f407]) ).
thf(f409,plain,
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f407]) ).
thf(f410,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) )
= $true ),
inference(and_proxy_clausification,[],[f409]) ).
thf(f411,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
= $true ),
inference(and_proxy_clausification,[],[f409]) ).
thf(f412,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f411]) ).
thf(f413,plain,
! [X1: reg] :
( ( ( c @ X1 @ paris )
=> ( c @ X1 @ catalunya ) )
= $true ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f414,plain,
! [X1: reg] :
( ( ( c @ X1 @ catalunya )
= $true )
| ( ( c @ X1 @ paris )
= $false ) ),
inference(imp_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f410]) ).
thf(f416,plain,
! [X1: reg] :
( ( ( c @ X1 @ catalunya )
=> ( c @ X1 @ paris ) )
= $true ),
inference(beta-eta_normalization,[],[f415]) ).
thf(f417,plain,
! [X1: reg] :
( ( ( c @ X1 @ catalunya )
= $false )
| ( ( c @ X1 @ paris )
= $true ) ),
inference(imp_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f408]) ).
thf(f419,plain,
! [X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f418]) ).
thf(f420,plain,
! [X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) )
= $false )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f419]) ).
thf(f421,plain,
! [X1: reg] :
( ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) )
@ ( sK17 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f421]) ).
thf(f423,plain,
! [X1: reg] :
( ( $false
= ( ( c @ ( sK17 @ X1 ) @ X1 )
=> ( c @ ( sK17 @ X1 ) @ france ) ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false ) ),
inference(beta-eta_normalization,[],[f422]) ).
thf(f424,plain,
! [X1: reg] :
( ( ( c @ ( sK17 @ X1 ) @ france )
= $false )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X1: reg] :
( ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( ( c @ ( sK17 @ X1 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f423]) ).
thf(f426,plain,
! [X1: reg] :
( ( ( c @ ( sK17 @ X1 ) @ X1 )
= $true )
| ( $false
= ( c @ ( sK16 @ X1 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f425]) ).
thf(f427,plain,
! [X1: reg] :
( ( ( c @ ( sK17 @ X1 ) @ X1 )
= $true )
| ( ( c @ ( sK16 @ X1 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f425]) ).
thf(f428,plain,
! [X1: reg] :
( ( ( c @ ( sK17 @ X1 ) @ france )
= $false )
| ( $false
= ( c @ ( sK16 @ X1 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f424]) ).
thf(f429,plain,
! [X1: reg] :
( ( ( c @ ( sK17 @ X1 ) @ france )
= $false )
| ( ( c @ ( sK16 @ X1 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f424]) ).
thf(f430,plain,
( ( a @ sK14 @ sK15 )
= $true ),
inference(not_proxy_clausification,[],[f406]) ).
thf(f436,definition,
( spl18_2
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f437,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f436]) ).
thf(f445,definition,
( spl18_4
<=> ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
thf(f446,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f445]) ).
thf(f447,plain,
( spl18_2
| spl18_4 ),
inference(avatar_split_clause,[],[f233,f445,f436]) ).
thf(f499,definition,
( spl18_17
<=> ! [X3: reg] :
( ( ( c @ X3 @ spain )
= $true )
| ( ( c @ X3 @ catalunya )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_17])],[avatar_definition]) ).
thf(f500,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ catalunya )
= $false )
| ( ( c @ X3 @ spain )
= $true ) )
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f499]) ).
thf(f501,plain,
( spl18_17
| spl18_2 ),
inference(avatar_split_clause,[],[f365,f436,f499]) ).
thf(f606,plain,
( ( $false = $true )
| ~ spl18_2 ),
inference(constrained_superposition,[],[f437,f430]) ).
thf(f610,plain,
( $false
| ~ spl18_2 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f611,plain,
~ spl18_2,
inference(avatar_contradiction_clause,[],[f610]) ).
thf(f621,plain,
! [X0: reg] :
( ( $true != $true )
| ( ( c @ X0 @ paris )
= $false )
| ( ( c @ catalunya @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f158,f414]) ).
thf(f643,plain,
! [X0: reg] :
( ( ( c @ X0 @ paris )
= $false )
| ( ( c @ catalunya @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f621]) ).
thf(f664,plain,
( ( ( c @ catalunya @ ( sK17 @ paris ) )
= $true )
| ( $false = $true )
| ( ( c @ ( sK16 @ paris ) @ paris )
= $true ) ),
inference(constrained_superposition,[],[f643,f427]) ).
thf(f671,plain,
( ( $false = $true )
| ( ( c @ catalunya @ ( sK17 @ paris ) )
= $true )
| ( ( c @ ( sK16 @ paris ) @ spain )
= $false ) ),
inference(constrained_superposition,[],[f426,f643]) ).
thf(f682,plain,
( ( ( c @ ( sK16 @ paris ) @ paris )
= $true )
| ( ( c @ catalunya @ ( sK17 @ paris ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f664]) ).
thf(f684,plain,
( ( ( c @ catalunya @ ( sK17 @ paris ) )
= $true )
| ( ( c @ ( sK16 @ paris ) @ spain )
= $false ) ),
inference(trivial_inequality_removal,[],[f671]) ).
thf(f686,definition,
( spl18_33
<=> ( ( c @ catalunya @ ( sK17 @ paris ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_33])],[avatar_definition]) ).
thf(f688,plain,
( ( ( c @ catalunya @ ( sK17 @ paris ) )
= $true )
| ~ spl18_33 ),
inference(avatar_component_clause,[],[f686]) ).
thf(f690,definition,
( spl18_34
<=> ( ( c @ ( sK16 @ paris ) @ spain )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_34])],[avatar_definition]) ).
thf(f692,plain,
( ( ( c @ ( sK16 @ paris ) @ spain )
= $false )
| ~ spl18_34 ),
inference(avatar_component_clause,[],[f690]) ).
thf(f695,definition,
( spl18_35
<=> ( ( c @ ( sK16 @ paris ) @ paris )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_35])],[avatar_definition]) ).
thf(f697,plain,
( ( ( c @ ( sK16 @ paris ) @ paris )
= $true )
| ~ spl18_35 ),
inference(avatar_component_clause,[],[f695]) ).
thf(f699,plain,
( spl18_33
| spl18_35 ),
inference(avatar_split_clause,[],[f682,f695,f686]) ).
thf(f700,plain,
( spl18_33
| spl18_34 ),
inference(avatar_split_clause,[],[f684,f690,f686]) ).
thf(f701,plain,
( ( $true != $true )
| ( ( c @ ( sK17 @ paris ) @ catalunya )
= $true )
| ~ spl18_33 ),
inference(constrained_superposition,[],[f158,f688]) ).
thf(f702,plain,
( ( ( c @ ( sK17 @ paris ) @ catalunya )
= $true )
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f701]) ).
thf(f705,plain,
( ( $false = $true )
| ( ( c @ ( sK17 @ paris ) @ paris )
= $true )
| ~ spl18_33 ),
inference(constrained_superposition,[],[f702,f417]) ).
thf(f708,plain,
( ( ( c @ ( sK17 @ paris ) @ paris )
= $true )
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f705]) ).
thf(f823,plain,
( ( $false = $true )
| ( ( c @ ( sK17 @ paris ) @ france )
= $true )
| ~ spl18_4
| ~ spl18_33 ),
inference(constrained_superposition,[],[f708,f446]) ).
thf(f832,plain,
( ( ( c @ ( sK17 @ paris ) @ france )
= $true )
| ~ spl18_4
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f823]) ).
thf(f848,definition,
( spl18_36
<=> ( ( c @ ( sK17 @ paris ) @ france )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_36])],[avatar_definition]) ).
thf(f850,plain,
( ( ( c @ ( sK17 @ paris ) @ france )
= $true )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f848]) ).
thf(f853,plain,
( spl18_36
| ~ spl18_4
| ~ spl18_33 ),
inference(avatar_split_clause,[],[f832,f686,f445,f848]) ).
thf(f881,plain,
( ( $false = $true )
| ( ( c @ ( sK16 @ paris ) @ paris )
= $true )
| ~ spl18_36 ),
inference(constrained_superposition,[],[f850,f429]) ).
thf(f886,plain,
( ( $false = $true )
| ( ( c @ ( sK16 @ paris ) @ spain )
= $false )
| ~ spl18_36 ),
inference(constrained_superposition,[],[f428,f850]) ).
thf(f887,plain,
( ( ( c @ ( sK16 @ paris ) @ paris )
= $true )
| ~ spl18_36 ),
inference(trivial_inequality_removal,[],[f881]) ).
thf(f888,plain,
( ( ( c @ ( sK16 @ paris ) @ spain )
= $false )
| ~ spl18_36 ),
inference(trivial_inequality_removal,[],[f886]) ).
thf(f894,plain,
( spl18_35
| ~ spl18_36 ),
inference(avatar_split_clause,[],[f887,f848,f695]) ).
thf(f895,plain,
( spl18_34
| ~ spl18_36 ),
inference(avatar_split_clause,[],[f888,f848,f690]) ).
thf(f902,plain,
( ( $false = $true )
| ( ( c @ catalunya @ ( sK16 @ paris ) )
= $true )
| ~ spl18_35 ),
inference(constrained_superposition,[],[f643,f697]) ).
thf(f905,plain,
( ( ( c @ catalunya @ ( sK16 @ paris ) )
= $true )
| ~ spl18_35 ),
inference(trivial_inequality_removal,[],[f902]) ).
thf(f933,plain,
( ( $true != $true )
| ( ( c @ ( sK16 @ paris ) @ catalunya )
= $true )
| ~ spl18_35 ),
inference(constrained_superposition,[],[f158,f905]) ).
thf(f934,plain,
( ( ( c @ ( sK16 @ paris ) @ catalunya )
= $true )
| ~ spl18_35 ),
inference(trivial_inequality_removal,[],[f933]) ).
thf(f976,plain,
( ( $false = $true )
| ( ( c @ ( sK16 @ paris ) @ spain )
= $true )
| ~ spl18_17
| ~ spl18_35 ),
inference(constrained_superposition,[],[f500,f934]) ).
thf(f999,plain,
( ( ( c @ ( sK16 @ paris ) @ spain )
= $true )
| ~ spl18_17
| ~ spl18_35 ),
inference(trivial_inequality_removal,[],[f976]) ).
thf(f1029,plain,
( ( $false = $true )
| ~ spl18_17
| ~ spl18_34
| ~ spl18_35 ),
inference(forward_demodulation,[],[f999,f692]) ).
thf(f1030,plain,
( $false
| ~ spl18_17
| ~ spl18_34
| ~ spl18_35 ),
inference(trivial_inequality_removal,[],[f1029]) ).
thf(f1031,plain,
( ~ spl18_17
| ~ spl18_34
| ~ spl18_35 ),
inference(avatar_contradiction_clause,[],[f1030]) ).
cnf(s3,plain,
( spl18_2
| spl18_4 ),
inference(sat_conversion,[],[f447]) ).
cnf(s15,plain,
( spl18_2
| spl18_17 ),
inference(sat_conversion,[],[f501]) ).
cnf(s37,plain,
~ spl18_2,
inference(sat_conversion,[],[f611]) ).
cnf(s40,plain,
( spl18_33
| spl18_35 ),
inference(sat_conversion,[],[f699]) ).
cnf(s41,plain,
( spl18_33
| spl18_34 ),
inference(sat_conversion,[],[f700]) ).
cnf(s44,plain,
( ~ spl18_4
| ~ spl18_33
| spl18_36 ),
inference(sat_conversion,[],[f853]) ).
cnf(s50,plain,
( spl18_35
| ~ spl18_36 ),
inference(sat_conversion,[],[f894]) ).
cnf(s51,plain,
( spl18_34
| ~ spl18_36 ),
inference(sat_conversion,[],[f895]) ).
cnf(s59,plain,
( ~ spl18_17
| ~ spl18_34
| ~ spl18_35 ),
inference(sat_conversion,[],[f1031]) ).
cnf(s72,plain,
spl18_17,
inference(rat,[],[s15,s37]) ).
cnf(s79,plain,
spl18_4,
inference(rat,[],[s3,s37]) ).
cnf(s82,plain,
spl18_33,
inference(rat,[],[s59,s40,s41,s72]) ).
cnf(s83,plain,
spl18_36,
inference(rat,[],[s44,s79,s82]) ).
cnf(s85,plain,
spl18_34,
inference(rat,[],[s51,s83]) ).
cnf(s86,plain,
spl18_35,
inference(rat,[],[s50,s83]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s59,s72,s86,s85]) ).
thf(f1038,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG008^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:36:38 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.24/0.30 % (1681897)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (1681907)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2878796682:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.30 % (1681914)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.30 % (1681914)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
% 0.24/0.30 % (1681908)lrs+10_16_si=on:nwc=1.5:random_seed=727999615:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.30 % (1681909)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1123774364:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.30 % (1681912)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3651053120:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.30 % (1681910)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=3226067154: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)
% 0.24/0.30 % (1681913)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2825806818:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.30 % (1681914)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=807825580:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.30 % (1681909)Instruction limit reached!
% 0.24/0.30 % (1681909)------------------------------
% 0.24/0.30 % (1681909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (1681909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (1681909)CaDiCaL version: 2.1.3
% 0.24/0.30 % (1681909)Termination reason: Instruction limit
% 0.24/0.30 % (1681909)Termination phase: Property scanning
% 0.24/0.30 % (1681909)Time elapsed: 0.002 s
% 0.24/0.30 % (1681909)Peak memory usage: 10 MB
% 0.24/0.30 % (1681909)Instructions burned: 4 (million)
% 0.24/0.30 % (1681907) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1681897-1681907"...
% 0.24/0.30 % (1681908)Instruction limit reached!
% 0.24/0.30 % (1681908)------------------------------
% 0.24/0.30 % (1681908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (1681908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (1681908)CaDiCaL version: 2.1.3
% 0.24/0.30 % (1681908)Termination reason: Instruction limit
% 0.24/0.30 % (1681908)Termination phase: Saturation
% 0.24/0.30 % (1681908)Time elapsed: 0.008 s
% 0.24/0.30 % (1681908)Peak memory usage: 11 MB
% 0.24/0.30 % (1681908)Instructions burned: 18 (million)
% 0.24/0.30 % (1681907)...printing done.
% 0.24/0.30 % (1681907)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.30 % (1681907)------------------------------
% 0.24/0.30 % (1681907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (1681907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (1681907)CaDiCaL version: 2.1.3
% 0.24/0.30 % (1681907)Termination reason: Refutation
% 0.24/0.30 % (1681907)Time elapsed: 0.020 s
% 0.24/0.30 % (1681907)Peak memory usage: 14 MB
% 0.24/0.30 % (1681907)Instructions burned: 71 (million)
% 0.24/0.30 % (1681897)Success in time 0.036 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------