%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG009^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 2.19s 0.68s
% Output : Refutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 25
% Syntax : Number of formulae : 242 ( 90 unt; 0 typ; 11 def)
% Number of atoms : 1987 ( 350 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3664 ( 233 ~; 261 |; 206 &;2426 @)
% ( 11 <=>; 225 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 90 usr; 24 con; 0-4 aty)
% ( 217 !!; 85 ??; 0 @@+; 0 @@-)
% Number of variables : 780 ( 17 sgn 212 !; 9 ?; 780 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
vNOT: $o > $o ).
thf(func_def_59,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_62,type,
vOR: $o > $o > $o ).
thf(func_def_63,type,
sK0: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK1: reg > reg ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg ).
thf(func_def_67,type,
sK4: reg ).
thf(func_def_68,type,
sK5: reg ).
thf(func_def_69,type,
sK6: reg > reg ).
thf(func_def_70,type,
sK7: reg > reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg > reg ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > reg ).
thf(func_def_79,type,
sK16: $i > ( $i > $o ) > $i ).
thf(func_def_80,type,
sK17: $i > ( $i > $o ) > $i ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/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(f32,axiom,
! [X0: reg] : ( c @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_reflexive) ).
thf(f33,axiom,
! [X1: reg,X0: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).
thf(f35,axiom,
( ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) )
= p ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f36,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ 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,
( ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) )
= tpp ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= ntpp ),
file('/export/starexec/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] :
? [X1: reg] :
( ~ ( o @ X1 @ paris )
& ~ ( eq @ X1 @ spain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg] :
( ~ ( o @ X1 @ paris )
& ~ ( eq @ X1 @ spain ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f55,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f56,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f68,plain,
! [X0: reg] : ( c @ X0 @ X0 ),
inference(rectify,[],[f32]) ).
thf(f69,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f68]) ).
thf(f72,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f73,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f75,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f78,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f79,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f82,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg] :
( ~ ( o @ X1 @ paris )
& ~ ( eq @ X1 @ spain ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f83,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( eq @ Y1 @ spain )
& ~ ( o @ Y1 @ paris ) ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f84,plain,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
inference(rectify,[],[f36]) ).
thf(f85,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f86,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f87,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f96,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f97,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f117,plain,
! [X0: reg,X1: reg] :
( ( c @ X1 @ X0 )
=> ( c @ X0 @ X1 ) ),
inference(rectify,[],[f33]) ).
thf(f118,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
= $true )
=> ( ( c @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f117]) ).
thf(f122,plain,
( ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) )
= p ),
inference(rectify,[],[f35]) ).
thf(f123,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f124,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f125,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f126,plain,
( ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) )
= tpp ),
inference(rectify,[],[f41]) ).
thf(f127,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f126]) ).
thf(f128,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f129,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(fool_elimination,[],[f128]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( eq @ Y1 @ spain )
& ~ ( o @ Y1 @ paris ) ) ) ) ) ),
inference(flattening,[],[f83]) ).
thf(f139,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f118]) ).
thf(f140,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f143,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f97]) ).
thf(f144,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f145,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f147,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( eq @ Y1 @ spain )
& ~ ( o @ Y1 @ paris ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f151,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f154,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f155,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f156,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f159,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f160,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f69]) ).
thf(f162,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f127]) ).
thf(f164,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f165,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) )
= $true ),
inference(cnf_transformation,[],[f129]) ).
thf(f168,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f154,f151,f151]) ).
thf(f171,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f156,f151,f151]) ).
thf(f172,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 ) ) )
@ Y0
@ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f144,f171]) ).
thf(f173,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,[],[f140,f151,f151]) ).
thf(f176,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 ) ) )
& ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f159,f172,f172,f173]) ).
thf(f177,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] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f162,f173,f172,f172]) ).
thf(f180,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 ) ) )
& ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f143,f155,f164,f176]) ).
thf(f181,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ^ [Y2: reg,Y3: reg] :
( ( ^ [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 ) )
@ Y1
@ spain )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 ) ) )
@ Y1
@ paris ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f147,f155,f164,f168,f171]) ).
thf(f184,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ 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] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ catalunya
@ spain ) ) )
= $true ),
inference(definition_unfolding,[],[f165,f155,f164,f177]) ).
thf(f200,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f201,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f206]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f207]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) )
@ sK3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( ( c @ sK3 @ france )
=> ( c @ sK3 @ paris ) ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( c @ sK3 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f255,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ spain ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f256,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ spain ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ spain ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ spain ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,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] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) ) )
| ~ ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) ) )
= $true )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) ) )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f260]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f262]) ).
thf(f265,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( ( ~ ( a @ X1 @ X2 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( ( c @ X3 @ spain )
= $true ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ( c @ sK4 @ spain )
=> ( c @ sK4 @ catalunya ) )
= $false ) ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( c @ sK4 @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ sK4 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f333,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
=> ( c @ Y3 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f334,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ spain )
=> ( c @ Y3 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ sK12 ) ),
inference(sigma_proxy_clausification,[],[f333]) ).
thf(f335,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) )
| ~ ( a @ sK12 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
( $false
= ( ^ [Y0: $i] :
( ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) )
| ~ ( a @ sK12 @ Y0 ) )
@ sK13 ) ),
inference(sigma_proxy_clausification,[],[f335]) ).
thf(f337,plain,
( $false
= ( ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ ( a @ sK12 @ sK13 ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f338,plain,
( ( ~ ( a @ sK12 @ sK13 ) )
= $false ),
inference(or_proxy_clausification,[],[f337]) ).
thf(f339,plain,
( ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f337]) ).
thf(f340,plain,
! [X1: reg] :
( $false
= ( ^ [Y0: reg] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X1: reg] :
( $false
= ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f340]) ).
thf(f342,plain,
! [X1: reg] :
( ( $false
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X1: reg] :
( ( $false
= ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) ) ) )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X1: reg] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) )
= $true )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) )
= $true )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) ) )
= $true )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f344]) ).
thf(f347,plain,
! [X2: reg,X1: reg] :
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) )
@ ( sK14 @ X1 ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ X1 ) )
@ X2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f347]) ).
thf(f349,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ X2 @ spain )
=> ( c @ X2 @ X1 ) )
= $true )
| ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f348]) ).
thf(f350,plain,
! [X2: reg,X1: reg] :
( ( $false
= ( c @ X2 @ spain ) )
| ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ X1 ) ) ) ) )
| ( ( c @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: reg,X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ X1 ) ) )
= $true )
| ( $false
= ( c @ X2 @ spain ) )
| ( ( c @ X2 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: reg,X1: reg] :
( ( ( c @ X2 @ X1 )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ paris ) ) )
= $true )
| ( $false
= ( c @ X2 @ spain ) ) ),
inference(and_proxy_clausification,[],[f350]) ).
thf(f353,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ X2 @ X1 )
= $true )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ paris ) )
@ X3 ) )
| ( $false
= ( c @ X2 @ spain ) ) ),
inference(pi_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $true
= ( ( c @ X3 @ ( sK14 @ X1 ) )
=> ( c @ X3 @ paris ) ) )
| ( ( c @ X2 @ X1 )
= $true )
| ( $false
= ( c @ X2 @ spain ) ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $false
= ( c @ X3 @ ( sK14 @ X1 ) ) )
| ( $false
= ( c @ X2 @ spain ) )
| ( ( c @ X2 @ X1 )
= $true )
| ( $true
= ( c @ X3 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $false
= ( c @ X2 @ spain ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK14 @ X1 ) )
=> ( c @ Y0 @ X1 ) )
@ X3 ) )
| ( ( c @ X2 @ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f351]) ).
thf(f357,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ X2 @ X1 )
= $true )
| ( $false
= ( c @ X2 @ spain ) )
| ( $true
= ( ( c @ X3 @ ( sK14 @ X1 ) )
=> ( c @ X3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f356]) ).
thf(f358,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $false
= ( c @ X3 @ ( sK14 @ X1 ) ) )
| ( $true
= ( c @ X3 @ X1 ) )
| ( $false
= ( c @ X2 @ spain ) )
| ( ( c @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: reg,X1: reg] :
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f345]) ).
thf(f360,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) )
@ ( sK15 @ X1 ) ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ X2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: reg,X1: reg] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ X1 ) ) ) )
= $true )
| ( ( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
= $true ) ),
inference(beta-eta_normalization,[],[f360]) ).
thf(f362,plain,
! [X2: reg,X1: reg] :
( ( ( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ X1 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: reg,X1: reg] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ paris ) ) ) )
| ( ( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
= $true ) ),
inference(and_proxy_clausification,[],[f361]) ).
thf(f364,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ( c @ X2 @ X1 )
=> ( c @ X2 @ spain ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ paris ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ paris ) )
@ X3 )
= $true )
| ( $true
= ( c @ X2 @ spain ) )
| ( ( c @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ( c @ X3 @ ( sK15 @ X1 ) )
=> ( c @ X3 @ paris ) )
= $true )
| ( $true
= ( c @ X2 @ spain ) )
| ( ( c @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f365]) ).
thf(f367,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $false
= ( c @ X3 @ ( sK15 @ X1 ) ) )
| ( $true
= ( c @ X3 @ paris ) )
| ( ( c @ X2 @ X1 )
= $false )
| ( $true
= ( c @ X2 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: reg,X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ X1 ) ) )
= $true )
| ( ( c @ X2 @ X1 )
= $false )
| ( $true
= ( c @ X2 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f362]) ).
thf(f369,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK15 @ X1 ) )
=> ( c @ Y0 @ X1 ) )
@ X3 ) )
| ( $true
= ( c @ X2 @ spain ) ) ),
inference(pi_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ( c @ X3 @ ( sK15 @ X1 ) )
=> ( c @ X3 @ X1 ) )
= $true )
| ( $true
= ( c @ X2 @ spain ) )
| ( ( c @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f369]) ).
thf(f371,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $false
= ( c @ X3 @ ( sK15 @ X1 ) ) )
| ( ( c @ X2 @ X1 )
= $false )
| ( $true
= ( c @ X2 @ spain ) )
| ( $true
= ( c @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f372,plain,
( ( a @ sK12 @ sK13 )
= $true ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f414,definition,
( spl18_2
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f415,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f414]) ).
thf(f439,definition,
( spl18_8
<=> ( $false
= ( c @ sK3 @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
thf(f441,plain,
( ( $false
= ( c @ sK3 @ paris ) )
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f439]) ).
thf(f442,plain,
( spl18_2
| spl18_8 ),
inference(avatar_split_clause,[],[f253,f439,f414]) ).
thf(f444,definition,
( spl18_9
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
thf(f445,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true ) )
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f444]) ).
thf(f446,plain,
( spl18_9
| spl18_2 ),
inference(avatar_split_clause,[],[f268,f414,f444]) ).
thf(f448,definition,
( spl18_10
<=> ( $true
= ( c @ sK4 @ spain ) ) ),
introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition]) ).
thf(f450,plain,
( ( $true
= ( c @ sK4 @ spain ) )
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f451,plain,
( spl18_2
| spl18_10 ),
inference(avatar_split_clause,[],[f274,f448,f414]) ).
thf(f453,definition,
( spl18_11
<=> ( $false
= ( c @ sK4 @ catalunya ) ) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
thf(f455,plain,
( ( $false
= ( c @ sK4 @ catalunya ) )
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f453]) ).
thf(f456,plain,
( spl18_2
| spl18_11 ),
inference(avatar_split_clause,[],[f273,f453,f414]) ).
thf(f523,plain,
! [X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ spain ) )
| ( ( c @ ( sK14 @ X0 ) @ paris )
= $true )
| ( $false = $true )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(superposition,[],[f355,f160]) ).
thf(f526,plain,
! [X0: reg,X1: reg] :
( ( ( c @ ( sK14 @ X0 ) @ paris )
= $true )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) ) ),
inference(trivial_inequality_removal,[],[f523]) ).
thf(f537,plain,
! [X0: reg,X1: reg] :
( ( ( c @ paris @ ( sK14 @ X0 ) )
= $true )
| ( $true != $true )
| ( $false
= ( c @ X1 @ spain ) )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(superposition,[],[f145,f526]) ).
thf(f540,plain,
! [X0: reg,X1: reg] :
( ( ( c @ paris @ ( sK14 @ X0 ) )
= $true )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) ) ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f610,plain,
! [X0: reg,X1: reg] :
( ( ( c @ ( sK14 @ X0 ) @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) )
| ( $false = $true )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(superposition,[],[f358,f160]) ).
thf(f616,plain,
! [X2: reg,X0: reg,X1: reg] :
( ( ( c @ X2 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false = $true )
| ( ( c @ paris @ X0 )
= $true )
| ( $false
= ( c @ X2 @ spain ) ) ),
inference(superposition,[],[f540,f358]) ).
thf(f617,plain,
! [X0: reg,X1: reg] :
( ( ( c @ ( sK14 @ X0 ) @ X0 )
= $true )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) ) ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f618,plain,
! [X2: reg,X0: reg,X1: reg] :
( ( $false
= ( c @ X2 @ spain ) )
| ( ( c @ paris @ X0 )
= $true )
| ( ( c @ X2 @ X0 )
= $true )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) ) ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f645,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ spain )
= $true )
| ( ( c @ X1 @ X0 )
= $false )
| ( $true
= ( c @ ( sK15 @ X0 ) @ X0 ) )
| ( $false = $true ) ),
inference(superposition,[],[f371,f160]) ).
thf(f650,plain,
! [X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK15 @ X0 ) @ X0 ) )
| ( ( c @ X1 @ spain )
= $true )
| ( ( c @ X1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f645]) ).
thf(f705,definition,
( spl18_30
<=> ( $true
= ( c @ ( sK15 @ spain ) @ spain ) ) ),
introduced(definition,[new_symbols(definition,[spl18_30])],[avatar_definition]) ).
thf(f706,plain,
( ( $true
!= ( c @ ( sK15 @ spain ) @ spain ) )
| spl18_30 ),
inference(avatar_component_clause,[],[f705]) ).
thf(f707,plain,
( ( $true
= ( c @ ( sK15 @ spain ) @ spain ) )
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f705]) ).
thf(f723,plain,
( ( ( c @ spain @ ( sK15 @ spain ) )
= $true )
| ( $true != $true )
| ~ spl18_30 ),
inference(superposition,[],[f145,f707]) ).
thf(f724,plain,
( ( ( c @ spain @ ( sK15 @ spain ) )
= $true )
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f723]) ).
thf(f741,plain,
( ! [X0: reg] :
( ( $false = $true )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ X0 @ spain )
= $false )
| ( ( c @ spain @ paris )
= $true ) )
| ~ spl18_30 ),
inference(superposition,[],[f724,f367]) ).
thf(f749,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ spain @ paris )
= $true ) )
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f741]) ).
thf(f751,definition,
( spl18_32
<=> ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( ( c @ X0 @ spain )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_32])],[avatar_definition]) ).
thf(f752,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( ( c @ X0 @ spain )
= $false ) )
| ~ spl18_32 ),
inference(avatar_component_clause,[],[f751]) ).
thf(f754,definition,
( spl18_33
<=> ( ( c @ spain @ paris )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_33])],[avatar_definition]) ).
thf(f756,plain,
( ( ( c @ spain @ paris )
= $true )
| ~ spl18_33 ),
inference(avatar_component_clause,[],[f754]) ).
thf(f758,plain,
( spl18_33
| spl18_32
| ~ spl18_30 ),
inference(avatar_split_clause,[],[f749,f705,f751,f754]) ).
thf(f759,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( $true != $true )
| ( ( c @ X0 @ spain )
= $false ) )
| spl18_30 ),
inference(superposition,[],[f706,f650]) ).
thf(f760,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( ( c @ X0 @ spain )
= $true ) )
| spl18_30 ),
inference(trivial_inequality_removal,[],[f759]) ).
thf(f761,plain,
( spl18_32
| spl18_30 ),
inference(avatar_split_clause,[],[f760,f705,f751]) ).
thf(f793,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( $true != $true )
| ( ( c @ spain @ X0 )
= $true ) )
| ~ spl18_32 ),
inference(superposition,[],[f145,f752]) ).
thf(f799,plain,
( ! [X0: reg] :
( ( ( c @ spain @ X0 )
= $true )
| ( ( c @ X0 @ spain )
= $false ) )
| ~ spl18_32 ),
inference(trivial_inequality_removal,[],[f793]) ).
thf(f806,plain,
( ! [X0: reg,X1: reg] :
( ( $false = $true )
| ( $false
= ( c @ X1 @ spain ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ spain @ paris )
= $true )
| ( $false
= ( c @ ( sK14 @ X0 ) @ spain ) ) )
| ~ spl18_32 ),
inference(superposition,[],[f799,f355]) ).
thf(f823,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ ( sK14 @ X0 ) @ spain ) )
| ( ( c @ spain @ paris )
= $true )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ spain ) ) )
| ~ spl18_32 ),
inference(trivial_inequality_removal,[],[f806]) ).
thf(f830,definition,
( spl18_35
<=> ! [X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ spain ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ ( sK14 @ X0 ) @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_35])],[avatar_definition]) ).
thf(f831,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ ( sK14 @ X0 ) @ spain ) )
| ( $false
= ( c @ X1 @ spain ) )
| ( ( c @ X1 @ X0 )
= $true ) )
| ~ spl18_35 ),
inference(avatar_component_clause,[],[f830]) ).
thf(f833,plain,
( spl18_35
| spl18_33
| ~ spl18_32 ),
inference(avatar_split_clause,[],[f823,f751,f754,f830]) ).
thf(f984,plain,
( ( $false = $true )
| ~ spl18_2 ),
inference(superposition,[],[f415,f372]) ).
thf(f1001,plain,
( $false
| ~ spl18_2 ),
inference(trivial_inequality_removal,[],[f984]) ).
thf(f1002,plain,
~ spl18_2,
inference(avatar_contradiction_clause,[],[f1001]) ).
thf(f1007,plain,
( ! [X0: reg] :
( ( $false = $true )
| ( $true
= ( c @ ( sK14 @ catalunya ) @ spain ) )
| ( ( c @ X0 @ spain )
= $false )
| ( $true
= ( c @ X0 @ catalunya ) ) )
| ~ spl18_9 ),
inference(superposition,[],[f445,f617]) ).
thf(f1017,plain,
( ! [X0: reg] :
( ( $true
= ( c @ X0 @ catalunya ) )
| ( $true
= ( c @ ( sK14 @ catalunya ) @ spain ) )
| ( ( c @ X0 @ spain )
= $false ) )
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f1007]) ).
thf(f1024,definition,
( spl18_36
<=> ! [X0: reg] :
( ( $true
= ( c @ X0 @ catalunya ) )
| ( ( c @ X0 @ spain )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_36])],[avatar_definition]) ).
thf(f1025,plain,
( ! [X0: reg] :
( ( $true
= ( c @ X0 @ catalunya ) )
| ( ( c @ X0 @ spain )
= $false ) )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f1024]) ).
thf(f1027,definition,
( spl18_37
<=> ( $true
= ( c @ ( sK14 @ catalunya ) @ spain ) ) ),
introduced(definition,[new_symbols(definition,[spl18_37])],[avatar_definition]) ).
thf(f1029,plain,
( ( $true
= ( c @ ( sK14 @ catalunya ) @ spain ) )
| ~ spl18_37 ),
inference(avatar_component_clause,[],[f1027]) ).
thf(f1031,plain,
( spl18_36
| spl18_37
| ~ spl18_9 ),
inference(avatar_split_clause,[],[f1017,f444,f1027,f1024]) ).
thf(f1106,plain,
( ( $false
= ( c @ sK4 @ spain ) )
| ( $false = $true )
| ~ spl18_11
| ~ spl18_36 ),
inference(superposition,[],[f455,f1025]) ).
thf(f1110,plain,
( ( $false
= ( c @ sK4 @ spain ) )
| ~ spl18_11
| ~ spl18_36 ),
inference(trivial_inequality_removal,[],[f1106]) ).
thf(f1113,plain,
( ( $false = $true )
| ~ spl18_10
| ~ spl18_11
| ~ spl18_36 ),
inference(superposition,[],[f1110,f450]) ).
thf(f1120,plain,
( $false
| ~ spl18_10
| ~ spl18_11
| ~ spl18_36 ),
inference(trivial_inequality_removal,[],[f1113]) ).
thf(f1121,plain,
( ~ spl18_10
| ~ spl18_11
| ~ spl18_36 ),
inference(avatar_contradiction_clause,[],[f1120]) ).
thf(f1131,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( $false = $true )
| ( $true
= ( c @ X0 @ catalunya ) ) )
| ~ spl18_35
| ~ spl18_37 ),
inference(superposition,[],[f1029,f831]) ).
thf(f1137,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( $true
= ( c @ X0 @ catalunya ) ) )
| ~ spl18_35
| ~ spl18_37 ),
inference(trivial_inequality_removal,[],[f1131]) ).
thf(f1141,plain,
( spl18_36
| ~ spl18_35
| ~ spl18_37 ),
inference(avatar_split_clause,[],[f1137,f1027,f830,f1024]) ).
thf(f1144,plain,
( ( $true != $true )
| ( ( c @ paris @ spain )
= $true )
| ~ spl18_33 ),
inference(superposition,[],[f145,f756]) ).
thf(f1145,plain,
( ( ( c @ paris @ spain )
= $true )
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f1144]) ).
thf(f1795,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( ( c @ X0 @ X1 )
= $true )
| ( ( c @ paris @ X1 )
= $true )
| ( ( c @ X0 @ X1 )
= $true )
| ( $false != $false ) ),
inference(equality_factoring,[],[f618]) ).
thf(f1813,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ spain )
= $false )
| ( $false != $false )
| ( ( c @ paris @ X1 )
= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[],[f1795]) ).
thf(f1814,plain,
! [X0: reg,X1: reg] :
( ( ( c @ paris @ X1 )
= $true )
| ( ( c @ X0 @ X1 )
= $true )
| ( ( c @ X0 @ spain )
= $false ) ),
inference(trivial_inequality_removal,[],[f1813]) ).
thf(f1966,plain,
! [X0: reg] :
( ( $true != $true )
| ( ( c @ paris @ X0 )
= $true )
| ( $false
= ( c @ paris @ spain ) ) ),
inference(equality_factoring,[],[f1814]) ).
thf(f1968,plain,
! [X0: reg] :
( ( ( c @ paris @ X0 )
= $true )
| ( $false
= ( c @ paris @ spain ) ) ),
inference(trivial_inequality_removal,[],[f1966]) ).
thf(f1994,plain,
( ! [X0: reg] :
( ( ( c @ paris @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl18_33 ),
inference(forward_demodulation,[],[f1968,f1145]) ).
thf(f1995,plain,
( ! [X0: reg] :
( ( c @ paris @ X0 )
= $true )
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f1994]) ).
thf(f2007,plain,
( ! [X0: reg] :
( ( $true != $true )
| ( ( c @ X0 @ paris )
= $true ) )
| ~ spl18_33 ),
inference(superposition,[],[f145,f1995]) ).
thf(f2037,plain,
( ! [X0: reg] :
( ( c @ X0 @ paris )
= $true )
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f2007]) ).
thf(f2082,plain,
( ( $false = $true )
| ~ spl18_8
| ~ spl18_33 ),
inference(superposition,[],[f441,f2037]) ).
thf(f2088,plain,
( $false
| ~ spl18_8
| ~ spl18_33 ),
inference(trivial_inequality_removal,[],[f2082]) ).
thf(f2089,plain,
( ~ spl18_8
| ~ spl18_33 ),
inference(avatar_contradiction_clause,[],[f2088]) ).
cnf(s7,plain,
( spl18_2
| spl18_8 ),
inference(sat_conversion,[],[f442]) ).
cnf(s8,plain,
( spl18_2
| spl18_9 ),
inference(sat_conversion,[],[f446]) ).
cnf(s9,plain,
( spl18_2
| spl18_10 ),
inference(sat_conversion,[],[f451]) ).
cnf(s10,plain,
( spl18_2
| spl18_11 ),
inference(sat_conversion,[],[f456]) ).
cnf(s29,plain,
( ~ spl18_30
| spl18_32
| spl18_33 ),
inference(sat_conversion,[],[f758]) ).
cnf(s30,plain,
( spl18_30
| spl18_32 ),
inference(sat_conversion,[],[f761]) ).
cnf(s36,plain,
( ~ spl18_32
| spl18_33
| spl18_35 ),
inference(sat_conversion,[],[f833]) ).
cnf(s38,plain,
~ spl18_2,
inference(sat_conversion,[],[f1002]) ).
cnf(s40,plain,
( ~ spl18_9
| spl18_36
| spl18_37 ),
inference(sat_conversion,[],[f1031]) ).
cnf(s42,plain,
( ~ spl18_10
| ~ spl18_11
| ~ spl18_36 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s45,plain,
( ~ spl18_35
| spl18_36
| ~ spl18_37 ),
inference(sat_conversion,[],[f1141]) ).
cnf(s91,plain,
( ~ spl18_8
| ~ spl18_33 ),
inference(sat_conversion,[],[f2089]) ).
cnf(s108,plain,
spl18_11,
inference(rat,[],[s10,s38]) ).
cnf(s109,plain,
spl18_10,
inference(rat,[],[s9,s38]) ).
cnf(s110,plain,
~ spl18_36,
inference(rat,[],[s42,s108,s109]) ).
cnf(s111,plain,
spl18_9,
inference(rat,[],[s8,s38]) ).
cnf(s113,plain,
spl18_37,
inference(rat,[],[s40,s110,s111]) ).
cnf(s115,plain,
~ spl18_35,
inference(rat,[],[s45,s110,s113]) ).
cnf(s116,plain,
spl18_8,
inference(rat,[],[s7,s38]) ).
cnf(s117,plain,
~ spl18_33,
inference(rat,[],[s91,s116]) ).
cnf(s118,plain,
~ spl18_32,
inference(rat,[],[s36,s115,s117]) ).
cnf(s120,plain,
spl18_30,
inference(rat,[],[s30,s118]) ).
cnf(s121,plain,
$false,
inference(rat,[],[s29,s117,s118,s120]) ).
thf(f2090,plain,
$false,
inference(avatar_sat_refutation,[],[s121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEG009^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n007.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 18:31:56 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.10/0.50 % (3754347)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.10/0.50 % (3754354)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=227539419:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.10/0.50 % (3754354)Instruction limit reached!
% 1.10/0.50 % (3754354)------------------------------
% 1.10/0.50 % (3754354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.50 % (3754354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.50 % (3754354)CaDiCaL version: 2.1.3
% 1.10/0.50 % (3754354)Termination reason: Instruction limit
% 1.10/0.50 % (3754354)Termination phase: Property scanning
% 1.10/0.50 % (3754354)Time elapsed: 0.002 s
% 1.10/0.50 % (3754354)Peak memory usage: 10 MB
% 1.10/0.50 % (3754354)Instructions burned: 4 (million)
% 1.10/0.50 % (3754358)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.10/0.50 % (3754358)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.10/0.50 % (3754352)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1305812768:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.10/0.50 % (3754353)lrs+10_16_si=on:nwc=1.5:random_seed=1636362224:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.10/0.50 % (3754356)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3833742356:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.10/0.50 % (3754355)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=2029934292:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.10/0.50 % (3754357)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3870909846:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.10/0.50 % (3754358)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=2301261902:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.10/0.50 % (3754360)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2200968907:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.10/0.50 % (3754360)Instruction limit reached!
% 1.10/0.50 % (3754360)------------------------------
% 1.10/0.50 % (3754360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.50 % (3754360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.50 % (3754360)CaDiCaL version: 2.1.3
% 1.10/0.50 % (3754360)Termination reason: Instruction limit
% 1.10/0.50 % (3754360)Termination phase: shuffling
% 1.10/0.50 % (3754360)Time elapsed: 0.001 s
% 1.10/0.50 % (3754360)Peak memory usage: 9 MB
% 1.10/0.50 % (3754360)Instructions burned: 2 (million)
% 1.10/0.50 % (3754353)Instruction limit reached!
% 1.10/0.50 % (3754353)------------------------------
% 1.10/0.50 % (3754353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.50 % (3754353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.50 % (3754353)CaDiCaL version: 2.1.3
% 1.10/0.50 % (3754353)Termination reason: Instruction limit
% 1.10/0.50 % (3754353)Termination phase: Saturation
% 1.10/0.50 % (3754353)Time elapsed: 0.016 s
% 1.10/0.50 % (3754353)Peak memory usage: 11 MB
% 1.10/0.50 % (3754353)Instructions burned: 19 (million)
% 1.10/0.50 % (3754356)Instruction limit reached!
% 1.10/0.50 % (3754356)------------------------------
% 1.10/0.50 % (3754356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.50 % (3754356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.50 % (3754356)CaDiCaL version: 2.1.3
% 1.10/0.50 % (3754356)Termination reason: Instruction limit
% 1.10/0.50 % (3754356)Termination phase: Saturation
% 1.10/0.50 % (3754356)Time elapsed: 0.024 s
% 1.10/0.50 % (3754356)Peak memory usage: 11 MB
% 1.10/0.50 % (3754356)Instructions burned: 25 (million)
% 1.10/0.50 % (3754368)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3830265823:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.10/0.54 % (3754369)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.10/0.54 % (3754368)Instruction limit reached!
% 1.10/0.54 % (3754368)------------------------------
% 1.10/0.54 % (3754368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.54 % (3754368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.54 % (3754368)CaDiCaL version: 2.1.3
% 1.10/0.54 % (3754368)Termination reason: Instruction limit
% 1.10/0.54 % (3754368)Termination phase: Property scanning
% 1.10/0.54 % (3754368)Time elapsed: 0.003 s
% 1.10/0.54 % (3754368)Peak memory usage: 10 MB
% 1.10/0.54 % (3754368)Instructions burned: 7 (million)
% 1.10/0.54 % (3754369)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4335405:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.10/0.54 % (3754369)Instruction limit reached!
% 1.10/0.54 % (3754369)------------------------------
% 1.10/0.54 % (3754369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.54 % (3754369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.54 % (3754369)CaDiCaL version: 2.1.3
% 1.10/0.54 % (3754369)Termination reason: Instruction limit
% 1.10/0.54 % (3754369)Termination phase: Property scanning
% 1.10/0.54 % (3754369)Time elapsed: 0.003 s
% 1.10/0.54 % (3754369)Peak memory usage: 10 MB
% 1.10/0.54 % (3754369)Instructions burned: 7 (million)
% 1.10/0.54 % (3754373)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.10/0.54 % (3754373)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.10/0.54 % (3754374)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4112030412:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.10/0.54 % (3754370)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3302111945:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.10/0.54 % (3754373)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2899676186:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.10/0.54 % (3754357)Instruction limit reached!
% 1.10/0.54 % (3754357)------------------------------
% 1.10/0.54 % (3754357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.54 % (3754357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.54 % (3754357)CaDiCaL version: 2.1.3
% 1.10/0.54 % (3754357)Termination reason: Instruction limit
% 1.10/0.54 % (3754357)Termination phase: Saturation
% 1.10/0.54 % (3754357)Time elapsed: 0.067 s
% 1.10/0.54 % (3754357)Peak memory usage: 13 MB
% 1.10/0.54 % (3754357)Instructions burned: 75 (million)
% 1.10/0.54 % (3754370)Instruction limit reached!
% 1.10/0.54 % (3754370)------------------------------
% 1.10/0.54 % (3754370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.54 % (3754370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.54 % (3754370)CaDiCaL version: 2.1.3
% 1.10/0.54 % (3754370)Termination reason: Instruction limit
% 1.10/0.54 % (3754370)Termination phase: Saturation
% 1.10/0.54 % (3754370)Time elapsed: 0.013 s
% 1.10/0.54 % (3754370)Peak memory usage: 12 MB
% 1.10/0.54 % (3754370)Instructions burned: 15 (million)
% 1.10/0.54 % (3754352)Instruction limit reached!
% 1.10/0.54 % (3754352)------------------------------
% 1.10/0.54 % (3754352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.54 % (3754352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.54 % (3754352)CaDiCaL version: 2.1.3
% 1.10/0.54 % (3754352)Termination reason: Instruction limit
% 1.10/0.54 % (3754352)Termination phase: Saturation
% 1.10/0.54 % (3754352)Time elapsed: 0.074 s
% 1.10/0.54 % (3754352)Peak memory usage: 12 MB
% 1.10/0.54 % (3754352)Instructions burned: 87 (million)
% 1.10/0.54 % (3754373)Instruction limit reached!
% 1.10/0.54 % (3754373)------------------------------
% 1.10/0.54 % (3754373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3754373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3754373)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3754373)Termination reason: Instruction limit
% 1.80/0.60 % (3754373)Termination phase: Saturation
% 1.80/0.60 % (3754373)Time elapsed: 0.022 s
% 1.80/0.60 % (3754373)Peak memory usage: 11 MB
% 1.80/0.60 % (3754373)Instructions burned: 29 (million)
% 1.80/0.60 % (3754374)Instruction limit reached!
% 1.80/0.60 % (3754374)------------------------------
% 1.80/0.60 % (3754374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3754374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3754374)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3754374)Termination reason: Instruction limit
% 1.80/0.60 % (3754374)Termination phase: Saturation
% 1.80/0.60 % (3754374)Time elapsed: 0.041 s
% 1.80/0.60 % (3754374)Peak memory usage: 13 MB
% 1.80/0.60 % (3754374)Instructions burned: 87 (million)
% 1.80/0.60 % (3754379)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.80/0.60 % (3754379)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=983190675:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.80/0.60 % (3754378)lrs+10_1_si=on:cs=on:random_seed=2837218685:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.80/0.60 % (3754379)Instruction limit reached!
% 1.80/0.60 % (3754379)------------------------------
% 1.80/0.60 % (3754379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3754379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3754379)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3754379)Termination reason: Instruction limit
% 1.80/0.60 % (3754379)Termination phase: shuffling
% 1.80/0.60 % (3754379)Time elapsed: 0.002 s
% 1.80/0.60 % (3754379)Peak memory usage: 9 MB
% 1.80/0.60 % (3754379)Instructions burned: 2 (million)
% 1.80/0.60 % (3754378)Instruction limit reached!
% 1.80/0.60 % (3754378)------------------------------
% 1.80/0.60 % (3754378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3754378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3754378)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3754378)Termination reason: Instruction limit
% 1.80/0.60 % (3754378)Termination phase: Function definition elimination
% 1.80/0.60 % (3754378)Time elapsed: 0.007 s
% 1.80/0.60 % (3754378)Peak memory usage: 10 MB
% 1.80/0.60 % (3754378)Instructions burned: 8 (million)
% 1.80/0.60 % (3754381)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=210601256:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.80/0.60 % (3754380)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1301851821:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.80/0.60 % (3754382)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=420936641:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.80/0.60 % (3754381)Refutation not found, incomplete strategy
% 1.80/0.60 % (3754381)------------------------------
% 1.80/0.60 % (3754381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3754381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3754381)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3754381)Termination reason: Refutation not found, incomplete strategy
% 1.80/0.60 % (3754381)Time elapsed: 0.010 s
% 1.80/0.60 % (3754381)Peak memory usage: 12 MB
% 1.80/0.60 % (3754381)Instructions burned: 10 (million)
% 1.80/0.60 % (3754381)------------------------------
% 1.80/0.60 % (3754381)------------------------------
% 1.80/0.60 % (3754380)Refutation not found, incomplete strategy
% 1.80/0.60 % (3754380)------------------------------
% 1.80/0.60 % (3754380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.80/0.60 % (3754380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.80/0.60 % (3754380)CaDiCaL version: 2.1.3
% 1.80/0.60 % (3754380)Termination reason: Refutation not found, incomplete strategy
% 1.80/0.60 % (3754380)Time elapsed: 0.013 s
% 1.80/0.60 % (3754380)Peak memory usage: 12 MB
% 1.80/0.60 % (3754380)Instructions burned: 15 (million)
% 2.19/0.67 % (3754386)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3088251163:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.19/0.67 % (3754380)------------------------------
% 2.19/0.67 % (3754380)------------------------------
% 2.19/0.67 % (3754382)Instruction limit reached!
% 2.19/0.67 % (3754382)------------------------------
% 2.19/0.67 % (3754382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.67 % (3754382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.67 % (3754382)CaDiCaL version: 2.1.3
% 2.19/0.67 % (3754382)Termination reason: Instruction limit
% 2.19/0.67 % (3754382)Termination phase: Saturation
% 2.19/0.67 % (3754382)Time elapsed: 0.013 s
% 2.19/0.67 % (3754382)Peak memory usage: 12 MB
% 2.19/0.67 % (3754382)Instructions burned: 27 (million)
% 2.19/0.67 % (3754386)Instruction limit reached!
% 2.19/0.67 % (3754386)------------------------------
% 2.19/0.67 % (3754386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.67 % (3754386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.67 % (3754386)CaDiCaL version: 2.1.3
% 2.19/0.67 % (3754386)Termination reason: Instruction limit
% 2.19/0.67 % (3754386)Termination phase: Saturation
% 2.19/0.67 % (3754386)Time elapsed: 0.007 s
% 2.19/0.67 % (3754386)Peak memory usage: 12 MB
% 2.19/0.67 % (3754386)Instructions burned: 14 (million)
% 2.19/0.67 % (3754358)Instruction limit reached!
% 2.19/0.67 % (3754358)------------------------------
% 2.19/0.67 % (3754358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.67 % (3754358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.67 % (3754358)CaDiCaL version: 2.1.3
% 2.19/0.67 % (3754358)Termination reason: Instruction limit
% 2.19/0.67 % (3754358)Termination phase: Saturation
% 2.19/0.67 % (3754358)Time elapsed: 0.139 s
% 2.19/0.67 % (3754358)Peak memory usage: 12 MB
% 2.19/0.67 % (3754358)Instructions burned: 157 (million)
% 2.19/0.67 % (3754388)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=339473775:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.19/0.67 % (3754393)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=112342289:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.19/0.67 % (3754393)Instruction limit reached!
% 2.19/0.67 % (3754393)------------------------------
% 2.19/0.67 % (3754393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.67 % (3754393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.67 % (3754393)CaDiCaL version: 2.1.3
% 2.19/0.67 % (3754393)Termination reason: Instruction limit
% 2.19/0.67 % (3754393)Termination phase: Property scanning
% 2.19/0.67 % (3754393)Time elapsed: 0.002 s
% 2.19/0.67 % (3754393)Peak memory usage: 10 MB
% 2.19/0.67 % (3754393)Instructions burned: 4 (million)
% 2.19/0.67 % (3754391)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=119535881:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.19/0.67 % (3754395)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2974567085:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.19/0.67 % (3754394)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2018814455:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.19/0.67 % (3754401)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 2.19/0.67 % (3754401)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.19/0.67 % (3754391)Instruction limit reached!
% 2.19/0.67 % (3754391)------------------------------
% 2.19/0.67 % (3754391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.67 % (3754391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.67 % (3754391)CaDiCaL version: 2.1.3
% 2.19/0.67 % (3754391)Termination reason: Instruction limit
% 2.19/0.67 % (3754391)Termination phase: Saturation
% 2.19/0.67 % (3754391)Time elapsed: 0.012 s
% 2.19/0.67 % (3754391)Peak memory usage: 11 MB
% 2.19/0.68 % (3754391)Instructions burned: 14 (million)
% 2.19/0.68 % (3754395)Instruction limit reached!
% 2.19/0.68 % (3754395)------------------------------
% 2.19/0.68 % (3754395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754395)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754395)Termination reason: Instruction limit
% 2.19/0.68 % (3754395)Termination phase: Saturation
% 2.19/0.68 % (3754395)Time elapsed: 0.012 s
% 2.19/0.68 % (3754395)Peak memory usage: 11 MB
% 2.19/0.68 % (3754395)Instructions burned: 24 (million)
% 2.19/0.68 % (3754398)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=475957386:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.19/0.68 % (3754401)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3578394659:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.19/0.68 % (3754394)Instruction limit reached!
% 2.19/0.68 % (3754394)------------------------------
% 2.19/0.68 % (3754394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754394)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754394)Termination reason: Instruction limit
% 2.19/0.68 % (3754394)Termination phase: Saturation
% 2.19/0.68 % (3754394)Time elapsed: 0.023 s
% 2.19/0.68 % (3754394)Peak memory usage: 11 MB
% 2.19/0.68 % (3754394)Instructions burned: 26 (million)
% 2.19/0.68 % (3754401)Instruction limit reached!
% 2.19/0.68 % (3754401)------------------------------
% 2.19/0.68 % (3754401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754401)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754401)Termination reason: Instruction limit
% 2.19/0.68 % (3754401)Termination phase: Saturation
% 2.19/0.68 % (3754401)Time elapsed: 0.011 s
% 2.19/0.68 % (3754401)Peak memory usage: 11 MB
% 2.19/0.68 % (3754401)Instructions burned: 15 (million)
% 2.19/0.68 % (3754405)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.19/0.68 % (3754405)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3047783887:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.19/0.68 % (3754405)Instruction limit reached!
% 2.19/0.68 % (3754405)------------------------------
% 2.19/0.68 % (3754405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754405)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754405)Termination reason: Instruction limit
% 2.19/0.68 % (3754405)Termination phase: Property scanning
% 2.19/0.68 % (3754405)Time elapsed: 0.004 s
% 2.19/0.68 % (3754405)Peak memory usage: 10 MB
% 2.19/0.68 % (3754405)Instructions burned: 9 (million)
% 2.19/0.68 % (3754406)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3808760480:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.19/0.68 % (3754412)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4073916801:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.19/0.68 % (3754410)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3729950437:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.19/0.68 % (3754410)Instruction limit reached!
% 2.19/0.68 % (3754410)------------------------------
% 2.19/0.68 % (3754410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754410)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754410)Termination reason: Instruction limit
% 2.19/0.68 % (3754410)Termination phase: Property scanning
% 2.19/0.68 % (3754410)Time elapsed: 0.007 s
% 2.19/0.68 % (3754410)Peak memory usage: 10 MB
% 2.19/0.68 % (3754410)Instructions burned: 8 (million)
% 2.19/0.68 % (3754412)Instruction limit reached!
% 2.19/0.68 % (3754412)------------------------------
% 2.19/0.68 % (3754412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754412)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754412)Termination reason: Instruction limit
% 2.19/0.68 % (3754412)Termination phase: Saturation
% 2.19/0.68 % (3754412)Time elapsed: 0.012 s
% 2.19/0.68 % (3754412)Peak memory usage: 11 MB
% 2.19/0.68 % (3754412)Instructions burned: 25 (million)
% 2.19/0.68 % (3754414)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=763552238:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.19/0.68 % (3754398)Instruction limit reached!
% 2.19/0.68 % (3754398)------------------------------
% 2.19/0.68 % (3754398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754398)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754398)Termination reason: Instruction limit
% 2.19/0.68 % (3754398)Termination phase: Saturation
% 2.19/0.68 % (3754398)Time elapsed: 0.057 s
% 2.19/0.68 % (3754398)Peak memory usage: 12 MB
% 2.19/0.68 % (3754398)Instructions burned: 61 (million)
% 2.19/0.68 % (3754406)Instruction limit reached!
% 2.19/0.68 % (3754406)------------------------------
% 2.19/0.68 % (3754406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754406)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754406)Termination reason: Instruction limit
% 2.19/0.68 % (3754406)Termination phase: Saturation
% 2.19/0.68 % (3754406)Time elapsed: 0.030 s
% 2.19/0.68 % (3754406)Peak memory usage: 12 MB
% 2.19/0.68 % (3754406)Instructions burned: 32 (million)
% 2.19/0.68 % (3754414)Instruction limit reached!
% 2.19/0.68 % (3754414)------------------------------
% 2.19/0.68 % (3754414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754414)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754414)Termination reason: Instruction limit
% 2.19/0.68 % (3754414)Termination phase: Saturation
% 2.19/0.68 % (3754414)Time elapsed: 0.012 s
% 2.19/0.68 % (3754414)Peak memory usage: 12 MB
% 2.19/0.68 % (3754414)Instructions burned: 23 (million)
% 2.19/0.68 % (3754423)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=59752754:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.19/0.68 % (3754422)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3171284406:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.19/0.68 % (3754420)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2632392255:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.19/0.68 % (3754424)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3310844075:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.19/0.68 % (3754425)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.19/0.68 % (3754425)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1623483390:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.19/0.68 % (3754425)Instruction limit reached!
% 2.19/0.68 % (3754425)------------------------------
% 2.19/0.68 % (3754425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754425)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754425)Termination reason: Instruction limit
% 2.19/0.68 % (3754425)Termination phase: Property scanning
% 2.19/0.68 % (3754425)Time elapsed: 0.006 s
% 2.19/0.68 % (3754425)Peak memory usage: 10 MB
% 2.19/0.68 % (3754425)Instructions burned: 7 (million)
% 2.19/0.68 % (3754388) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3754347-3754388"...
% 2.19/0.68 % (3754424)Instruction limit reached!
% 2.19/0.68 % (3754424)------------------------------
% 2.19/0.68 % (3754424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.68 % (3754424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.68 % (3754424)CaDiCaL version: 2.1.3
% 2.19/0.68 % (3754424)Termination reason: Instruction limit
% 2.19/0.68 % (3754424)Termination phase: Saturation
% 2.19/0.68 % (3754424)Time elapsed: 0.034 s
% 2.19/0.68 % (3754424)Peak memory usage: 12 MB
% 2.19/0.68 % (3754424)Instructions burned: 42 (million)
% 2.19/0.68 % (3754433)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=327083378:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.19/0.68 % (3754388)...printing done.
% 2.19/0.68 % (3754388)Refutation found. Thanks to Tanya!
% 2.19/0.68 % SZS status Theorem for theBenchmark
% 2.19/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.19/0.69 % (3754388)------------------------------
% 2.19/0.69 % (3754388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.69 % (3754388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.69 % (3754388)CaDiCaL version: 2.1.3
% 2.19/0.69 % (3754388)Termination reason: Refutation
% 2.19/0.69 % (3754388)Time elapsed: 0.157 s
% 2.19/0.69 % (3754388)Peak memory usage: 14 MB
% 2.19/0.69 % (3754388)Instructions burned: 175 (million)
% 2.19/0.69 % (3754347)Success in time 0.348 s
% 2.19/0.69 % Vampire exiting
%------------------------------------------------------------------------------