%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG006^1 : 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 : n006.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 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 24
% Syntax : Number of formulae : 238 ( 76 unt; 0 typ; 12 def)
% Number of atoms : 1950 ( 338 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3656 ( 210 ~; 319 |; 184 &;2450 @)
% ( 12 <=>; 216 =>; 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 : 98 ( 93 usr; 25 con; 0-4 aty)
% ( 192 !!; 73 ??; 0 @@+; 0 @@-)
% Number of variables : 681 ( 17 sgn 167 !; 6 ?; 681 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db0:
!>[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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
vAND: $o > $o > $o ).
thf(func_def_57,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
vNOT: $o > $o ).
thf(func_def_59,type,
vOR: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
sK0: reg > reg ).
thf(func_def_64,type,
sK1: reg > reg ).
thf(func_def_65,type,
sK2: reg ).
thf(func_def_66,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_67,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_68,type,
sK5: reg > reg ).
thf(func_def_69,type,
sK6: reg > reg ).
thf(func_def_70,type,
sK7: reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg > reg ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_75,type,
sK12: reg ).
thf(func_def_76,type,
sK13: $i > ( $i > $o ) > $i ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: reg > reg ).
thf(func_def_81,type,
sK18: reg > reg ).
thf(func_def_82,type,
sK19: reg > reg ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ 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,
! [X1: reg,X0: 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 @ X1 )
& ( p @ X2 @ X0 ) ) )
= o ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) )
= ntpp ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f60,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f61,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f66,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f67,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f76,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f77,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f81,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f82,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f90,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f100,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f101,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f104,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f105,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f104]) ).
thf(f106,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f107,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( o @ france @ paris )
& ( o @ catalunya @ spain ) ) ) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f115,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f116,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f115]) ).
thf(f126,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f127,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f126]) ).
thf(f130,plain,
! [X0: reg,X1: reg] :
( ( c @ X1 @ X0 )
=> ( c @ X0 @ X1 ) ),
inference(rectify,[],[f33]) ).
thf(f131,plain,
! [X1: reg,X0: reg] :
( ( ( c @ X1 @ X0 )
= $true )
=> ( ( c @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f130]) ).
thf(f132,plain,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) )
= o ),
inference(rectify,[],[f37]) ).
thf(f133,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f132]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( o @ france @ paris )
& ( o @ catalunya @ spain ) ) ) ) ),
inference(flattening,[],[f107]) ).
thf(f139,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
| ( ( c @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f131]) ).
thf(f142,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f143,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f147,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f152,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f163,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f165,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f116]) ).
thf(f170,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f177,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f178,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f133]) ).
thf(f180,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( o @ france @ paris )
& ( o @ catalunya @ spain ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f184,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f187,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f127]) ).
thf(f201,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f178,f142,f142]) ).
thf(f203,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,[],[f184,f201]) ).
thf(f204,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,[],[f163,f142,f142]) ).
thf(f205,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
@ 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 ) ) )
& ( ^ [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,[],[f187,f203,f203,f204]) ).
thf(f206,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
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ 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
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ 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,[],[f143,f203,f203,f204]) ).
thf(f209,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ?? @ 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 ) ) )
& ( ^ [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 ) ) ) ),
inference(definition_unfolding,[],[f152,f170,f177,f205]) ).
thf(f211,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ~ ( ?? @ 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
@ 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
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ 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 ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f165,f170,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] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ( ^ [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
@ 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 ) ) )
@ catalunya
@ spain ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f180,f170,f177,f201,f201]) ).
thf(f214,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ paris )
& ~ ( ?? @ 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
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f215,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ paris )
& ~ ( ?? @ 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
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ paris )
& ~ ( ?? @ 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
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ paris )
& ~ ( ?? @ 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
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ~ ( a @ X1 @ X2 )
| ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ 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
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ 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
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f219]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( a @ X1 @ X2 ) ) )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f220]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f268,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f329,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ 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 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f330,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ 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 ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( ?? @ 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 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( ?? @ 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 ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( ?? @ 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 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ?? @ 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 ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( a @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f334]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f335]) ).
thf(f373,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f372]) ).
thf(f380,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f381,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f380]) ).
thf(f382,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ X3 @ catalunya )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( c @ X3 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f381]) ).
thf(f398,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f399,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) )
@ sK14 )
= $false ),
inference(sigma_proxy_clausification,[],[f398]) ).
thf(f400,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK14 @ Y0 )
| ( ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f399]) ).
thf(f401,plain,
( ( ^ [Y0: $i] :
( ~ ( a @ sK14 @ Y0 )
| ( ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) )
@ sK15 )
= $false ),
inference(sigma_proxy_clausification,[],[f400]) ).
thf(f402,plain,
( ( ~ ( a @ sK14 @ sK15 )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f401]) ).
thf(f403,plain,
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f402]) ).
thf(f404,plain,
( ( ~ ( a @ sK14 @ sK15 ) )
= $false ),
inference(or_proxy_clausification,[],[f402]) ).
thf(f405,plain,
( $true
= ( a @ sK14 @ sK15 ) ),
inference(not_proxy_clausification,[],[f404]) ).
thf(f406,plain,
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
= $false )
| ( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f403]) ).
thf(f407,plain,
! [X1: reg] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X1 )
= $false )
| ( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f406]) ).
thf(f408,plain,
! [X2: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X1 )
= $false )
| ( $false
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f407]) ).
thf(f409,plain,
! [X2: reg,X1: reg] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f408]) ).
thf(f410,plain,
! [X2: reg,X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f410]) ).
thf(f412,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f411]) ).
thf(f413,plain,
! [X2: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) )
@ ( sK17 @ X2 ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) ) )
= $false )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) )
@ ( sK18 @ X1 ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) )
@ ( sK17 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK16 @ X1 ) ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ catalunya ) )
@ ( sK18 @ X1 ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) )
@ ( sK17 @ X2 ) )
= $false )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ paris ) )
@ ( sK19 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ ( sK17 @ X2 ) @ X2 )
=> ( c @ ( sK17 @ X2 ) @ france ) )
= $false )
| ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false ) ),
inference(beta-eta_normalization,[],[f415]) ).
thf(f417,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false )
| ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f416]) ).
thf(f419,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f418]) ).
thf(f420,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f418]) ).
thf(f421,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f420]) ).
thf(f422,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( ( c @ ( sK18 @ X1 ) @ X1 )
=> ( c @ ( sK18 @ X1 ) @ catalunya ) )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f420]) ).
thf(f423,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f422]) ).
thf(f424,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f422]) ).
thf(f425,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false ) ),
inference(imp_proxy_clausification,[],[f421]) ).
thf(f426,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f421]) ).
thf(f427,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f419]) ).
thf(f428,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f419]) ).
thf(f429,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false ) ),
inference(imp_proxy_clausification,[],[f428]) ).
thf(f430,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) ) ),
inference(imp_proxy_clausification,[],[f428]) ).
thf(f431,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f427]) ).
thf(f432,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f427]) ).
thf(f433,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f417]) ).
thf(f434,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) ) ),
inference(imp_proxy_clausification,[],[f417]) ).
thf(f435,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) ) ),
inference(imp_proxy_clausification,[],[f434]) ).
thf(f436,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK19 @ X2 ) @ X2 )
=> ( c @ ( sK19 @ X2 ) @ paris ) ) ) ),
inference(imp_proxy_clausification,[],[f434]) ).
thf(f437,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f436]) ).
thf(f438,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f436]) ).
thf(f439,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f435]) ).
thf(f440,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f435]) ).
thf(f441,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f433]) ).
thf(f442,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( ( ( c @ ( sK16 @ X1 ) @ X1 )
=> ( c @ ( sK16 @ X1 ) @ spain ) )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f433]) ).
thf(f443,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f442]) ).
thf(f444,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f442]) ).
thf(f445,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f441]) ).
thf(f446,plain,
! [X2: reg,X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f441]) ).
thf(f448,definition,
( spl20_1
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f449,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f477,definition,
( spl20_8
<=> ! [X3: reg] :
( ( $true
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f478,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( c @ X3 @ france ) ) )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f477]) ).
thf(f479,plain,
( spl20_8
| spl20_1 ),
inference(avatar_split_clause,[],[f270,f448,f477]) ).
thf(f557,definition,
( spl20_27
<=> ! [X3: reg] :
( ( ( c @ X3 @ catalunya )
= $false )
| ( $true
= ( c @ X3 @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_27])],[avatar_definition]) ).
thf(f558,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ catalunya )
= $false )
| ( $true
= ( c @ X3 @ spain ) ) )
| ~ spl20_27 ),
inference(avatar_component_clause,[],[f557]) ).
thf(f559,plain,
( spl20_27
| spl20_1 ),
inference(avatar_split_clause,[],[f382,f448,f557]) ).
thf(f561,definition,
( spl20_28
<=> ! [X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
thf(f562,plain,
( ! [X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) )
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f561]) ).
thf(f564,definition,
( spl20_29
<=> ! [X2: reg] :
( ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_29])],[avatar_definition]) ).
thf(f565,plain,
( ! [X2: reg] :
( ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) ) )
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f564]) ).
thf(f566,plain,
( spl20_28
| spl20_29 ),
inference(avatar_split_clause,[],[f424,f564,f561]) ).
thf(f568,definition,
( spl20_30
<=> ! [X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_30])],[avatar_definition]) ).
thf(f569,plain,
( ! [X1: reg] :
( ( $true
= ( c @ ( sK16 @ X1 ) @ X1 ) )
| ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false ) )
| ~ spl20_30 ),
inference(avatar_component_clause,[],[f568]) ).
thf(f570,plain,
( spl20_30
| spl20_29 ),
inference(avatar_split_clause,[],[f423,f564,f568]) ).
thf(f572,definition,
( spl20_31
<=> ! [X1: reg] :
( ( ( c @ ( sK16 @ X1 ) @ spain )
= $false )
| ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_31])],[avatar_definition]) ).
thf(f573,plain,
( ! [X1: reg] :
( ( $true
= ( c @ ( sK18 @ X1 ) @ X1 ) )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false ) )
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f572]) ).
thf(f574,plain,
( spl20_31
| spl20_29 ),
inference(avatar_split_clause,[],[f426,f564,f572]) ).
thf(f576,definition,
( spl20_32
<=> ! [X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_32])],[avatar_definition]) ).
thf(f577,plain,
( ! [X1: reg] :
( ( ( c @ ( sK18 @ X1 ) @ catalunya )
= $false )
| ( ( c @ ( sK16 @ X1 ) @ spain )
= $false ) )
| ~ spl20_32 ),
inference(avatar_component_clause,[],[f576]) ).
thf(f578,plain,
( spl20_32
| spl20_29 ),
inference(avatar_split_clause,[],[f425,f564,f576]) ).
thf(f580,definition,
( spl20_33
<=> ! [X2: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_33])],[avatar_definition]) ).
thf(f581,plain,
( ! [X2: reg] :
( ( $true
= ( c @ ( sK17 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) ) )
| ~ spl20_33 ),
inference(avatar_component_clause,[],[f580]) ).
thf(f582,plain,
( spl20_28
| spl20_33 ),
inference(avatar_split_clause,[],[f430,f580,f561]) ).
thf(f583,plain,
( spl20_33
| spl20_31 ),
inference(avatar_split_clause,[],[f429,f572,f580]) ).
thf(f584,plain,
( spl20_30
| spl20_33 ),
inference(avatar_split_clause,[],[f432,f580,f568]) ).
thf(f585,plain,
( spl20_33
| spl20_32 ),
inference(avatar_split_clause,[],[f431,f576,f580]) ).
thf(f587,definition,
( spl20_34
<=> ! [X2: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_34])],[avatar_definition]) ).
thf(f588,plain,
( ! [X2: reg] :
( ( $true
= ( c @ ( sK19 @ X2 ) @ X2 ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false ) )
| ~ spl20_34 ),
inference(avatar_component_clause,[],[f587]) ).
thf(f589,plain,
( spl20_28
| spl20_34 ),
inference(avatar_split_clause,[],[f438,f587,f561]) ).
thf(f591,definition,
( spl20_35
<=> ! [X2: reg] :
( ( ( c @ ( sK17 @ X2 ) @ france )
= $false )
| ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_35])],[avatar_definition]) ).
thf(f592,plain,
( ! [X2: reg] :
( ( $false
= ( c @ ( sK19 @ X2 ) @ paris ) )
| ( ( c @ ( sK17 @ X2 ) @ france )
= $false ) )
| ~ spl20_35 ),
inference(avatar_component_clause,[],[f591]) ).
thf(f593,plain,
( spl20_35
| spl20_28 ),
inference(avatar_split_clause,[],[f437,f561,f591]) ).
thf(f594,plain,
( spl20_34
| spl20_31 ),
inference(avatar_split_clause,[],[f440,f572,f587]) ).
thf(f595,plain,
( spl20_35
| spl20_31 ),
inference(avatar_split_clause,[],[f439,f572,f591]) ).
thf(f596,plain,
( spl20_30
| spl20_34 ),
inference(avatar_split_clause,[],[f444,f587,f568]) ).
thf(f597,plain,
( spl20_32
| spl20_34 ),
inference(avatar_split_clause,[],[f443,f587,f576]) ).
thf(f598,plain,
( spl20_35
| spl20_30 ),
inference(avatar_split_clause,[],[f446,f568,f591]) ).
thf(f599,plain,
( spl20_32
| spl20_35 ),
inference(avatar_split_clause,[],[f445,f591,f576]) ).
thf(f600,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK16 @ catalunya ) @ catalunya ) )
| ( $true
= ( c @ ( sK16 @ catalunya ) @ catalunya ) )
| ~ spl20_28
| ~ spl20_30 ),
inference(constrained_superposition,[],[f569,f562]) ).
thf(f604,plain,
( ( $true
= ( c @ ( sK16 @ catalunya ) @ catalunya ) )
| ( $true = $false )
| ~ spl20_28
| ~ spl20_30 ),
inference(duplicate_literal_removal,[],[f600]) ).
thf(f610,plain,
( ( $false
= ( c @ ( sK16 @ catalunya ) @ spain ) )
| ( $true = $false )
| ( $false
= ( c @ ( sK16 @ catalunya ) @ spain ) )
| ~ spl20_31
| ~ spl20_32 ),
inference(constrained_superposition,[],[f577,f573]) ).
thf(f614,plain,
( ( $true = $false )
| ( $false
= ( c @ ( sK16 @ catalunya ) @ spain ) )
| ~ spl20_31
| ~ spl20_32 ),
inference(duplicate_literal_removal,[],[f610]) ).
thf(f756,definition,
( spl20_42
<=> ( $true
= ( c @ ( sK17 @ paris ) @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl20_42])],[avatar_definition]) ).
thf(f757,plain,
( ( $true
!= ( c @ ( sK17 @ paris ) @ paris ) )
| spl20_42 ),
inference(avatar_component_clause,[],[f756]) ).
thf(f758,plain,
( ( $true
= ( c @ ( sK17 @ paris ) @ paris ) )
| ~ spl20_42 ),
inference(avatar_component_clause,[],[f756]) ).
thf(f765,plain,
( ( $false
= ( c @ ( sK16 @ catalunya ) @ spain ) )
| ~ spl20_31
| ~ spl20_32 ),
inference(trivial_inequality_removal,[],[f614]) ).
thf(f768,plain,
( ( $true
= ( c @ ( sK16 @ catalunya ) @ catalunya ) )
| ~ spl20_28
| ~ spl20_30 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f820,plain,
( ! [X0: reg] :
( ( $true != $true )
| ( $true
= ( c @ X0 @ ( sK17 @ X0 ) ) )
| ( ( c @ ( sK19 @ X0 ) @ paris )
= $false ) )
| ~ spl20_33 ),
inference(constrained_superposition,[],[f147,f581]) ).
thf(f822,plain,
( ! [X0: reg] :
( ( $true
= ( c @ X0 @ ( sK17 @ X0 ) ) )
| ( ( c @ ( sK19 @ X0 ) @ paris )
= $false ) )
| ~ spl20_33 ),
inference(trivial_inequality_removal,[],[f820]) ).
thf(f877,plain,
( ( $true = $false )
| ~ spl20_1 ),
inference(constrained_superposition,[],[f449,f405]) ).
thf(f881,plain,
( $false
| ~ spl20_1 ),
inference(trivial_inequality_removal,[],[f877]) ).
thf(f882,plain,
~ spl20_1,
inference(avatar_contradiction_clause,[],[f881]) ).
thf(f946,plain,
( ( $true
= ( c @ ( sK16 @ catalunya ) @ spain ) )
| ( $true = $false )
| ~ spl20_27
| ~ spl20_28
| ~ spl20_30 ),
inference(constrained_superposition,[],[f768,f558]) ).
thf(f959,plain,
( ( $true
= ( c @ ( sK16 @ catalunya ) @ spain ) )
| ~ spl20_27
| ~ spl20_28
| ~ spl20_30 ),
inference(trivial_inequality_removal,[],[f946]) ).
thf(f967,plain,
( ( $true = $false )
| ~ spl20_27
| ~ spl20_28
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32 ),
inference(forward_demodulation,[],[f959,f765]) ).
thf(f968,plain,
( $false
| ~ spl20_27
| ~ spl20_28
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32 ),
inference(trivial_inequality_removal,[],[f967]) ).
thf(f969,plain,
( ~ spl20_27
| ~ spl20_28
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32 ),
inference(avatar_contradiction_clause,[],[f968]) ).
thf(f990,plain,
( ( ( c @ ( sK17 @ paris ) @ france )
= $true )
| ( $true = $false )
| ~ spl20_8
| ~ spl20_42 ),
inference(constrained_superposition,[],[f478,f758]) ).
thf(f991,plain,
( ( ( c @ ( sK17 @ paris ) @ france )
= $true )
| ~ spl20_8
| ~ spl20_42 ),
inference(trivial_inequality_removal,[],[f990]) ).
thf(f1030,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK17 @ paris ) @ paris ) )
| ( $true
= ( c @ paris @ ( sK17 @ paris ) ) )
| ~ spl20_29
| ~ spl20_33 ),
inference(constrained_superposition,[],[f565,f822]) ).
thf(f1049,plain,
( ( $true
= ( c @ ( sK17 @ paris ) @ paris ) )
| ( $true
= ( c @ paris @ ( sK17 @ paris ) ) )
| ~ spl20_29
| ~ spl20_33 ),
inference(trivial_inequality_removal,[],[f1030]) ).
thf(f1083,plain,
( ( $true = $false )
| ( ( c @ ( sK17 @ paris ) @ france )
= $false )
| ( ( c @ ( sK17 @ paris ) @ france )
= $false )
| ~ spl20_34
| ~ spl20_35 ),
inference(constrained_superposition,[],[f592,f588]) ).
thf(f1092,plain,
( ( $true = $false )
| ( ( c @ ( sK17 @ paris ) @ france )
= $false )
| ~ spl20_34
| ~ spl20_35 ),
inference(duplicate_literal_removal,[],[f1083]) ).
thf(f1093,plain,
( ( ( c @ ( sK17 @ paris ) @ france )
= $false )
| ~ spl20_34
| ~ spl20_35 ),
inference(trivial_inequality_removal,[],[f1092]) ).
thf(f1110,plain,
( ( $true = $false )
| ~ spl20_8
| ~ spl20_34
| ~ spl20_35
| ~ spl20_42 ),
inference(forward_demodulation,[],[f1093,f991]) ).
thf(f1111,plain,
( $false
| ~ spl20_8
| ~ spl20_34
| ~ spl20_35
| ~ spl20_42 ),
inference(trivial_inequality_removal,[],[f1110]) ).
thf(f1112,plain,
( ~ spl20_8
| ~ spl20_34
| ~ spl20_35
| ~ spl20_42 ),
inference(avatar_contradiction_clause,[],[f1111]) ).
thf(f1127,plain,
( ( $true
= ( c @ ( sK17 @ paris ) @ paris ) )
| ~ spl20_29
| ~ spl20_33 ),
inference(forward_subsumption_resolution,[],[f1049,f147]) ).
thf(f1129,plain,
( $false
| ~ spl20_29
| ~ spl20_33
| spl20_42 ),
inference(forward_subsumption_resolution,[],[f1127,f757]) ).
thf(f1130,plain,
( ~ spl20_29
| ~ spl20_33
| spl20_42 ),
inference(avatar_contradiction_clause,[],[f1129]) ).
cnf(s7,plain,
( spl20_1
| spl20_8 ),
inference(sat_conversion,[],[f479]) ).
cnf(s25,plain,
( spl20_1
| spl20_27 ),
inference(sat_conversion,[],[f559]) ).
cnf(s26,plain,
( spl20_28
| spl20_29 ),
inference(sat_conversion,[],[f566]) ).
cnf(s27,plain,
( spl20_29
| spl20_30 ),
inference(sat_conversion,[],[f570]) ).
cnf(s28,plain,
( spl20_29
| spl20_31 ),
inference(sat_conversion,[],[f574]) ).
cnf(s29,plain,
( spl20_29
| spl20_32 ),
inference(sat_conversion,[],[f578]) ).
cnf(s30,plain,
( spl20_28
| spl20_33 ),
inference(sat_conversion,[],[f582]) ).
cnf(s31,plain,
( spl20_31
| spl20_33 ),
inference(sat_conversion,[],[f583]) ).
cnf(s32,plain,
( spl20_30
| spl20_33 ),
inference(sat_conversion,[],[f584]) ).
cnf(s33,plain,
( spl20_32
| spl20_33 ),
inference(sat_conversion,[],[f585]) ).
cnf(s34,plain,
( spl20_28
| spl20_34 ),
inference(sat_conversion,[],[f589]) ).
cnf(s35,plain,
( spl20_28
| spl20_35 ),
inference(sat_conversion,[],[f593]) ).
cnf(s36,plain,
( spl20_31
| spl20_34 ),
inference(sat_conversion,[],[f594]) ).
cnf(s37,plain,
( spl20_31
| spl20_35 ),
inference(sat_conversion,[],[f595]) ).
cnf(s38,plain,
( spl20_30
| spl20_34 ),
inference(sat_conversion,[],[f596]) ).
cnf(s39,plain,
( spl20_32
| spl20_34 ),
inference(sat_conversion,[],[f597]) ).
cnf(s40,plain,
( spl20_30
| spl20_35 ),
inference(sat_conversion,[],[f598]) ).
cnf(s41,plain,
( spl20_32
| spl20_35 ),
inference(sat_conversion,[],[f599]) ).
cnf(s55,plain,
~ spl20_1,
inference(sat_conversion,[],[f882]) ).
cnf(s64,plain,
( ~ spl20_27
| ~ spl20_28
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32 ),
inference(sat_conversion,[],[f969]) ).
cnf(s74,plain,
( ~ spl20_8
| ~ spl20_34
| ~ spl20_35
| ~ spl20_42 ),
inference(sat_conversion,[],[f1112]) ).
cnf(s84,plain,
( ~ spl20_29
| ~ spl20_33
| spl20_42 ),
inference(sat_conversion,[],[f1130]) ).
cnf(s85,plain,
spl20_27,
inference(rat,[],[s25,s55]) ).
cnf(s98,plain,
spl20_8,
inference(rat,[],[s7,s55]) ).
cnf(s105,plain,
spl20_28,
inference(rat,[],[s84,s74,s26,s30,s34,s35,s98]) ).
cnf(s106,plain,
( spl20_30
| ~ spl20_29 ),
inference(rat,[],[s84,s74,s32,s38,s40,s98]) ).
cnf(s107,plain,
( spl20_35
| ~ spl20_30 ),
inference(rat,[],[s64,s37,s41,s85,s105]) ).
cnf(s108,plain,
( spl20_34
| ~ spl20_30 ),
inference(rat,[],[s64,s36,s39,s85,s105]) ).
cnf(s109,plain,
~ spl20_29,
inference(rat,[],[s64,s31,s33,s84,s74,s108,s107,s106,s85,s105,s98]) ).
cnf(s110,plain,
spl20_32,
inference(rat,[],[s29,s109]) ).
cnf(s111,plain,
spl20_31,
inference(rat,[],[s28,s109]) ).
cnf(s112,plain,
spl20_30,
inference(rat,[],[s27,s109]) ).
cnf(s113,plain,
$false,
inference(rat,[],[s64,s112,s105,s85,s110,s111]) ).
thf(f1131,plain,
$false,
inference(avatar_sat_refutation,[],[s113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG006^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 18:33:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.34 % (1143867)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.34 % (1143874)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1701287508:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.34 % (1143874)Instruction limit reached!
% 0.20/0.34 % (1143874)------------------------------
% 0.20/0.34 % (1143874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143874)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143874)Termination reason: Instruction limit
% 0.20/0.34 % (1143874)Termination phase: Property scanning
% 0.20/0.34 % (1143874)Time elapsed: 0.001 s
% 0.20/0.34 % (1143874)Peak memory usage: 10 MB
% 0.20/0.34 % (1143874)Instructions burned: 5 (million)
% 0.20/0.34 % (1143878)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.34 % (1143878)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
% 0.20/0.34 % (1143873)lrs+10_16_si=on:nwc=1.5:random_seed=3424241064:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.34 % (1143872)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4137085712:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.34 % (1143876)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1274621394:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.34 % (1143875)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=3902471968: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)
% 0.20/0.34 % (1143877)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=882250634:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.34 % (1143878)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=3664014836:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.34 % (1143880)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3142943302:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.34 % (1143873)Instruction limit reached!
% 0.20/0.34 % (1143873)------------------------------
% 0.20/0.34 % (1143873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143873)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143873)Termination reason: Instruction limit
% 0.20/0.34 % (1143873)Termination phase: Saturation
% 0.20/0.34 % (1143873)Time elapsed: 0.009 s
% 0.20/0.34 % (1143873)Peak memory usage: 11 MB
% 0.20/0.34 % (1143873)Instructions burned: 18 (million)
% 0.20/0.34 % (1143880)Instruction limit reached!
% 0.20/0.34 % (1143880)------------------------------
% 0.20/0.34 % (1143880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143880)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143880)Termination reason: Instruction limit
% 0.20/0.34 % (1143880)Termination phase: Property scanning
% 0.20/0.34 % (1143880)Time elapsed: 0.003 s
% 0.20/0.34 % (1143880)Peak memory usage: 10 MB
% 0.20/0.34 % (1143880)Instructions burned: 13 (million)
% 0.20/0.34 % (1143876)Instruction limit reached!
% 0.20/0.34 % (1143876)------------------------------
% 0.20/0.34 % (1143876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143876)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143876)Termination reason: Instruction limit
% 0.20/0.34 % (1143876)Termination phase: Saturation
% 0.20/0.34 % (1143876)Time elapsed: 0.014 s
% 0.20/0.34 % (1143876)Peak memory usage: 11 MB
% 0.20/0.34 % (1143876)Instructions burned: 25 (million)
% 0.20/0.34 % (1143889)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.34 % (1143889)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3953658675:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.34 % (1143889)Instruction limit reached!
% 0.20/0.34 % (1143889)------------------------------
% 0.20/0.34 % (1143889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143889)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143889)Termination reason: Instruction limit
% 0.20/0.34 % (1143889)Termination phase: Property scanning
% 0.20/0.34 % (1143889)Time elapsed: 0.002 s
% 0.20/0.34 % (1143889)Peak memory usage: 10 MB
% 0.20/0.34 % (1143889)Instructions burned: 10 (million)
% 0.20/0.34 % (1143888)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2971501276:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.34 % (1143888)Instruction limit reached!
% 0.20/0.34 % (1143888)------------------------------
% 0.20/0.34 % (1143888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143888)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143888)Termination reason: Instruction limit
% 0.20/0.34 % (1143888)Termination phase: Property scanning
% 0.20/0.34 % (1143888)Time elapsed: 0.003 s
% 0.20/0.34 % (1143888)Peak memory usage: 10 MB
% 0.20/0.34 % (1143888)Instructions burned: 6 (million)
% 0.20/0.34 % (1143872) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1143867-1143872"...
% 0.20/0.34 % (1143890)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=549815758:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.34 % (1143892)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
% 0.20/0.34 % (1143892)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.34 % (1143892)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1134798154:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.34 % (1143877)Instruction limit reached!
% 0.20/0.34 % (1143877)------------------------------
% 0.20/0.34 % (1143877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143877)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143877)Termination reason: Instruction limit
% 0.20/0.34 % (1143877)Termination phase: Saturation
% 0.20/0.34 % (1143877)Time elapsed: 0.040 s
% 0.20/0.34 % (1143877)Peak memory usage: 12 MB
% 0.20/0.34 % (1143877)Instructions burned: 75 (million)
% 0.20/0.34 % (1143890)Instruction limit reached!
% 0.20/0.34 % (1143890)------------------------------
% 0.20/0.34 % (1143890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143890)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143890)Termination reason: Instruction limit
% 0.20/0.34 % (1143890)Termination phase: Property scanning
% 0.20/0.34 % (1143890)Time elapsed: 0.007 s
% 0.20/0.34 % (1143890)Peak memory usage: 11 MB
% 0.20/0.34 % (1143890)Instructions burned: 12 (million)
% 0.20/0.34 % (1143872)...printing done.
% 0.20/0.34 % (1143892)Instruction limit reached!
% 0.20/0.34 % (1143892)------------------------------
% 0.20/0.34 % (1143892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143892)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143892)Termination reason: Instruction limit
% 0.20/0.34 % (1143892)Termination phase: Saturation
% 0.20/0.34 % (1143892)Time elapsed: 0.010 s
% 0.20/0.34 % (1143892)Peak memory usage: 12 MB
% 0.20/0.34 % (1143892)Instructions burned: 40 (million)
% 0.20/0.34 % (1143872)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (1143872)------------------------------
% 0.20/0.34 % (1143872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1143872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1143872)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1143872)Termination reason: Refutation
% 0.20/0.34 % (1143872)Time elapsed: 0.043 s
% 0.20/0.34 % (1143872)Peak memory usage: 13 MB
% 0.20/0.34 % (1143872)Instructions burned: 81 (million)
% 0.20/0.34 % (1143867)Success in time 0.092 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------