%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG008^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:28 AM UTC 2026
% Result : Theorem 42.32s 6.26s
% Output : Refutation 42.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 18
% Syntax : Number of formulae : 177 ( 88 unt; 0 typ; 5 def)
% Number of atoms : 1346 ( 194 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2766 ( 176 ~; 140 |; 169 &;1849 @)
% ( 5 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 84 usr; 18 con; 0-4 aty)
% ( 175 !!; 64 ??; 0 @@+; 0 @@-)
% Number of variables : 588 ( 17 sgn 92 !; 6 ?; 588 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vOR: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_67,type,
sK4: reg ).
thf(func_def_68,type,
sK5: reg > 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 ).
thf(func_def_73,type,
sK10: reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_75,type,
sK12: reg > reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: $i > ( $i > $o ) > $i ).
thf(func_def_79,type,
sK16: $i > ( $i > $o ) > $i ).
thf(func_def_80,type,
sK17: $i > ( $i > $o ) > $i ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f33,axiom,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).
thf(f35,axiom,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f36,axiom,
( eq
= ( ^ [X0: reg,X1: reg] :
( ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f71,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f72,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f94,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f104,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f105,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
=> ( ( c @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f104]) ).
thf(f108,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f109,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f110,plain,
( eq
= ( ^ [X0: reg,X1: reg] :
( ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f111,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f110]) ).
thf(f112,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f113,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f116,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f117,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f116]) ).
thf(f118,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f119,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f120,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f121,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f120]) ).
thf(f122,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f123,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f130,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f131,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f134,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f135,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f136,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f137,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ) ),
inference(flattening,[],[f137]) ).
thf(f139,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f105]) ).
thf(f155,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f167,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f172,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
!= $true )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f174,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f175,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f176,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f178,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f117]) ).
thf(f179,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f180,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f121]) ).
thf(f181,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f185,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f131]) ).
thf(f187,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f188,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( eq @ catalunya @ paris )
=> ( o @ france @ spain ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f200,plain,
( eq
= ( ^ [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,[],[f175,f174,f174]) ).
thf(f201,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f176,f174,f174]) ).
thf(f203,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f178,f201]) ).
thf(f204,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f179,f174,f174]) ).
thf(f205,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f180,f204,f203,f203]) ).
thf(f206,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f181,f204,f203,f203]) ).
thf(f210,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ catalunya
@ spain ) ) ) ),
inference(definition_unfolding,[],[f185,f167,f155,f205]) ).
thf(f212,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f187,f167,f155,f206]) ).
thf(f213,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y1
@ Y2 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) )
@ catalunya
@ paris )
=> ( ^ [Y1: reg,Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) ) )
@ france
@ spain ) ) ) ) ),
inference(definition_unfolding,[],[f188,f167,f155,f200,f201]) ).
thf(f214,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ catalunya ) ) ) )
=> ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ catalunya ) ) ) )
=> ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ catalunya ) ) ) )
=> ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ catalunya ) ) ) )
=> ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) ) )
=> ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( $false
= ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) ) )
=> ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( $true
= ( a @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f223,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f224,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f226,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ catalunya )
=> ( c @ X1 @ paris ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X1: reg] :
( ( $true
= ( c @ X1 @ paris ) )
| ( $false
= ( c @ X1 @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f230,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ paris )
=> ( c @ X1 @ catalunya ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X1: reg] :
( ( $false
= ( c @ X1 @ paris ) )
| ( $true
= ( c @ X1 @ catalunya ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: reg] :
( $false
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f222]) ).
thf(f233,plain,
! [X1: reg] :
( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X1: reg] :
( ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X1: reg] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ spain ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) )
@ ( sK3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: reg] :
( ( $false
= ( ( c @ ( sK2 @ X1 ) @ X1 )
=> ( c @ ( sK2 @ X1 ) @ spain ) ) )
| ( $false
= ( ( c @ ( sK3 @ X1 ) @ X1 )
=> ( c @ ( sK3 @ X1 ) @ france ) ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X1: reg] :
( ( $false
= ( c @ ( sK2 @ X1 ) @ spain ) )
| ( $false
= ( ( c @ ( sK3 @ X1 ) @ X1 )
=> ( c @ ( sK3 @ X1 ) @ france ) ) ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X1: reg] :
( ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( ( c @ ( sK3 @ X1 ) @ X1 )
=> ( c @ ( sK3 @ X1 ) @ france ) ) ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f240,plain,
! [X1: reg] :
( ( $false
= ( c @ ( sK3 @ X1 ) @ france ) )
| ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: reg] :
( ( $true
= ( c @ ( sK3 @ X1 ) @ X1 ) )
| ( $true
= ( c @ ( sK2 @ X1 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f242,plain,
! [X1: reg] :
( ( $false
= ( c @ ( sK3 @ X1 ) @ france ) )
| ( $false
= ( c @ ( sK2 @ X1 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f243,plain,
! [X1: reg] :
( ( $true
= ( c @ ( sK3 @ X1 ) @ X1 ) )
| ( $false
= ( c @ ( sK2 @ X1 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f244,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f245,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f251]) ).
thf(f254,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ X3 @ france ) ) ),
inference(imp_proxy_clausification,[],[f256]) ).
thf(f323,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f324,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) )
& ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) )
& ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) )
& ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f327]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f328]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f330]) ).
thf(f333,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( c @ X3 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f436,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK3 @ paris ) @ catalunya ) )
| ( $true
= ( c @ ( sK2 @ paris ) @ paris ) ) ),
inference(constrained_superposition,[],[f231,f241]) ).
thf(f440,plain,
( ( $true
= ( c @ ( sK3 @ paris ) @ catalunya ) )
| ( $true
= ( c @ ( sK2 @ paris ) @ paris ) ) ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f463,definition,
( spl18_1
<=> ( $true
= ( c @ ( sK2 @ paris ) @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
thf(f465,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f463]) ).
thf(f467,definition,
( spl18_2
<=> ( $true
= ( c @ ( sK3 @ paris ) @ catalunya ) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f468,plain,
( ( $true
!= ( c @ ( sK3 @ paris ) @ catalunya ) )
| spl18_2 ),
inference(avatar_component_clause,[],[f467]) ).
thf(f469,plain,
( ( $true
= ( c @ ( sK3 @ paris ) @ catalunya ) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f467]) ).
thf(f470,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f440,f467,f463]) ).
thf(f497,plain,
! [X0: reg] :
( ( $true != $true )
| ( $true
= ( c @ paris @ X0 ) )
| ( $false
= ( c @ X0 @ catalunya ) ) ),
inference(constrained_superposition,[],[f172,f228]) ).
thf(f515,plain,
! [X0: reg] :
( ( $true
= ( c @ paris @ X0 ) )
| ( $false
= ( c @ X0 @ catalunya ) ) ),
inference(trivial_inequality_removal,[],[f497]) ).
thf(f540,plain,
( ( $true = $false )
| ( $true
= ( c @ paris @ ( sK3 @ paris ) ) )
| ~ spl18_2 ),
inference(constrained_superposition,[],[f469,f515]) ).
thf(f541,plain,
( ( $true
= ( c @ paris @ ( sK3 @ paris ) ) )
| ~ spl18_2 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f552,plain,
( ( $true
= ( c @ ( sK3 @ paris ) @ paris ) )
| ~ spl18_2 ),
inference(unit_resulting_resolution,[],[f172,f541]) ).
thf(f27143,definition,
( spl18_7
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
thf(f27144,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f27143]) ).
thf(f27146,definition,
( spl18_8
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $true
= ( c @ X3 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
thf(f27147,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( $true
= ( c @ X3 @ france ) ) )
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f27146]) ).
thf(f27148,plain,
( spl18_7
| spl18_8 ),
inference(avatar_split_clause,[],[f257,f27146,f27143]) ).
thf(f29371,plain,
( ( $true = $false )
| ~ spl18_7 ),
inference(constrained_superposition,[],[f27144,f221]) ).
thf(f29399,plain,
( $false
| ~ spl18_7 ),
inference(trivial_inequality_removal,[],[f29371]) ).
thf(f29400,plain,
~ spl18_7,
inference(avatar_contradiction_clause,[],[f29399]) ).
thf(f30601,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK3 @ paris ) @ france ) )
| ~ spl18_2
| ~ spl18_8 ),
inference(constrained_superposition,[],[f552,f27147]) ).
thf(f30754,plain,
( ( $true
= ( c @ ( sK3 @ paris ) @ france ) )
| ~ spl18_2
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f30601]) ).
thf(f31209,plain,
( ( $true = $false )
| ( $false
= ( c @ ( sK2 @ paris ) @ spain ) )
| ~ spl18_2
| ~ spl18_8 ),
inference(constrained_superposition,[],[f242,f30754]) ).
thf(f31210,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl18_2
| ~ spl18_8 ),
inference(constrained_superposition,[],[f240,f30754]) ).
thf(f31223,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ paris ) )
| ~ spl18_2
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f31210]) ).
thf(f31224,plain,
( ( $false
= ( c @ ( sK2 @ paris ) @ spain ) )
| ~ spl18_2
| ~ spl18_8 ),
inference(trivial_inequality_removal,[],[f31209]) ).
thf(f31300,plain,
( spl18_1
| ~ spl18_2
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f31223,f27146,f467,f463]) ).
thf(f31328,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK2 @ paris ) @ catalunya ) )
| ~ spl18_1 ),
inference(constrained_superposition,[],[f231,f465]) ).
thf(f31380,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ catalunya ) )
| ~ spl18_1 ),
inference(trivial_inequality_removal,[],[f31328]) ).
thf(f31810,definition,
( spl18_14
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_14])],[avatar_definition]) ).
thf(f31811,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( $true
= ( c @ X3 @ spain ) ) )
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f31810]) ).
thf(f31812,plain,
( spl18_7
| spl18_14 ),
inference(avatar_split_clause,[],[f336,f31810,f27143]) ).
thf(f31829,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK2 @ paris ) @ spain ) )
| ~ spl18_1
| ~ spl18_14 ),
inference(constrained_superposition,[],[f31811,f31380]) ).
thf(f31903,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK2 @ paris ) @ spain ) )
| ~ spl18_1
| ~ spl18_14 ),
inference(constrained_superposition,[],[f31380,f31811]) ).
thf(f32054,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ spain ) )
| ~ spl18_1
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f31903]) ).
thf(f32163,plain,
( ( $true
= ( c @ ( sK2 @ paris ) @ spain ) )
| ~ spl18_1
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f31829]) ).
thf(f32193,plain,
( ( $true = $false )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_8
| ~ spl18_14 ),
inference(forward_demodulation,[],[f32163,f31224]) ).
thf(f32194,plain,
( $false
| ~ spl18_1
| ~ spl18_2
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f32193]) ).
thf(f32195,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_8
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f32194]) ).
thf(f32493,plain,
( ( $false
= ( c @ ( sK3 @ paris ) @ paris ) )
| spl18_2 ),
inference(unit_resulting_resolution,[],[f231,f468]) ).
thf(f32864,plain,
( ( $true = $false )
| ( $false
= ( c @ ( sK2 @ paris ) @ spain ) )
| spl18_2 ),
inference(constrained_superposition,[],[f243,f32493]) ).
thf(f32932,plain,
( ( $false
= ( c @ ( sK2 @ paris ) @ spain ) )
| spl18_2 ),
inference(trivial_inequality_removal,[],[f32864]) ).
thf(f33680,plain,
( ( $true = $false )
| ~ spl18_1
| spl18_2
| ~ spl18_14 ),
inference(constrained_superposition,[],[f32932,f32054]) ).
thf(f33715,plain,
( $false
| ~ spl18_1
| spl18_2
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f33680]) ).
thf(f33716,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_14 ),
inference(avatar_contradiction_clause,[],[f33715]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f470]) ).
cnf(s7,plain,
( spl18_7
| spl18_8 ),
inference(sat_conversion,[],[f27148]) ).
cnf(s23,plain,
~ spl18_7,
inference(sat_conversion,[],[f29400]) ).
cnf(s24,plain,
( spl18_1
| ~ spl18_2
| ~ spl18_8 ),
inference(sat_conversion,[],[f31300]) ).
cnf(s25,plain,
( spl18_7
| spl18_14 ),
inference(sat_conversion,[],[f31812]) ).
cnf(s28,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_8
| ~ spl18_14 ),
inference(sat_conversion,[],[f32195]) ).
cnf(s32,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_14 ),
inference(sat_conversion,[],[f33716]) ).
cnf(s33,plain,
spl18_14,
inference(rat,[],[s25,s23]) ).
cnf(s42,plain,
spl18_8,
inference(rat,[],[s7,s23]) ).
cnf(s44,plain,
spl18_1,
inference(rat,[],[s1,s24,s42]) ).
cnf(s45,plain,
spl18_2,
inference(rat,[],[s32,s33,s44]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s28,s33,s42,s45,s44]) ).
thf(f33718,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG008^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:34:01 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.82/0.96 % (483525)Will run a generic schedule for satisfiability detection.
% 3.82/0.96 % (483531)% WARNING: option uhcvi not known.
% 3.82/0.96 % (483533)dis+10_1_sil=32000:sp=arity:random_seed=1165543143:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.82/0.96 % (483534)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3477294237:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.82/0.96 % (483530)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2386566340_2999 on theBenchmark for (2999ds/0Mi)
% 3.82/0.96 % (483531)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=872491947:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.82/0.96 % (483532)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=708354776:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.82/0.96 % (483536)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=175892126:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.82/0.96 % (483534)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.96 % (483531)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.96 % (483535)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3361716022:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.82/0.96 % Exception at run slice level
% 3.82/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.96 % (483531)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.82/0.96 % (483544)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3539559916:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.82/0.96 % Exception at run slice level
% 3.82/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.82/0.96 % (483536)Instruction limit reached!
% 3.82/0.96 % (483536)------------------------------
% 3.82/0.96 % (483536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.96 % (483536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.96 % (483536)CaDiCaL version: 2.1.3
% 3.82/0.96 % (483536)Termination reason: Instruction limit
% 3.82/0.96 % (483536)Termination phase: Saturation
% 3.82/0.96 % (483536)Time elapsed: 0.041 s
% 3.82/0.96 % (483536)Peak memory usage: 13 MB
% 3.82/0.96 % (483536)Instructions burned: 161 (million)
% 3.82/0.96 % (483533)Instruction limit reached!
% 3.82/0.96 % (483533)------------------------------
% 3.82/0.96 % (483533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.96 % (483533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.96 % (483533)CaDiCaL version: 2.1.3
% 3.82/0.96 % (483533)Termination reason: Instruction limit
% 3.82/0.96 % (483533)Termination phase: Saturation
% 3.82/0.96 % (483533)Time elapsed: 0.051 s
% 3.82/0.96 % (483533)Peak memory usage: 12 MB
% 3.82/0.96 % (483533)Instructions burned: 103 (million)
% 3.82/0.96 % (483546)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1085165542:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.82/0.96 % (483547)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=850666905:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.82/0.97 % (483534)Instruction limit reached!
% 3.82/0.97 % (483534)------------------------------
% 3.82/0.97 % (483534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.97 % (483534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/0.97 % (483534)CaDiCaL version: 2.1.3
% 3.82/0.97 % (483534)Termination reason: Instruction limit
% 3.82/0.97 % (483534)Termination phase: Saturation
% 3.82/0.97 % (483534)Time elapsed: 0.056 s
% 3.82/0.97 % (483534)Peak memory usage: 13 MB
% 3.82/0.97 % (483534)Instructions burned: 116 (million)
% 3.82/0.97 % (483547)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.82/0.97 % (483547)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.82/0.97 % (483535)Instruction limit reached!
% 3.82/0.97 % (483535)------------------------------
% 3.82/0.97 % (483535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.82/0.97 % (483535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/3.97 % (483535)CaDiCaL version: 2.1.3
% 25.22/3.97 % (483535)Termination reason: Instruction limit
% 25.22/3.97 % (483535)Termination phase: Saturation
% 25.22/3.97 % (483535)Time elapsed: 0.064 s
% 25.22/3.97 % (483535)Peak memory usage: 13 MB
% 25.22/3.97 % (483535)Instructions burned: 132 (million)
% 25.22/3.97 % (483548)ott-21_1_sil=16000:fs=off:random_seed=4142466164:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 25.22/3.97 % (483551)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1003753571:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 25.22/3.97 % (483552)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=951544607:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 25.22/3.97 % Exception at run slice level
% 25.22/3.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 25.22/3.97 % (483556)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1056571149:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 25.22/3.97 % (483546)Instruction limit reached!
% 25.22/3.97 % (483546)------------------------------
% 25.22/3.97 % (483546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 25.22/3.97 % (483546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/3.97 % (483546)CaDiCaL version: 2.1.3
% 25.22/3.97 % (483546)Termination reason: Instruction limit
% 25.22/3.97 % (483546)Termination phase: Saturation
% 25.22/3.97 % (483546)Time elapsed: 0.068 s
% 25.22/3.97 % (483546)Peak memory usage: 13 MB
% 25.22/3.97 % (483546)Instructions burned: 133 (million)
% 25.22/3.97 % (483558)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3923082307:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 25.22/3.97 % Exception at run slice level
% 25.22/3.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 25.22/3.97 % (483560)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3830957645:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 25.22/3.97 % (483560)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 25.22/3.97 % (483547)Instruction limit reached!
% 25.22/3.97 % (483547)------------------------------
% 25.22/3.97 % (483547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 25.22/3.97 % (483547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/3.97 % (483547)CaDiCaL version: 2.1.3
% 25.22/3.97 % (483547)Termination reason: Instruction limit
% 25.22/3.97 % (483547)Termination phase: Saturation
% 25.22/3.97 % (483547)Time elapsed: 0.169 s
% 25.22/3.97 % (483547)Peak memory usage: 15 MB
% 25.22/3.97 % (483547)Instructions burned: 685 (million)
% 25.22/3.97 % (483548)Instruction limit reached!
% 25.22/3.97 % (483548)------------------------------
% 25.22/3.97 % (483548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 25.22/3.97 % (483548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.22/3.97 % (483548)CaDiCaL version: 2.1.3
% 25.22/3.97 % (483548)Termination reason: Instruction limit
% 25.22/3.97 % (483548)Termination phase: Saturation
% 25.22/3.97 % (483548)Time elapsed: 0.154 s
% 25.22/3.97 % (483548)Peak memory usage: 12 MB
% 25.22/3.97 % (483548)Instructions burned: 180 (million)
% 25.22/3.97 % (483562)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2635929742:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 25.22/3.97 % (483562)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 25.22/3.97 % (483563)fmb+10_1_sil=64000:random_seed=844007554:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 25.22/3.97 % (483563)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 25.22/3.97 % Exception at run slice level
% 25.22/3.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 25.22/3.97 % (483566)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2459061020:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 25.22/3.97 % Exception at run slice level
% 25.22/3.97 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 25.22/3.97 % (483573)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=354796858:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 42.32/6.26 % (483551)Instruction limit reached!
% 42.32/6.26 % (483551)------------------------------
% 42.32/6.26 % (483551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483551)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483551)Termination reason: Instruction limit
% 42.32/6.26 % (483551)Termination phase: Saturation
% 42.32/6.26 % (483551)Time elapsed: 0.241 s
% 42.32/6.26 % (483551)Peak memory usage: 13 MB
% 42.32/6.26 % (483551)Instructions burned: 477 (million)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483583)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1579264668:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 42.32/6.26 % (483583)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 42.32/6.26 % (483585)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2826599686:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 42.32/6.26 % (483585)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 42.32/6.26 % (483585)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 42.32/6.26 % (483562)Instruction limit reached!
% 42.32/6.26 % (483562)------------------------------
% 42.32/6.26 % (483562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483562)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483562)Termination reason: Instruction limit
% 42.32/6.26 % (483562)Termination phase: Saturation
% 42.32/6.26 % (483562)Time elapsed: 0.226 s
% 42.32/6.26 % (483562)Peak memory usage: 16 MB
% 42.32/6.26 % (483562)Instructions burned: 883 (million)
% 42.32/6.26 % (483640)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3019097684:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483643)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3551074125:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483560)Instruction limit reached!
% 42.32/6.26 % (483560)------------------------------
% 42.32/6.26 % (483560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483560)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483560)Termination reason: Instruction limit
% 42.32/6.26 % (483560)Termination phase: Saturation
% 42.32/6.26 % (483560)Time elapsed: 0.323 s
% 42.32/6.26 % (483560)Peak memory usage: 14 MB
% 42.32/6.26 % (483560)Instructions burned: 692 (million)
% 42.32/6.26 % (483649)ott-2_1_sil=16000:newcnf=on:random_seed=2573299685:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 42.32/6.26 % (483649)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 42.32/6.26 % (483650)ott+10_1_sil=32000:tgt=ground:random_seed=114021944:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 42.32/6.26 % (483556)Instruction limit reached!
% 42.32/6.26 % (483556)------------------------------
% 42.32/6.26 % (483556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483556)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483556)Termination reason: Instruction limit
% 42.32/6.26 % (483556)Termination phase: Saturation
% 42.32/6.26 % (483556)Time elapsed: 0.548 s
% 42.32/6.26 % (483556)Peak memory usage: 16 MB
% 42.32/6.26 % (483556)Instructions burned: 1179 (million)
% 42.32/6.26 % (483691)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3242620061:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483649)Instruction limit reached!
% 42.32/6.26 % (483649)------------------------------
% 42.32/6.26 % (483649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483649)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483649)Termination reason: Instruction limit
% 42.32/6.26 % (483649)Termination phase: Saturation
% 42.32/6.26 % (483649)Time elapsed: 0.193 s
% 42.32/6.26 % (483649)Peak memory usage: 14 MB
% 42.32/6.26 % (483649)Instructions burned: 874 (million)
% 42.32/6.26 % (483697)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3630565377:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 42.32/6.26 % (483697)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 42.32/6.26 % (483700)dis+21_1_sil=32000:sas=cadical:random_seed=2070202231:i=3773:amm=off_2992 on theBenchmark for (2992ds/3773Mi)
% 42.32/6.26 % (483585)Instruction limit reached!
% 42.32/6.26 % (483585)------------------------------
% 42.32/6.26 % (483585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483585)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483585)Termination reason: Instruction limit
% 42.32/6.26 % (483585)Termination phase: Saturation
% 42.32/6.26 % (483585)Time elapsed: 0.980 s
% 42.32/6.26 % (483585)Peak memory usage: 17 MB
% 42.32/6.26 % (483585)Instructions burned: 1473 (million)
% 42.32/6.26 % (483760)ott+11_1_sil=16000:gs=on:random_seed=3558455695:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2986 on theBenchmark for (2986ds/2251Mi)
% 42.32/6.26 % (483760)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 42.32/6.26 % (483697)Instruction limit reached!
% 42.32/6.26 % (483697)------------------------------
% 42.32/6.26 % (483697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483697)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483697)Termination reason: Instruction limit
% 42.32/6.26 % (483697)Termination phase: Saturation
% 42.32/6.26 % (483697)Time elapsed: 1.284 s
% 42.32/6.26 % (483697)Peak memory usage: 19 MB
% 42.32/6.26 % (483697)Instructions burned: 3513 (million)
% 42.32/6.26 % (483775)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=688755970:fmbsr=1.6:i=67534_2979 on theBenchmark for (2979ds/67534Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483778)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1377513411:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2979 on theBenchmark for (2979ds/4591Mi)
% 42.32/6.26 % (483760)Instruction limit reached!
% 42.32/6.26 % (483760)------------------------------
% 42.32/6.26 % (483760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483760)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483760)Termination reason: Instruction limit
% 42.32/6.26 % (483760)Termination phase: Saturation
% 42.32/6.26 % (483760)Time elapsed: 1.862 s
% 42.32/6.26 % (483760)Peak memory usage: 18 MB
% 42.32/6.26 % (483760)Instructions burned: 2251 (million)
% 42.32/6.26 % (483650)Instruction limit reached!
% 42.32/6.26 % (483650)------------------------------
% 42.32/6.26 % (483650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483650)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483650)Termination reason: Instruction limit
% 42.32/6.26 % (483650)Termination phase: Saturation
% 42.32/6.26 % (483650)Time elapsed: 2.733 s
% 42.32/6.26 % (483650)Peak memory usage: 24 MB
% 42.32/6.26 % (483650)Instructions burned: 5115 (million)
% 42.32/6.26 % (483784)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=4038770610:i=29340_2967 on theBenchmark for (2967ds/29340Mi)
% 42.32/6.26 % (483785)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2208725426:i=5211_2967 on theBenchmark for (2967ds/5211Mi)
% 42.32/6.26 % (483700)Instruction limit reached!
% 42.32/6.26 % (483700)------------------------------
% 42.32/6.26 % (483700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483700)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483700)Termination reason: Instruction limit
% 42.32/6.26 % (483700)Termination phase: Saturation
% 42.32/6.26 % (483700)Time elapsed: 2.982 s
% 42.32/6.26 % (483700)Peak memory usage: 20 MB
% 42.32/6.26 % (483700)Instructions burned: 3773 (million)
% 42.32/6.26 % (483792)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=930863526:i=5497:nm=2_2962 on theBenchmark for (2962ds/5497Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483794)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=2434416704:fmbsr=2:i=46332_2962 on theBenchmark for (2962ds/46332Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483796)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=2742336396:i=14071_2961 on theBenchmark for (2961ds/14071Mi)
% 42.32/6.26 % Exception at run slice level
% 42.32/6.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 42.32/6.26 % (483798)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3268568094:i=22565:add=on:rawr=on_2961 on theBenchmark for (2961ds/22565Mi)
% 42.32/6.26 % (483583)Instruction limit reached!
% 42.32/6.26 % (483583)------------------------------
% 42.32/6.26 % (483583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483583)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483583)Termination reason: Instruction limit
% 42.32/6.26 % (483583)Termination phase: Saturation
% 42.32/6.26 % (483583)Time elapsed: 3.563 s
% 42.32/6.26 % (483583)Peak memory usage: 21 MB
% 42.32/6.26 % (483583)Instructions burned: 5131 (million)
% 42.32/6.26 % (483800)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=3408430066:i=8173:av=off_2960 on theBenchmark for (2960ds/8173Mi)
% 42.32/6.26 % (483785)Instruction limit reached!
% 42.32/6.26 % (483785)------------------------------
% 42.32/6.26 % (483785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483785)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483785)Termination reason: Instruction limit
% 42.32/6.26 % (483785)Termination phase: Saturation
% 42.32/6.26 % (483785)Time elapsed: 2.228 s
% 42.32/6.26 % (483785)Peak memory usage: 25 MB
% 42.32/6.26 % (483785)Instructions burned: 5213 (million)
% 42.32/6.26 % (483814)dis+10_16:1_sil=16000:random_seed=4221501767:i=9155:fsr=off_2944 on theBenchmark for (2944ds/9155Mi)
% 42.32/6.26 % (483778)Instruction limit reached!
% 42.32/6.26 % (483778)------------------------------
% 42.32/6.26 % (483778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483778)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483778)Termination reason: Instruction limit
% 42.32/6.26 % (483778)Termination phase: Saturation
% 42.32/6.26 % (483778)Time elapsed: 3.668 s
% 42.32/6.26 % (483778)Peak memory usage: 21 MB
% 42.32/6.26 % (483778)Instructions burned: 4592 (million)
% 42.32/6.26 % (483818)ott-3_8_sil=64000:random_seed=1556596114:i=20139:bs=on_2942 on theBenchmark for (2942ds/20139Mi)
% 42.32/6.26 % (483784) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-483525-483784"...
% 42.32/6.26 % (483784)...printing done.
% 42.32/6.26 % (483784)Refutation found. Thanks to Tanya!
% 42.32/6.26 % SZS status Theorem for theBenchmark
% 42.32/6.26 % SZS output start Proof for theBenchmark
% See solution above
% 42.32/6.26 % (483784)------------------------------
% 42.32/6.26 % (483784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.32/6.26 % (483784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.32/6.26 % (483784)CaDiCaL version: 2.1.3
% 42.32/6.26 % (483784)Termination reason: Refutation
% 42.32/6.26 % (483784)Time elapsed: 2.714 s
% 42.32/6.26 % (483784)Peak memory usage: 18 MB
% 42.32/6.26 % (483784)Instructions burned: 3423 (million)
% 42.32/6.26 % (483525)Success in time 6.021 s
% 42.32/6.26 % Vampire exiting
%------------------------------------------------------------------------------