%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG010^1 : 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 : n008.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 0.26s 0.37s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 28
% Syntax : Number of formulae : 248 ( 120 unt; 0 typ; 10 def)
% Number of atoms : 1746 ( 280 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3439 ( 272 ~; 239 |; 173 &;2255 @)
% ( 10 <=>; 201 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 88 usr; 24 con; 0-4 aty)
% ( 220 !!; 69 ??; 0 @@+; 0 @@-)
% Number of variables : 780 ( 22 sgn 175 !; 6 ?; 780 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_58,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_59,type,
vNOT: $o > $o ).
thf(func_def_60,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
vOR: $o > $o > $o ).
thf(func_def_62,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_63,type,
sK0: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK1: $i > ( $i > $o ) > $i ).
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: reg > reg ).
thf(func_def_69,type,
sK6: reg ).
thf(func_def_72,type,
sK9: reg ).
thf(func_def_73,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_74,type,
sK11: reg ).
thf(func_def_75,type,
sK12: reg > reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > reg ).
thf(func_def_79,type,
sK16: reg ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
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(f37,axiom,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
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] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= ntpp ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f43,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f47,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
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] :
( ( p @ X1 @ catalunya )
=> ~ ( p @ X1 @ paris ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
! [X1: reg] :
( ( p @ X1 @ catalunya )
=> ~ ( p @ X1 @ paris ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f53,plain,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
inference(rectify,[],[f47]) ).
thf(f54,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f61,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f62,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f69,plain,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f43]) ).
thf(f70,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f73,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f74,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f89,plain,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f90,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f93,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f94,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f96,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f97,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f100,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
! [X1: reg] :
( ( p @ X1 @ catalunya )
=> ~ ( p @ X1 @ paris ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f101,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( p @ Y1 @ catalunya )
=> ~ ( p @ Y1 @ paris ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f100]) ).
thf(f102,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f103,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f104,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f105,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f104]) ).
thf(f107,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f108,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f110,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f112,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f118,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f119,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
=> ( ( c @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f118]) ).
thf(f126,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f127,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(fool_elimination,[],[f126]) ).
thf(f128,plain,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
inference(rectify,[],[f37]) ).
thf(f129,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f128]) ).
thf(f134,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f136,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f137,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( p @ Y1 @ catalunya )
=> ~ ( p @ Y1 @ paris ) ) ) ) )
!= $true ),
inference(flattening,[],[f101]) ).
thf(f139,plain,
! [X1: reg,X0: reg] :
( ( ( c @ X0 @ X1 )
!= $true )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f119]) ).
thf(f140,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f139]) ).
thf(f141,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f137]) ).
thf(f144,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f129]) ).
thf(f145,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f147,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f149,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f150,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f151,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f152,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f161,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f163,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( ( p @ Y1 @ catalunya )
=> ~ ( p @ Y1 @ paris ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f165,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f166,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f168,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f140]) ).
thf(f169,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f172,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(cnf_transformation,[],[f127]) ).
thf(f182,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f184,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f189,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f193,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f169,f182,f184]) ).
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
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f144,f145,f145]) ).
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
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 ) ) )
@ Y0
@ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f165,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,[],[f189,f145,f145]) ).
thf(f206,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ 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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ 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,[],[f147,f204,f204,f205]) ).
thf(f207,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ 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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ 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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ 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,[],[f151,f204,f204,f205]) ).
thf(f208,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] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ 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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ 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 ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f141,f150,f149,f207]) ).
thf(f209,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ fool
@ Y0 )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f152,f150,f161,f193,f149]) ).
thf(f211,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] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ catalunya )
=> ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ paris ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f163,f150,f149,f145,f145]) ).
thf(f212,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 ) ) )
@ fool
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ~ ( ^ [Y3: reg,Y4: reg] :
( ?? @ 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 ) ) )
@ Y5
@ Y3 ) ) )
@ Y1
@ Y2 )
& ( c @ Y1 @ Y2 ) )
@ spain
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f166,f150,f149,f204]) ).
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] :
( ( ?? @ 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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ 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 ) )
@ catalunya
@ spain ) ) )
= $true ),
inference(definition_unfolding,[],[f172,f150,f149,f206]) ).
thf(f257,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f258,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
= $true )
| ( ( ~ ( fool @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( fool @ X1 @ X2 ) )
= $true )
| ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f262]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $true )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) ) ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK2 @ X3 ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK3 @ X3 ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK2 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( c @ ( sK2 @ X3 ) @ X3 )
=> ( c @ ( sK2 @ X3 ) @ france ) )
= $false )
| ( ( ( c @ ( sK3 @ X3 ) @ X3 )
=> ( c @ ( sK3 @ X3 ) @ spain ) )
= $false ) ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( c @ ( sK3 @ X3 ) @ X3 )
=> ( c @ ( sK3 @ X3 ) @ spain ) )
= $false )
| ( ( c @ ( sK2 @ X3 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ ( sK3 @ X3 ) @ X3 )
=> ( c @ ( sK3 @ X3 ) @ spain ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f275,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK3 @ X3 ) @ spain )
= $false ) ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK3 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f277,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK2 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK3 @ X3 ) @ spain )
= $false ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f278,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK2 @ X3 ) @ france )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK3 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f280,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris ) ) )
& ~ ( !! @ 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,[],[f208]) ).
thf(f281,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris ) ) )
& ~ ( !! @ 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,[],[f280]) ).
thf(f282,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris ) ) )
& ~ ( !! @ 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,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) )
& ~ ( !! @ 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,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f286]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f287]) ).
thf(f333,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f326]) ).
thf(f334,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) )
= $true ) ),
inference(beta-eta_normalization,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( ( c @ X3 @ france )
= $true ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f336,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f337,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ sK7 )
= $false ),
inference(sigma_proxy_clausification,[],[f336]) ).
thf(f338,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
| ~ ( a @ sK7 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f337]) ).
thf(f339,plain,
( ( ^ [Y0: $i] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
| ~ ( a @ sK7 @ Y0 ) )
@ sK8 )
= $false ),
inference(sigma_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) )
| ~ ( a @ sK7 @ sK8 ) )
= $false ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
( $false
= ( ~ ( a @ sK7 @ sK8 ) ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f342,plain,
( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f343,plain,
( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) )
@ sK9 )
= $false ),
inference(sigma_proxy_clausification,[],[f342]) ).
thf(f344,plain,
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ catalunya ) ) )
=> ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ paris ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
( $false
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ paris ) ) ) ) ),
inference(imp_proxy_clausification,[],[f344]) ).
thf(f346,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ catalunya ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f344]) ).
thf(f347,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ catalunya ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK9 )
=> ( c @ X1 @ catalunya ) )
= $true ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK9 )
= $false )
| ( ( c @ X1 @ catalunya )
= $true ) ),
inference(imp_proxy_clausification,[],[f348]) ).
thf(f350,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ paris ) ) ) ),
inference(not_proxy_clausification,[],[f345]) ).
thf(f351,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK9 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK9 )
=> ( c @ X1 @ paris ) )
= $true ),
inference(beta-eta_normalization,[],[f351]) ).
thf(f353,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK9 )
= $false )
| ( ( c @ X1 @ paris )
= $true ) ),
inference(imp_proxy_clausification,[],[f352]) ).
thf(f354,plain,
( ( a @ sK7 @ sK8 )
= $true ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f355,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( fool @ Y0 @ Y2 ) ) )
| ( Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f356,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( fool @ Y0 @ Y2 ) ) )
| ( Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( fool @ X1 @ Y1 ) ) )
| ( Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f356]) ).
thf(f358,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( fool @ X1 @ Y1 ) ) )
| ( Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) ) )
| ( X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) ) ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) )
@ ( sK10 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ( X2 @ ( sK10 @ X1 @ X2 ) )
| ~ ( fool @ X1 @ ( sK10 @ X1 @ X2 ) ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f362]) ).
thf(f364,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ~ ( fool @ X1 @ ( sK10 @ X1 @ X2 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f363]) ).
thf(f366,plain,
! [X2: $i > $o,X1: $i] :
( ( ( fool @ X1 @ ( sK10 @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f367,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ spain ) ) )
& ~ ( !! @ 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,[],[f213]) ).
thf(f368,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ spain ) ) )
& ~ ( !! @ 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,[],[f367]) ).
thf(f369,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ spain ) ) )
& ~ ( !! @ 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,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ spain ) ) )
& ~ ( !! @ 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,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X1: $i] :
( ( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) )
& ~ ( !! @ 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,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) )
& ~ ( !! @ 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,[],[f371]) ).
thf(f373,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f372]) ).
thf(f410,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f373]) ).
thf(f411,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f410]) ).
thf(f418,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f411]) ).
thf(f419,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) )
= $true ) ),
inference(beta-eta_normalization,[],[f418]) ).
thf(f420,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f419]) ).
thf(f422,definition,
( spl17_1
<=> ! [X3: reg] :
( ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK3 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
thf(f423,plain,
( ! [X3: reg] :
( ( ( c @ ( sK3 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f422]) ).
thf(f425,definition,
( spl17_2
<=> ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
thf(f426,plain,
( ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false )
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f425]) ).
thf(f427,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f276,f425,f422]) ).
thf(f429,definition,
( spl17_3
<=> ! [X3: reg] :
( ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK3 @ X3 ) @ spain )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
thf(f430,plain,
( ! [X3: reg] :
( ( ( c @ ( sK2 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK3 @ X3 ) @ spain )
= $false ) )
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f431,plain,
( spl17_3
| spl17_2 ),
inference(avatar_split_clause,[],[f275,f425,f429]) ).
thf(f433,definition,
( spl17_4
<=> ! [X3: reg] :
( ( ( c @ ( sK2 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK3 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
thf(f434,plain,
( ! [X3: reg] :
( ( ( c @ ( sK3 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK2 @ X3 ) @ france )
= $false ) )
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f435,plain,
( spl17_2
| spl17_4 ),
inference(avatar_split_clause,[],[f278,f433,f425]) ).
thf(f437,definition,
( spl17_5
<=> ! [X3: reg] :
( ( ( c @ ( sK2 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK3 @ X3 ) @ spain )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
thf(f438,plain,
( ! [X3: reg] :
( ( ( c @ ( sK3 @ X3 ) @ spain )
= $false )
| ( ( c @ ( sK2 @ X3 ) @ france )
= $false ) )
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f437]) ).
thf(f439,plain,
( spl17_5
| spl17_2 ),
inference(avatar_split_clause,[],[f277,f425,f437]) ).
thf(f449,definition,
( spl17_8
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
thf(f450,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f449]) ).
thf(f475,definition,
( spl17_14
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( ( c @ X3 @ france )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_14])],[avatar_definition]) ).
thf(f476,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl17_14 ),
inference(avatar_component_clause,[],[f475]) ).
thf(f477,plain,
( spl17_14
| spl17_8 ),
inference(avatar_split_clause,[],[f335,f449,f475]) ).
thf(f531,definition,
( spl17_27
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl17_27])],[avatar_definition]) ).
thf(f532,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ spain )
= $true )
| ( $false
= ( c @ X3 @ catalunya ) ) )
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f531]) ).
thf(f533,plain,
( spl17_27
| spl17_8 ),
inference(avatar_split_clause,[],[f420,f449,f531]) ).
thf(f534,plain,
( ( $false = $true )
| ~ spl17_8 ),
inference(constrained_superposition,[],[f450,f354]) ).
thf(f538,plain,
( $false
| ~ spl17_8 ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f539,plain,
~ spl17_8,
inference(avatar_contradiction_clause,[],[f538]) ).
thf(f556,plain,
( ! [X0: reg] :
( ( $true != $true )
| ( ( c @ spain @ X0 )
= $true )
| ( $false
= ( c @ X0 @ catalunya ) ) )
| ~ spl17_27 ),
inference(constrained_superposition,[],[f168,f532]) ).
thf(f570,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ catalunya ) )
| ( ( c @ spain @ X0 )
= $true ) )
| ~ spl17_27 ),
inference(trivial_inequality_removal,[],[f556]) ).
thf(f694,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $false = $true )
| ( ( X1 @ X0 )
= $true ) )
| ~ spl17_2 ),
inference(constrained_superposition,[],[f426,f366]) ).
thf(f696,plain,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ X0 )
= $true )
| ~ spl17_2 ),
inference(trivial_inequality_removal,[],[f694]) ).
thf(f741,plain,
( ! [X2: $i > $o,X0: $i] :
( ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X0 )
= $true )
| ~ spl17_2 ),
inference(primitive_instantiation,[],[f696]) ).
thf(f762,plain,
( ! [X2: $i > $o,X0: $i] :
( ( ~ ( X2 @ X0 ) )
= $true )
| ~ spl17_2 ),
inference(beta-eta_normalization,[],[f741]) ).
thf(f763,plain,
( ! [X2: $i > $o,X0: $i] :
( ( X2 @ X0 )
= $false )
| ~ spl17_2 ),
inference(not_proxy_clausification,[],[f762]) ).
thf(f766,plain,
( ( $false = $true )
| ~ spl17_2 ),
inference(forward_demodulation,[],[f763,f696]) ).
thf(f767,plain,
( $false
| ~ spl17_2 ),
inference(trivial_inequality_removal,[],[f766]) ).
thf(f768,plain,
~ spl17_2,
inference(avatar_contradiction_clause,[],[f767]) ).
thf(f777,plain,
( ( $false = $true )
| ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ( ( c @ ( sK2 @ sK9 ) @ sK9 )
= $true )
| ~ spl17_1 ),
inference(constrained_superposition,[],[f349,f423]) ).
thf(f784,plain,
( ( ( c @ ( sK2 @ sK9 ) @ sK9 )
= $true )
| ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ~ spl17_1 ),
inference(trivial_inequality_removal,[],[f777]) ).
thf(f806,definition,
( spl17_32
<=> ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_32])],[avatar_definition]) ).
thf(f808,plain,
( ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ~ spl17_32 ),
inference(avatar_component_clause,[],[f806]) ).
thf(f810,definition,
( spl17_33
<=> ( ( c @ ( sK2 @ sK9 ) @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_33])],[avatar_definition]) ).
thf(f811,plain,
( ( ( c @ ( sK2 @ sK9 ) @ sK9 )
!= $true )
| spl17_33 ),
inference(avatar_component_clause,[],[f810]) ).
thf(f812,plain,
( ( ( c @ ( sK2 @ sK9 ) @ sK9 )
= $true )
| ~ spl17_33 ),
inference(avatar_component_clause,[],[f810]) ).
thf(f820,plain,
( spl17_32
| spl17_33
| ~ spl17_1 ),
inference(avatar_split_clause,[],[f784,f422,f810,f806]) ).
thf(f826,plain,
( ( $false = $true )
| ( ( c @ ( sK2 @ sK9 ) @ paris )
= $true )
| ~ spl17_33 ),
inference(constrained_superposition,[],[f353,f812]) ).
thf(f830,plain,
( ( ( c @ ( sK2 @ sK9 ) @ paris )
= $true )
| ~ spl17_33 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f841,plain,
( ( ( c @ ( sK2 @ sK9 ) @ france )
= $true )
| ( $false = $true )
| ~ spl17_14
| ~ spl17_33 ),
inference(constrained_superposition,[],[f476,f830]) ).
thf(f843,plain,
( ( ( c @ ( sK2 @ sK9 ) @ france )
= $true )
| ~ spl17_14
| ~ spl17_33 ),
inference(trivial_inequality_removal,[],[f841]) ).
thf(f910,plain,
( ( $false = $true )
| ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ( ( c @ ( sK2 @ sK9 ) @ france )
= $false )
| ~ spl17_4 ),
inference(constrained_superposition,[],[f349,f434]) ).
thf(f913,plain,
( ( ( c @ ( sK2 @ sK9 ) @ france )
= $false )
| ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ~ spl17_4 ),
inference(trivial_inequality_removal,[],[f910]) ).
thf(f923,plain,
( ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ( $false = $true )
| ~ spl17_4
| ~ spl17_14
| ~ spl17_33 ),
inference(forward_demodulation,[],[f913,f843]) ).
thf(f924,plain,
( ( ( c @ ( sK3 @ sK9 ) @ catalunya )
= $true )
| ~ spl17_4
| ~ spl17_14
| ~ spl17_33 ),
inference(trivial_inequality_removal,[],[f923]) ).
thf(f931,plain,
( spl17_32
| ~ spl17_4
| ~ spl17_14
| ~ spl17_33 ),
inference(avatar_split_clause,[],[f924,f810,f475,f433,f806]) ).
thf(f933,plain,
( ( $false = $true )
| ( ( c @ spain @ ( sK3 @ sK9 ) )
= $true )
| ~ spl17_27
| ~ spl17_32 ),
inference(constrained_superposition,[],[f808,f570]) ).
thf(f936,plain,
( ( ( c @ spain @ ( sK3 @ sK9 ) )
= $true )
| ~ spl17_27
| ~ spl17_32 ),
inference(trivial_inequality_removal,[],[f933]) ).
thf(f953,plain,
( ( $true
= ( c @ ( sK3 @ sK9 ) @ spain ) )
| ( $true != $true )
| ~ spl17_27
| ~ spl17_32 ),
inference(constrained_superposition,[],[f168,f936]) ).
thf(f954,plain,
( ( $true
= ( c @ ( sK3 @ sK9 ) @ spain ) )
| ~ spl17_27
| ~ spl17_32 ),
inference(trivial_inequality_removal,[],[f953]) ).
thf(f955,plain,
( ( $false = $true )
| ( ( c @ ( sK2 @ sK9 ) @ sK9 )
= $true )
| ~ spl17_3
| ~ spl17_27
| ~ spl17_32 ),
inference(constrained_superposition,[],[f954,f430]) ).
thf(f958,plain,
( ( ( c @ ( sK2 @ sK9 ) @ sK9 )
= $true )
| ~ spl17_3
| ~ spl17_27
| ~ spl17_32 ),
inference(trivial_inequality_removal,[],[f955]) ).
thf(f965,plain,
( ( ( c @ ( sK2 @ sK9 ) @ france )
= $false )
| ( $false = $true )
| ~ spl17_5
| ~ spl17_27
| ~ spl17_32 ),
inference(constrained_superposition,[],[f438,f954]) ).
thf(f979,plain,
( ( ( c @ ( sK2 @ sK9 ) @ france )
= $false )
| ~ spl17_5
| ~ spl17_27
| ~ spl17_32 ),
inference(trivial_inequality_removal,[],[f965]) ).
thf(f987,plain,
( ( $false = $true )
| ~ spl17_5
| ~ spl17_14
| ~ spl17_27
| ~ spl17_32
| ~ spl17_33 ),
inference(forward_demodulation,[],[f979,f843]) ).
thf(f988,plain,
( $false
| ~ spl17_5
| ~ spl17_14
| ~ spl17_27
| ~ spl17_32
| ~ spl17_33 ),
inference(trivial_inequality_removal,[],[f987]) ).
thf(f989,plain,
( ~ spl17_5
| ~ spl17_14
| ~ spl17_27
| ~ spl17_32
| ~ spl17_33 ),
inference(avatar_contradiction_clause,[],[f988]) ).
thf(f992,plain,
( $false
| ~ spl17_3
| ~ spl17_27
| ~ spl17_32
| spl17_33 ),
inference(forward_subsumption_resolution,[],[f958,f811]) ).
thf(f993,plain,
( ~ spl17_3
| ~ spl17_27
| ~ spl17_32
| spl17_33 ),
inference(avatar_contradiction_clause,[],[f992]) ).
cnf(s1,plain,
( spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f427]) ).
cnf(s2,plain,
( spl17_2
| spl17_3 ),
inference(sat_conversion,[],[f431]) ).
cnf(s3,plain,
( spl17_2
| spl17_4 ),
inference(sat_conversion,[],[f435]) ).
cnf(s4,plain,
( spl17_2
| spl17_5 ),
inference(sat_conversion,[],[f439]) ).
cnf(s12,plain,
( spl17_8
| spl17_14 ),
inference(sat_conversion,[],[f477]) ).
cnf(s25,plain,
( spl17_8
| spl17_27 ),
inference(sat_conversion,[],[f533]) ).
cnf(s27,plain,
~ spl17_8,
inference(sat_conversion,[],[f539]) ).
cnf(s33,plain,
~ spl17_2,
inference(sat_conversion,[],[f768]) ).
cnf(s39,plain,
( ~ spl17_1
| spl17_32
| spl17_33 ),
inference(sat_conversion,[],[f820]) ).
cnf(s44,plain,
( ~ spl17_4
| ~ spl17_14
| spl17_32
| ~ spl17_33 ),
inference(sat_conversion,[],[f931]) ).
cnf(s49,plain,
( ~ spl17_5
| ~ spl17_14
| ~ spl17_27
| ~ spl17_32
| ~ spl17_33 ),
inference(sat_conversion,[],[f989]) ).
cnf(s51,plain,
( ~ spl17_3
| ~ spl17_27
| ~ spl17_32
| spl17_33 ),
inference(sat_conversion,[],[f993]) ).
cnf(s52,plain,
spl17_27,
inference(rat,[],[s25,s27]) ).
cnf(s65,plain,
spl17_14,
inference(rat,[],[s12,s27]) ).
cnf(s73,plain,
spl17_5,
inference(rat,[],[s4,s33]) ).
cnf(s74,plain,
spl17_4,
inference(rat,[],[s3,s33]) ).
cnf(s75,plain,
spl17_3,
inference(rat,[],[s2,s33]) ).
cnf(s76,plain,
spl17_1,
inference(rat,[],[s1,s33]) ).
cnf(s78,plain,
spl17_32,
inference(rat,[],[s44,s39,s65,s74,s76]) ).
cnf(s79,plain,
spl17_33,
inference(rat,[],[s51,s75,s52,s78]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s49,s73,s65,s52,s79,s78]) ).
thf(f994,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG010^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n008.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 18:34:39 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.28 Running higher-order theorem proving
% 0.26/0.30 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
% 0.26/0.37 % (3554628)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.37 % (3554633)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2480326721:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.37 % (3554635)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3773322530:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.37 % (3554639)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.37 % (3554639)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
% 0.26/0.37 % (3554635)Instruction limit reached!
% 0.26/0.37 % (3554635)------------------------------
% 0.26/0.37 % (3554635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.37 % (3554635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.37 % (3554635)CaDiCaL version: 2.1.3
% 0.26/0.37 % (3554635)Termination reason: Instruction limit
% 0.26/0.37 % (3554635)Termination phase: shuffling
% 0.26/0.37 % (3554635)Time elapsed: 0.003 s
% 0.26/0.37 % (3554635)Peak memory usage: 10 MB
% 0.26/0.37 % (3554635)Instructions burned: 3 (million)
% 0.26/0.37 % (3554634)lrs+10_16_si=on:nwc=1.5:random_seed=3214891398:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.37 % (3554637)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3775977085:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.37 % (3554636)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=364586614: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)
% 0.26/0.37 % (3554638)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3539293881:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.37 % (3554639)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=3712058438:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.37 % (3554633) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3554628-3554633"...
% 0.26/0.37 % (3554634)Instruction limit reached!
% 0.26/0.37 % (3554634)------------------------------
% 0.26/0.37 % (3554634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.37 % (3554634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.37 % (3554634)CaDiCaL version: 2.1.3
% 0.26/0.37 % (3554634)Termination reason: Instruction limit
% 0.26/0.37 % (3554634)Termination phase: Saturation
% 0.26/0.37 % (3554634)Time elapsed: 0.015 s
% 0.26/0.37 % (3554634)Peak memory usage: 11 MB
% 0.26/0.37 % (3554634)Instructions burned: 19 (million)
% 0.26/0.37 % (3554637)Instruction limit reached!
% 0.26/0.37 % (3554637)------------------------------
% 0.26/0.37 % (3554637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.37 % (3554637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.37 % (3554637)CaDiCaL version: 2.1.3
% 0.26/0.37 % (3554637)Termination reason: Instruction limit
% 0.26/0.37 % (3554637)Termination phase: Saturation
% 0.26/0.37 % (3554637)Time elapsed: 0.023 s
% 0.26/0.37 % (3554637)Peak memory usage: 11 MB
% 0.26/0.37 % (3554637)Instructions burned: 24 (million)
% 0.26/0.37 % (3554633)...printing done.
% 0.26/0.37 % (3554633)Refutation found. Thanks to Tanya!
% 0.26/0.37 % SZS status Theorem for theBenchmark
% 0.26/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.38 % (3554633)------------------------------
% 0.26/0.38 % (3554633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (3554633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (3554633)CaDiCaL version: 2.1.3
% 0.26/0.38 % (3554633)Termination reason: Refutation
% 0.26/0.38 % (3554633)Time elapsed: 0.036 s
% 0.26/0.38 % (3554633)Peak memory usage: 13 MB
% 0.26/0.38 % (3554633)Instructions burned: 74 (million)
% 0.26/0.38 % (3554628)Success in time 0.062 s
% 0.26/0.38 % Vampire exiting
%------------------------------------------------------------------------------