%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG006^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:28 AM UTC 2026
% Result : Theorem 6.90s 1.23s
% Output : Refutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 25
% Syntax : Number of formulae : 242 ( 80 unt; 0 typ; 14 def)
% Number of atoms : 1934 ( 331 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3622 ( 210 ~; 319 |; 183 &;2422 @)
% ( 14 <=>; 212 =>; 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 : 100 ( 95 usr; 27 con; 0-4 aty)
% ( 189 !!; 73 ??; 0 @@+; 0 @@-)
% Number of variables : 670 ( 17 sgn 157 !; 6 ?; 670 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vOR: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
sK2: reg > 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_70,type,
sK7: reg > 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 ).
thf(func_def_75,type,
sK12: reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > reg ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_81,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_82,type,
sK19: $i > ( $i > $o ) > $i ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f35,axiom,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( o @ france @ paris )
& ( o @ catalunya @ spain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( o @ france @ paris )
& ( o @ catalunya @ spain ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f71,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f72,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f94,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f108,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f109,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f112,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f113,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f116,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f117,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f116]) ).
thf(f118,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f119,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f120,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f121,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f120]) ).
thf(f122,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f123,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f130,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f131,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f134,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f135,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f136,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( o @ france @ paris )
& ( o @ catalunya @ spain ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f137,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ) ),
inference(flattening,[],[f137]) ).
thf(f155,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f167,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f174,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f176,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f178,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f117]) ).
thf(f179,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f180,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f121]) ).
thf(f181,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f185,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f131]) ).
thf(f187,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f188,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f201,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f176,f174,f174]) ).
thf(f203,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f178,f201]) ).
thf(f204,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f179,f174,f174]) ).
thf(f205,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f180,f204,f203,f203]) ).
thf(f206,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f181,f204,f203,f203]) ).
thf(f210,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ catalunya
@ spain ) ) ) ),
inference(definition_unfolding,[],[f185,f167,f155,f205]) ).
thf(f212,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f187,f167,f155,f206]) ).
thf(f213,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ( ^ [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 )
& ( ^ [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 ) ) ) ) ),
inference(definition_unfolding,[],[f188,f167,f155,f201,f201]) ).
thf(f214,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( $false
= ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( $true
= ( a @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) )
| ( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f219]) ).
thf(f223,plain,
! [X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) )
@ X1 ) )
| ( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) ) ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(and_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ paris ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ spain ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ catalunya ) )
@ ( sK5 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( ( c @ ( sK2 @ X1 ) @ X1 )
=> ( c @ ( sK2 @ X1 ) @ paris ) ) )
| ( $false
= ( ( c @ ( sK3 @ X2 ) @ X2 )
=> ( c @ ( sK3 @ X2 ) @ spain ) ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( ( c @ ( sK3 @ X2 ) @ X2 )
=> ( c @ ( sK3 @ X2 ) @ spain ) ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK3 @ X2 ) @ X2 )
=> ( c @ ( sK3 @ X2 ) @ spain ) ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f235,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f237,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f239,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f241,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f242,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f243,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f235]) ).
thf(f244,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f235]) ).
thf(f245,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f247,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f248,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f249,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f250,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( ( c @ ( sK4 @ X1 ) @ X1 )
=> ( c @ ( sK4 @ X1 ) @ france ) ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f251,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f253,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f255,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f256,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f257,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f258,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK5 @ X2 ) @ X2 )
=> ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f259,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f261,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f262,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f263,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f264,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f270]) ).
thf(f273,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ X3 @ france ) ) ),
inference(imp_proxy_clausification,[],[f275]) ).
thf(f342,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f343,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f346]) ).
thf(f349,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f347]) ).
thf(f351,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f349]) ).
thf(f352,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ X3 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f354]) ).
thf(f449,definition,
( spl20_1
<=> ! [X2: reg] :
( ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
thf(f450,plain,
( ! [X2: reg] :
( ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) )
| ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) ) )
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f449]) ).
thf(f452,definition,
( spl20_2
<=> ! [X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f453,plain,
( ! [X1: reg] :
( ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) ) )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f452]) ).
thf(f454,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f240,f452,f449]) ).
thf(f456,definition,
( spl20_3
<=> ! [X2: reg] :
( ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
thf(f457,plain,
( ! [X2: reg] :
( ( $true
= ( c @ ( sK3 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) )
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f456]) ).
thf(f458,plain,
( spl20_3
| spl20_2 ),
inference(avatar_split_clause,[],[f239,f452,f456]) ).
thf(f460,definition,
( spl20_4
<=> ! [X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
thf(f461,plain,
( ! [X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) ) )
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f460]) ).
thf(f462,plain,
( spl20_1
| spl20_4 ),
inference(avatar_split_clause,[],[f242,f460,f449]) ).
thf(f463,plain,
( spl20_3
| spl20_4 ),
inference(avatar_split_clause,[],[f241,f460,f456]) ).
thf(f465,definition,
( spl20_5
<=> ! [X2: reg] :
( ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition]) ).
thf(f466,plain,
( ! [X2: reg] :
( ( $true
= ( c @ ( sK5 @ X2 ) @ X2 ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) ) )
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f465]) ).
thf(f467,plain,
( spl20_5
| spl20_2 ),
inference(avatar_split_clause,[],[f246,f452,f465]) ).
thf(f469,definition,
( spl20_6
<=> ! [X2: reg] :
( ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) )
| ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
thf(f470,plain,
( ! [X2: reg] :
( ( $false
= ( c @ ( sK5 @ X2 ) @ catalunya ) )
| ( $false
= ( c @ ( sK3 @ X2 ) @ spain ) ) )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f469]) ).
thf(f471,plain,
( spl20_6
| spl20_2 ),
inference(avatar_split_clause,[],[f245,f452,f469]) ).
thf(f472,plain,
( spl20_5
| spl20_4 ),
inference(avatar_split_clause,[],[f248,f460,f465]) ).
thf(f473,plain,
( spl20_6
| spl20_4 ),
inference(avatar_split_clause,[],[f247,f460,f469]) ).
thf(f475,definition,
( spl20_7
<=> ! [X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f476,plain,
( ! [X1: reg] :
( ( $true
= ( c @ ( sK4 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) ) )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f475]) ).
thf(f477,plain,
( spl20_1
| spl20_7 ),
inference(avatar_split_clause,[],[f254,f475,f449]) ).
thf(f478,plain,
( spl20_3
| spl20_7 ),
inference(avatar_split_clause,[],[f253,f475,f456]) ).
thf(f480,definition,
( spl20_8
<=> ! [X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) )
| ( $false
= ( c @ ( sK4 @ X1 ) @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f481,plain,
( ! [X1: reg] :
( ( $false
= ( c @ ( sK4 @ X1 ) @ france ) )
| ( $false
= ( c @ ( sK2 @ X1 ) @ paris ) ) )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f482,plain,
( spl20_1
| spl20_8 ),
inference(avatar_split_clause,[],[f256,f480,f449]) ).
thf(f483,plain,
( spl20_3
| spl20_8 ),
inference(avatar_split_clause,[],[f255,f480,f456]) ).
thf(f484,plain,
( spl20_5
| spl20_7 ),
inference(avatar_split_clause,[],[f260,f475,f465]) ).
thf(f485,plain,
( spl20_6
| spl20_7 ),
inference(avatar_split_clause,[],[f259,f475,f469]) ).
thf(f486,plain,
( spl20_5
| spl20_8 ),
inference(avatar_split_clause,[],[f262,f480,f465]) ).
thf(f487,plain,
( spl20_6
| spl20_8 ),
inference(avatar_split_clause,[],[f261,f480,f469]) ).
thf(f489,definition,
( spl20_9
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
thf(f490,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f489]) ).
thf(f492,definition,
( spl20_10
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $true
= ( c @ X3 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
thf(f493,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $true
= ( c @ X3 @ france ) ) )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f492]) ).
thf(f494,plain,
( spl20_9
| spl20_10 ),
inference(avatar_split_clause,[],[f276,f492,f489]) ).
thf(f546,definition,
( spl20_23
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition]) ).
thf(f547,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) )
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f546]) ).
thf(f548,plain,
( spl20_9
| spl20_23 ),
inference(avatar_split_clause,[],[f355,f546,f489]) ).
thf(f610,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK3 @ catalunya ) @ catalunya ) )
| ( $true
= ( c @ ( sK3 @ catalunya ) @ catalunya ) )
| ~ spl20_1
| ~ spl20_3 ),
inference(constrained_superposition,[],[f450,f457]) ).
thf(f611,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK3 @ catalunya ) @ catalunya ) )
| ~ spl20_1
| ~ spl20_3 ),
inference(duplicate_literal_removal,[],[f610]) ).
thf(f612,plain,
( ( $true
= ( c @ ( sK3 @ catalunya ) @ catalunya ) )
| ~ spl20_1
| ~ spl20_3 ),
inference(trivial_inequality_removal,[],[f611]) ).
thf(f1498,plain,
( ( $true = $false )
| ( $false
= ( c @ ( sK3 @ catalunya ) @ spain ) )
| ( $false
= ( c @ ( sK3 @ catalunya ) @ spain ) )
| ~ spl20_5
| ~ spl20_6 ),
inference(constrained_superposition,[],[f466,f470]) ).
thf(f1513,plain,
( ( $true = $false )
| ( $false
= ( c @ ( sK3 @ catalunya ) @ spain ) )
| ~ spl20_5
| ~ spl20_6 ),
inference(duplicate_literal_removal,[],[f1498]) ).
thf(f1514,plain,
( ( $false
= ( c @ ( sK3 @ catalunya ) @ spain ) )
| ~ spl20_5
| ~ spl20_6 ),
inference(trivial_inequality_removal,[],[f1513]) ).
thf(f1903,plain,
( ( $true = $false )
| ~ spl20_9 ),
inference(constrained_superposition,[],[f490,f221]) ).
thf(f1929,plain,
( $false
| ~ spl20_9 ),
inference(trivial_inequality_removal,[],[f1903]) ).
thf(f1930,plain,
~ spl20_9,
inference(avatar_contradiction_clause,[],[f1929]) ).
thf(f2037,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK4 @ paris ) @ france ) )
| ( $false
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_7
| ~ spl20_10 ),
inference(constrained_superposition,[],[f493,f476]) ).
thf(f2038,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK4 @ paris ) @ france ) )
| ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_2
| ~ spl20_10 ),
inference(constrained_superposition,[],[f493,f453]) ).
thf(f2086,plain,
( ( $true
= ( c @ ( sK4 @ paris ) @ france ) )
| ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_2
| ~ spl20_10 ),
inference(trivial_inequality_removal,[],[f2038]) ).
thf(f2087,plain,
( ( $true
= ( c @ ( sK4 @ paris ) @ france ) )
| ( $false
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_7
| ~ spl20_10 ),
inference(trivial_inequality_removal,[],[f2037]) ).
thf(f2103,definition,
( spl20_39
<=> ( $true
= ( c @ ( sK4 @ paris ) @ france ) ) ),
introduced(definition,[new_symbols(definition,[spl20_39])],[avatar_definition]) ).
thf(f2105,plain,
( ( $true
= ( c @ ( sK4 @ paris ) @ france ) )
| ~ spl20_39 ),
inference(avatar_component_clause,[],[f2103]) ).
thf(f2107,definition,
( spl20_40
<=> ( $true
= ( c @ ( sK2 @ paris ) @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl20_40])],[avatar_definition]) ).
thf(f2109,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_40 ),
inference(avatar_component_clause,[],[f2107]) ).
thf(f2112,definition,
( spl20_41
<=> ( $false
= ( c @ ( sK2 @ paris ) @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl20_41])],[avatar_definition]) ).
thf(f2114,plain,
( ( $false
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_41 ),
inference(avatar_component_clause,[],[f2112]) ).
thf(f2118,plain,
( spl20_40
| spl20_39
| ~ spl20_2
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f2086,f492,f452,f2103,f2107]) ).
thf(f2119,plain,
( spl20_41
| spl20_39
| ~ spl20_7
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f2087,f492,f475,f2103,f2112]) ).
thf(f2150,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK3 @ catalunya ) @ spain ) )
| ~ spl20_1
| ~ spl20_3
| ~ spl20_23 ),
inference(constrained_superposition,[],[f547,f612]) ).
thf(f2192,plain,
( ( $true
= ( c @ ( sK3 @ catalunya ) @ spain ) )
| ~ spl20_1
| ~ spl20_3
| ~ spl20_23 ),
inference(trivial_inequality_removal,[],[f2150]) ).
thf(f2216,plain,
( ( $true = $false )
| ~ spl20_1
| ~ spl20_3
| ~ spl20_5
| ~ spl20_6
| ~ spl20_23 ),
inference(forward_demodulation,[],[f2192,f1514]) ).
thf(f2217,plain,
( $false
| ~ spl20_1
| ~ spl20_3
| ~ spl20_5
| ~ spl20_6
| ~ spl20_23 ),
inference(trivial_inequality_removal,[],[f2216]) ).
thf(f2218,plain,
( ~ spl20_1
| ~ spl20_3
| ~ spl20_5
| ~ spl20_6
| ~ spl20_23 ),
inference(avatar_contradiction_clause,[],[f2217]) ).
thf(f2458,plain,
( ( $true = $false )
| ( $false
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_8
| ~ spl20_39 ),
inference(constrained_superposition,[],[f481,f2105]) ).
thf(f2459,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_4
| ~ spl20_39 ),
inference(constrained_superposition,[],[f461,f2105]) ).
thf(f2472,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_4
| ~ spl20_39 ),
inference(trivial_inequality_removal,[],[f2459]) ).
thf(f2473,plain,
( ( $false
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl20_8
| ~ spl20_39 ),
inference(trivial_inequality_removal,[],[f2458]) ).
thf(f2485,plain,
( spl20_40
| ~ spl20_4
| ~ spl20_39 ),
inference(avatar_split_clause,[],[f2472,f2103,f460,f2107]) ).
thf(f2486,plain,
( spl20_41
| ~ spl20_8
| ~ spl20_39 ),
inference(avatar_split_clause,[],[f2473,f2103,f480,f2112]) ).
thf(f2839,plain,
( ( $true = $false )
| ~ spl20_40
| ~ spl20_41 ),
inference(constrained_superposition,[],[f2109,f2114]) ).
thf(f2859,plain,
( $false
| ~ spl20_40
| ~ spl20_41 ),
inference(trivial_inequality_removal,[],[f2839]) ).
thf(f2860,plain,
( ~ spl20_40
| ~ spl20_41 ),
inference(avatar_contradiction_clause,[],[f2859]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f454]) ).
cnf(s2,plain,
( spl20_2
| spl20_3 ),
inference(sat_conversion,[],[f458]) ).
cnf(s3,plain,
( spl20_1
| spl20_4 ),
inference(sat_conversion,[],[f462]) ).
cnf(s4,plain,
( spl20_3
| spl20_4 ),
inference(sat_conversion,[],[f463]) ).
cnf(s5,plain,
( spl20_2
| spl20_5 ),
inference(sat_conversion,[],[f467]) ).
cnf(s6,plain,
( spl20_2
| spl20_6 ),
inference(sat_conversion,[],[f471]) ).
cnf(s7,plain,
( spl20_4
| spl20_5 ),
inference(sat_conversion,[],[f472]) ).
cnf(s8,plain,
( spl20_4
| spl20_6 ),
inference(sat_conversion,[],[f473]) ).
cnf(s9,plain,
( spl20_1
| spl20_7 ),
inference(sat_conversion,[],[f477]) ).
cnf(s10,plain,
( spl20_3
| spl20_7 ),
inference(sat_conversion,[],[f478]) ).
cnf(s11,plain,
( spl20_1
| spl20_8 ),
inference(sat_conversion,[],[f482]) ).
cnf(s12,plain,
( spl20_3
| spl20_8 ),
inference(sat_conversion,[],[f483]) ).
cnf(s13,plain,
( spl20_5
| spl20_7 ),
inference(sat_conversion,[],[f484]) ).
cnf(s14,plain,
( spl20_6
| spl20_7 ),
inference(sat_conversion,[],[f485]) ).
cnf(s15,plain,
( spl20_5
| spl20_8 ),
inference(sat_conversion,[],[f486]) ).
cnf(s16,plain,
( spl20_6
| spl20_8 ),
inference(sat_conversion,[],[f487]) ).
cnf(s17,plain,
( spl20_9
| spl20_10 ),
inference(sat_conversion,[],[f494]) ).
cnf(s29,plain,
( spl20_9
| spl20_23 ),
inference(sat_conversion,[],[f548]) ).
cnf(s46,plain,
~ spl20_9,
inference(sat_conversion,[],[f1930]) ).
cnf(s53,plain,
( ~ spl20_2
| ~ spl20_10
| spl20_39
| spl20_40 ),
inference(sat_conversion,[],[f2118]) ).
cnf(s54,plain,
( ~ spl20_7
| ~ spl20_10
| spl20_39
| spl20_41 ),
inference(sat_conversion,[],[f2119]) ).
cnf(s58,plain,
( ~ spl20_1
| ~ spl20_3
| ~ spl20_5
| ~ spl20_6
| ~ spl20_23 ),
inference(sat_conversion,[],[f2218]) ).
cnf(s63,plain,
( ~ spl20_4
| ~ spl20_39
| spl20_40 ),
inference(sat_conversion,[],[f2485]) ).
cnf(s64,plain,
( ~ spl20_8
| ~ spl20_39
| spl20_41 ),
inference(sat_conversion,[],[f2486]) ).
cnf(s67,plain,
( ~ spl20_40
| ~ spl20_41 ),
inference(sat_conversion,[],[f2860]) ).
cnf(s81,plain,
spl20_23,
inference(rat,[],[s29,s46]) ).
cnf(s93,plain,
spl20_10,
inference(rat,[],[s17,s46]) ).
cnf(s94,plain,
( spl20_39
| spl20_1 ),
inference(rat,[],[s67,s54,s53,s9,s1,s93]) ).
cnf(s95,plain,
spl20_1,
inference(rat,[],[s67,s63,s64,s94,s3,s11]) ).
cnf(s96,plain,
( spl20_39
| ~ spl20_7
| ~ spl20_2 ),
inference(rat,[],[s67,s54,s53,s93]) ).
cnf(s97,plain,
spl20_8,
inference(rat,[],[s58,s12,s15,s16,s95,s81]) ).
cnf(s98,plain,
spl20_4,
inference(rat,[],[s58,s4,s7,s8,s95,s81]) ).
cnf(s99,plain,
~ spl20_39,
inference(rat,[],[s67,s63,s64,s98,s97]) ).
cnf(s100,plain,
spl20_7,
inference(rat,[],[s58,s10,s13,s14,s95,s81]) ).
cnf(s101,plain,
~ spl20_2,
inference(rat,[],[s96,s99,s100]) ).
cnf(s103,plain,
spl20_6,
inference(rat,[],[s6,s101]) ).
cnf(s104,plain,
spl20_5,
inference(rat,[],[s5,s101]) ).
cnf(s105,plain,
spl20_3,
inference(rat,[],[s2,s101]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s58,s81,s105,s95,s103,s104]) ).
thf(f2876,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG006^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 18:34:03 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.36/0.99 % (1188332)Will run a generic schedule for satisfiability detection.
% 4.36/0.99 % (1188343)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1149057373:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.36/0.99 % (1188338)% WARNING: option uhcvi not known.
% 4.36/0.99 % (1188339)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2780602647:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.36/0.99 % (1188337)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1700701339_2999 on theBenchmark for (2999ds/0Mi)
% 4.36/0.99 % (1188338)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4129947337:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.36/0.99 % (1188341)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=313933282:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.36/0.99 % (1188340)dis+10_1_sil=32000:sp=arity:random_seed=2698752878:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.36/0.99 % (1188338)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.36/0.99 % (1188342)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4030762763:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.36/0.99 % (1188341)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.36/0.99 % Exception at run slice level
% 4.36/0.99 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.36/0.99 % (1188338)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.36/0.99 % (1188351)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1103794796:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.36/0.99 % Exception at run slice level
% 4.36/0.99 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.36/0.99 % (1188343)Instruction limit reached!
% 4.36/0.99 % (1188343)------------------------------
% 4.36/0.99 % (1188343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.36/0.99 % (1188343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/0.99 % (1188343)CaDiCaL version: 2.1.3
% 4.36/0.99 % (1188343)Termination reason: Instruction limit
% 4.36/0.99 % (1188343)Termination phase: Saturation
% 4.36/0.99 % (1188343)Time elapsed: 0.045 s
% 4.36/0.99 % (1188343)Peak memory usage: 13 MB
% 4.36/0.99 % (1188343)Instructions burned: 161 (million)
% 4.36/0.99 % (1188353)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1881809506:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.36/0.99 % (1188340)Instruction limit reached!
% 4.36/0.99 % (1188340)------------------------------
% 4.36/0.99 % (1188340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.36/0.99 % (1188340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/0.99 % (1188340)CaDiCaL version: 2.1.3
% 4.36/0.99 % (1188340)Termination reason: Instruction limit
% 4.36/0.99 % (1188340)Termination phase: Saturation
% 4.36/0.99 % (1188340)Time elapsed: 0.054 s
% 4.36/0.99 % (1188340)Peak memory usage: 12 MB
% 4.36/0.99 % (1188340)Instructions burned: 105 (million)
% 4.36/0.99 % (1188354)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3997238592:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.36/0.99 % (1188354)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.36/0.99 % (1188354)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.36/0.99 % (1188341)Instruction limit reached!
% 4.36/0.99 % (1188341)------------------------------
% 4.36/0.99 % (1188341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.36/0.99 % (1188341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.36/0.99 % (1188341)CaDiCaL version: 2.1.3
% 4.36/0.99 % (1188341)Termination reason: Instruction limit
% 4.36/0.99 % (1188341)Termination phase: Saturation
% 4.36/0.99 % (1188341)Time elapsed: 0.074 s
% 4.36/0.99 % (1188341)Peak memory usage: 13 MB
% 4.36/0.99 % (1188341)Instructions burned: 117 (million)
% 4.36/0.99 % (1188356)ott-21_1_sil=16000:fs=off:random_seed=2330478486:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.36/0.99 % (1188358)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3976340991:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.90/1.23 % (1188353)Instruction limit reached!
% 6.90/1.23 % (1188353)------------------------------
% 6.90/1.23 % (1188353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188353)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188353)Termination reason: Instruction limit
% 6.90/1.23 % (1188353)Termination phase: Saturation
% 6.90/1.23 % (1188353)Time elapsed: 0.067 s
% 6.90/1.23 % (1188353)Peak memory usage: 13 MB
% 6.90/1.23 % (1188353)Instructions burned: 131 (million)
% 6.90/1.23 % (1188342)Instruction limit reached!
% 6.90/1.23 % (1188342)------------------------------
% 6.90/1.23 % (1188342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188342)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188342)Termination reason: Instruction limit
% 6.90/1.23 % (1188342)Termination phase: Saturation
% 6.90/1.23 % (1188342)Time elapsed: 0.118 s
% 6.90/1.23 % (1188342)Peak memory usage: 12 MB
% 6.90/1.23 % (1188342)Instructions burned: 132 (million)
% 6.90/1.23 % (1188361)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3110678603:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.90/1.23 % (1188362)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=685275499:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188365)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2241968384:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188367)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=319898309:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 6.90/1.23 % (1188367)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.23 % (1188356)Instruction limit reached!
% 6.90/1.23 % (1188356)------------------------------
% 6.90/1.23 % (1188356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188356)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188356)Termination reason: Instruction limit
% 6.90/1.23 % (1188356)Termination phase: Saturation
% 6.90/1.23 % (1188356)Time elapsed: 0.095 s
% 6.90/1.23 % (1188356)Peak memory usage: 12 MB
% 6.90/1.23 % (1188356)Instructions burned: 182 (million)
% 6.90/1.23 % (1188369)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3097215528:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.90/1.23 % (1188369)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.23 % (1188367)Instruction limit reached!
% 6.90/1.23 % (1188367)------------------------------
% 6.90/1.23 % (1188367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188367)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188367)Termination reason: Instruction limit
% 6.90/1.23 % (1188367)Termination phase: Saturation
% 6.90/1.23 % (1188367)Time elapsed: 0.180 s
% 6.90/1.23 % (1188367)Peak memory usage: 16 MB
% 6.90/1.23 % (1188367)Instructions burned: 695 (million)
% 6.90/1.23 % (1188373)fmb+10_1_sil=64000:random_seed=4229120510:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 6.90/1.23 % (1188373)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188375)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=410261262:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188377)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2942298171:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188379)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4275740236:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 6.90/1.23 % (1188379)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.23 % (1188358)Instruction limit reached!
% 6.90/1.23 % (1188358)------------------------------
% 6.90/1.23 % (1188358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188358)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188358)Termination reason: Instruction limit
% 6.90/1.23 % (1188358)Termination phase: Saturation
% 6.90/1.23 % (1188358)Time elapsed: 0.346 s
% 6.90/1.23 % (1188358)Peak memory usage: 13 MB
% 6.90/1.23 % (1188358)Instructions burned: 477 (million)
% 6.90/1.23 % (1188381)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4235905820:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 6.90/1.23 % (1188381)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.90/1.23 % (1188381)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.90/1.23 % (1188354)Instruction limit reached!
% 6.90/1.23 % (1188354)------------------------------
% 6.90/1.23 % (1188354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188354)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188354)Termination reason: Instruction limit
% 6.90/1.23 % (1188354)Termination phase: Saturation
% 6.90/1.23 % (1188354)Time elapsed: 0.489 s
% 6.90/1.23 % (1188354)Peak memory usage: 15 MB
% 6.90/1.23 % (1188354)Instructions burned: 684 (million)
% 6.90/1.23 % (1188383)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4009789364:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188385)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=423234601:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188387)ott-2_1_sil=16000:newcnf=on:random_seed=4086483115:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 6.90/1.23 % (1188387)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.23 % (1188369)Instruction limit reached!
% 6.90/1.23 % (1188369)------------------------------
% 6.90/1.23 % (1188369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188369)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188369)Termination reason: Instruction limit
% 6.90/1.23 % (1188369)Termination phase: Saturation
% 6.90/1.23 % (1188369)Time elapsed: 0.460 s
% 6.90/1.23 % (1188369)Peak memory usage: 16 MB
% 6.90/1.23 % (1188369)Instructions burned: 879 (million)
% 6.90/1.23 % (1188389)ott+10_1_sil=32000:tgt=ground:random_seed=1031236738:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.90/1.23 % (1188362)Instruction limit reached!
% 6.90/1.23 % (1188362)------------------------------
% 6.90/1.23 % (1188362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188362)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188362)Termination reason: Instruction limit
% 6.90/1.23 % (1188362)Termination phase: Saturation
% 6.90/1.23 % (1188362)Time elapsed: 0.583 s
% 6.90/1.23 % (1188362)Peak memory usage: 16 MB
% 6.90/1.23 % (1188362)Instructions burned: 1181 (million)
% 6.90/1.23 % (1188391)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1219624707:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 6.90/1.23 % Exception at run slice level
% 6.90/1.23 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.23 % (1188393)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3231675706:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 6.90/1.23 % (1188393)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.90/1.23 % (1188381)Instruction limit reached!
% 6.90/1.23 % (1188381)------------------------------
% 6.90/1.23 % (1188381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188381)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188381)Termination reason: Instruction limit
% 6.90/1.23 % (1188381)Termination phase: Saturation
% 6.90/1.23 % (1188381)Time elapsed: 0.419 s
% 6.90/1.23 % (1188381)Peak memory usage: 18 MB
% 6.90/1.23 % (1188381)Instructions burned: 1475 (million)
% 6.90/1.23 % (1188395)dis+21_1_sil=32000:sas=cadical:random_seed=1676631054:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 6.90/1.23 % (1188395) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1188332-1188395"...
% 6.90/1.23 % (1188395)...printing done.
% 6.90/1.23 % (1188395)Refutation found. Thanks to Tanya!
% 6.90/1.23 % SZS status Theorem for theBenchmark
% 6.90/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 6.90/1.23 % (1188395)------------------------------
% 6.90/1.23 % (1188395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.23 % (1188395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.23 % (1188395)CaDiCaL version: 2.1.3
% 6.90/1.23 % (1188395)Termination reason: Refutation
% 6.90/1.23 % (1188395)Time elapsed: 0.095 s
% 6.90/1.23 % (1188395)Peak memory usage: 14 MB
% 6.90/1.23 % (1188395)Instructions burned: 304 (million)
% 6.90/1.23 % (1188332)Success in time 1.023 s
% 6.90/1.23 % Vampire exiting
%------------------------------------------------------------------------------