%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG016^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 07:49:27 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 148 ( 73 unt; 0 typ; 7 def)
% Number of atoms : 983 ( 165 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1767 ( 115 ~; 127 |; 63 &;1175 @)
% ( 7 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 87 usr; 23 con; 0-4 aty)
% ( 129 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 352 ( 12 sgn 87 !; 2 ?; 352 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_61,type,
vIMP: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
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 > reg ).
thf(func_def_68,type,
sK5: reg > reg ).
thf(func_def_69,type,
sK6: reg ).
thf(func_def_70,type,
sK7: reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg > reg ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_77,type,
sK14: reg ).
thf(func_def_78,type,
sK15: reg ).
thf(func_def_79,type,
sK16: reg ).
thf(func_def_80,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_81,type,
sK18: $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/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f35,axiom,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f37,axiom,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f47,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] :
! [X2: reg,X1: reg] :
( ( ( p @ X2 @ france )
& ( p @ X1 @ spain ) )
=> ~ ( o @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] :
! [X2: reg,X1: reg] :
( ( ( p @ X2 @ france )
& ( p @ X1 @ spain ) )
=> ~ ( o @ X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f51,plain,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f52,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f74,plain,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
inference(rectify,[],[f47]) ).
thf(f75,plain,
( $true
= ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f93,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f94,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
inference(rectify,[],[f37]) ).
thf(f96,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f121,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f122,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f136,plain,
~ ( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] :
! [X1: reg,X2: reg] :
( ( ( p @ X1 @ france )
& ( p @ X2 @ spain ) )
=> ~ ( o @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f137,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( ( p @ Y1 @ spain )
& ( p @ Y2 @ france ) )
=> ~ ( o @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( ( p @ Y1 @ spain )
& ( p @ Y2 @ france ) )
=> ~ ( o @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f137]) ).
thf(f141,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f148,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f154,plain,
( $true
= ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f171,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f174,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f177,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( ( p @ Y1 @ spain )
& ( p @ Y2 @ france ) )
=> ~ ( o @ Y1 @ Y2 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f181,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f202,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f141,f148,f148]) ).
thf(f204,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 ) ) )
@ Y0
@ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f171,f202]) ).
thf(f208,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 ) ) )
@ fool
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ~ ( ^ [Y3: reg,Y4: reg] :
( ?? @ reg
@ ^ [Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y3 ) ) )
@ Y1
@ Y2 )
& ( c @ Y1 @ Y2 ) )
@ spain
@ france ) ) ) ),
inference(definition_unfolding,[],[f154,f174,f181,f204]) ).
thf(f212,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 ) ) )
@ fool
@ ^ [Y0: $i] :
( !! @ reg
@ ^ [Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y1
@ spain )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ france ) )
=> ~ ( ^ [Y3: reg,Y4: reg] :
( ?? @ reg
@ ^ [Y5: reg] :
( ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y3 ) ) )
@ Y1
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f177,f174,f181,f148,f148,f202]) ).
thf(f295,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f296,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
| ~ ( fool @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
& ( c @ spain @ france ) )
= $true )
| ( $true
= ( ~ ( fool @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f299]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) ) )
| ( $true
= ( ~ ( fool @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f300]) ).
thf(f303,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
= $false )
| ( $true
= ( ~ ( fool @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X3 )
= $false )
| ( $true
= ( ~ ( fool @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X3 )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK4 @ X3 ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK5 @ X3 ) ) )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK4 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( c @ ( sK4 @ X3 ) @ X3 )
=> ( c @ ( sK4 @ X3 ) @ spain ) )
= $false )
| ( ( ( c @ ( sK5 @ X3 ) @ X3 )
=> ( c @ ( sK5 @ X3 ) @ france ) )
= $false ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( ( ( c @ ( sK5 @ X3 ) @ X3 )
=> ( c @ ( sK5 @ X3 ) @ france ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ ( sK5 @ X3 ) @ X3 )
=> ( c @ ( sK5 @ X3 ) @ france ) )
= $false )
| ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f313,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) )
| ( ( c @ ( sK5 @ X3 ) @ france )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK5 @ X3 ) @ X3 )
= $true )
| ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f312]) ).
thf(f315,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK5 @ X3 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f316,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK5 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f372,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ reg
@ ^ [Y2: reg] :
( !! @ reg
@ ^ [Y3: reg] :
( ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) ) ) ) ) ) )
| ~ ( fool @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f373,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ reg
@ ^ [Y2: reg] :
( !! @ reg
@ ^ [Y3: reg] :
( ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y4: reg] :
( ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y4 )
=> ( c @ Y5 @ Y2 ) ) ) ) ) ) ) )
| ~ ( fool @ Y0 @ Y1 ) ) )
@ sK12 )
= $false ),
inference(sigma_proxy_clausification,[],[f372]) ).
thf(f374,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ reg
@ ^ [Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) ) ) ) ) ) )
| ~ ( fool @ sK12 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f373]) ).
thf(f375,plain,
( ( ^ [Y0: $i] :
( ( !! @ reg
@ ^ [Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y1 ) ) ) ) ) ) ) )
| ~ ( fool @ sK12 @ Y0 ) )
@ sK13 )
= $false ),
inference(sigma_proxy_clausification,[],[f374]) ).
thf(f376,plain,
( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) ) )
| ~ ( fool @ sK12 @ sK13 ) ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f377,plain,
( ( ~ ( fool @ sK12 @ sK13 ) )
= $false ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f379,plain,
( ( ^ [Y0: reg] :
( !! @ reg
@ ^ [Y1: reg] :
( ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y0 ) ) ) ) ) ) )
@ sK14 )
= $false ),
inference(sigma_proxy_clausification,[],[f378]) ).
thf(f380,plain,
( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ sK14 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK14 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
( ( ^ [Y0: reg] :
( ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ sK14 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ sK14 ) ) ) ) ) )
@ sK15 )
= $false ),
inference(sigma_proxy_clausification,[],[f380]) ).
thf(f382,plain,
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK14 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK15 )
=> ( c @ Y0 @ france ) ) ) )
=> ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK15 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK14 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
( $false
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK15 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK14 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f382]) ).
thf(f384,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK14 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK15 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(imp_proxy_clausification,[],[f382]) ).
thf(f385,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK15 )
=> ( c @ Y0 @ france ) ) ) ),
inference(and_proxy_clausification,[],[f384]) ).
thf(f386,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK14 )
=> ( c @ Y0 @ spain ) ) ) ),
inference(and_proxy_clausification,[],[f384]) ).
thf(f387,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK14 )
=> ( c @ Y0 @ spain ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f386]) ).
thf(f388,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ sK14 )
=> ( c @ X1 @ spain ) ) ),
inference(beta-eta_normalization,[],[f387]) ).
thf(f389,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK14 )
= $false )
| ( $true
= ( c @ X1 @ spain ) ) ),
inference(imp_proxy_clausification,[],[f388]) ).
thf(f390,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK15 )
=> ( c @ Y0 @ france ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f385]) ).
thf(f391,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK15 )
=> ( c @ X1 @ france ) )
= $true ),
inference(beta-eta_normalization,[],[f390]) ).
thf(f392,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK15 )
= $false )
| ( $true
= ( c @ X1 @ france ) ) ),
inference(imp_proxy_clausification,[],[f391]) ).
thf(f393,plain,
( $true
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK15 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK14 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f383]) ).
thf(f394,plain,
( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK15 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ sK14 ) ) ) )
@ sK16 )
= $true ),
inference(sigma_proxy_clausification,[],[f393]) ).
thf(f395,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK16 )
=> ( c @ Y0 @ sK15 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK16 )
=> ( c @ Y0 @ sK14 ) ) ) ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f396,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK16 )
=> ( c @ Y0 @ sK14 ) ) ) ),
inference(and_proxy_clausification,[],[f395]) ).
thf(f397,plain,
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK16 )
=> ( c @ Y0 @ sK15 ) ) ) ),
inference(and_proxy_clausification,[],[f395]) ).
thf(f398,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK16 )
=> ( c @ Y0 @ sK15 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f397]) ).
thf(f399,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ sK16 )
=> ( c @ X1 @ sK15 ) ) ),
inference(beta-eta_normalization,[],[f398]) ).
thf(f400,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK16 )
= $false )
| ( $true
= ( c @ X1 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f399]) ).
thf(f401,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK16 )
=> ( c @ Y0 @ sK14 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f402,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ sK16 )
=> ( c @ X1 @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f401]) ).
thf(f403,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK16 )
= $false )
| ( $true
= ( c @ X1 @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f402]) ).
thf(f404,plain,
( $true
= ( fool @ sK12 @ sK13 ) ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f466,definition,
( spl19_9
<=> ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
thf(f467,plain,
( ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false )
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f466]) ).
thf(f469,definition,
( spl19_10
<=> ! [X3: reg] :
( ( ( c @ ( sK5 @ X3 ) @ X3 )
= $true )
| ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
thf(f470,plain,
( ! [X3: reg] :
( ( ( c @ ( sK5 @ X3 ) @ X3 )
= $true )
| ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) ) )
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f469]) ).
thf(f471,plain,
( spl19_9
| spl19_10 ),
inference(avatar_split_clause,[],[f314,f469,f466]) ).
thf(f473,definition,
( spl19_11
<=> ! [X3: reg] :
( ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) )
| ( ( c @ ( sK5 @ X3 ) @ france )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
thf(f474,plain,
( ! [X3: reg] :
( ( ( c @ ( sK5 @ X3 ) @ france )
= $false )
| ( $true
= ( c @ ( sK4 @ X3 ) @ X3 ) ) )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f473]) ).
thf(f475,plain,
( spl19_9
| spl19_11 ),
inference(avatar_split_clause,[],[f313,f473,f466]) ).
thf(f477,definition,
( spl19_12
<=> ! [X3: reg] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( ( c @ ( sK5 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_12])],[avatar_definition]) ).
thf(f478,plain,
( ! [X3: reg] :
( ( ( c @ ( sK5 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK4 @ X3 ) @ spain )
= $false ) )
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f477]) ).
thf(f479,plain,
( spl19_9
| spl19_12 ),
inference(avatar_split_clause,[],[f316,f477,f466]) ).
thf(f481,definition,
( spl19_13
<=> ! [X3: reg] :
( ( ( c @ ( sK4 @ X3 ) @ spain )
= $false )
| ( ( c @ ( sK5 @ X3 ) @ france )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition]) ).
thf(f482,plain,
( ! [X3: reg] :
( ( ( c @ ( sK5 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK4 @ X3 ) @ spain )
= $false ) )
| ~ spl19_13 ),
inference(avatar_component_clause,[],[f481]) ).
thf(f483,plain,
( spl19_9
| spl19_13 ),
inference(avatar_split_clause,[],[f315,f481,f466]) ).
thf(f569,plain,
( ( $true = $false )
| ~ spl19_9 ),
inference(constrained_superposition,[],[f467,f404]) ).
thf(f573,plain,
( $false
| ~ spl19_9 ),
inference(trivial_inequality_removal,[],[f569]) ).
thf(f574,plain,
~ spl19_9,
inference(avatar_contradiction_clause,[],[f573]) ).
thf(f750,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK4 @ sK16 ) @ sK16 ) )
| ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ~ spl19_10 ),
inference(constrained_superposition,[],[f400,f470]) ).
thf(f759,plain,
( ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ( $true
= ( c @ ( sK4 @ sK16 ) @ sK16 ) )
| ~ spl19_10 ),
inference(trivial_inequality_removal,[],[f750]) ).
thf(f765,definition,
( spl19_28
<=> ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl19_28])],[avatar_definition]) ).
thf(f767,plain,
( ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f765]) ).
thf(f769,definition,
( spl19_29
<=> ( $true
= ( c @ ( sK4 @ sK16 ) @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl19_29])],[avatar_definition]) ).
thf(f771,plain,
( ( $true
= ( c @ ( sK4 @ sK16 ) @ sK16 ) )
| ~ spl19_29 ),
inference(avatar_component_clause,[],[f769]) ).
thf(f816,plain,
( spl19_29
| spl19_28
| ~ spl19_10 ),
inference(avatar_split_clause,[],[f759,f469,f765,f769]) ).
thf(f823,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK4 @ sK16 ) @ sK14 ) )
| ~ spl19_29 ),
inference(constrained_superposition,[],[f403,f771]) ).
thf(f825,plain,
( ( $true
= ( c @ ( sK4 @ sK16 ) @ sK14 ) )
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f823]) ).
thf(f838,plain,
( ( $true
= ( c @ ( sK4 @ sK16 ) @ spain ) )
| ( $true = $false )
| ~ spl19_29 ),
inference(constrained_superposition,[],[f825,f389]) ).
thf(f841,plain,
( ( $true
= ( c @ ( sK4 @ sK16 ) @ spain ) )
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f838]) ).
thf(f939,plain,
( ( $false
= ( c @ ( sK4 @ sK16 ) @ spain ) )
| ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ( $true = $false )
| ~ spl19_12 ),
inference(constrained_superposition,[],[f400,f478]) ).
thf(f950,plain,
( ( $false
= ( c @ ( sK4 @ sK16 ) @ spain ) )
| ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ~ spl19_12 ),
inference(trivial_inequality_removal,[],[f939]) ).
thf(f967,plain,
( ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ( $true = $false )
| ~ spl19_12
| ~ spl19_29 ),
inference(forward_demodulation,[],[f950,f841]) ).
thf(f968,plain,
( ( $true
= ( c @ ( sK5 @ sK16 ) @ sK15 ) )
| ~ spl19_12
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f967]) ).
thf(f980,plain,
( spl19_28
| ~ spl19_12
| ~ spl19_29 ),
inference(avatar_split_clause,[],[f968,f769,f477,f765]) ).
thf(f990,plain,
( ( ( c @ ( sK5 @ sK16 ) @ france )
= $true )
| ( $true = $false )
| ~ spl19_28 ),
inference(constrained_superposition,[],[f392,f767]) ).
thf(f991,plain,
( ( ( c @ ( sK5 @ sK16 ) @ france )
= $true )
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f990]) ).
thf(f1035,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK4 @ sK16 ) @ sK16 ) )
| ~ spl19_11
| ~ spl19_28 ),
inference(constrained_superposition,[],[f474,f991]) ).
thf(f1037,plain,
( ( $true
= ( c @ ( sK4 @ sK16 ) @ sK16 ) )
| ~ spl19_11
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f1035]) ).
thf(f1039,plain,
( spl19_29
| ~ spl19_11
| ~ spl19_28 ),
inference(avatar_split_clause,[],[f1037,f765,f473,f769]) ).
thf(f1100,plain,
( ( $false
= ( c @ ( sK4 @ sK16 ) @ spain ) )
| ( $true = $false )
| ~ spl19_13
| ~ spl19_28 ),
inference(constrained_superposition,[],[f482,f991]) ).
thf(f1113,plain,
( ( $false
= ( c @ ( sK4 @ sK16 ) @ spain ) )
| ~ spl19_13
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f1100]) ).
thf(f1119,plain,
( ( $true = $false )
| ~ spl19_13
| ~ spl19_28
| ~ spl19_29 ),
inference(forward_demodulation,[],[f1113,f841]) ).
thf(f1120,plain,
( $false
| ~ spl19_13
| ~ spl19_28
| ~ spl19_29 ),
inference(trivial_inequality_removal,[],[f1119]) ).
thf(f1121,plain,
( ~ spl19_13
| ~ spl19_28
| ~ spl19_29 ),
inference(avatar_contradiction_clause,[],[f1120]) ).
cnf(s8,plain,
( spl19_9
| spl19_10 ),
inference(sat_conversion,[],[f471]) ).
cnf(s9,plain,
( spl19_9
| spl19_11 ),
inference(sat_conversion,[],[f475]) ).
cnf(s10,plain,
( spl19_9
| spl19_12 ),
inference(sat_conversion,[],[f479]) ).
cnf(s11,plain,
( spl19_9
| spl19_13 ),
inference(sat_conversion,[],[f483]) ).
cnf(s27,plain,
~ spl19_9,
inference(sat_conversion,[],[f574]) ).
cnf(s36,plain,
( ~ spl19_10
| spl19_28
| spl19_29 ),
inference(sat_conversion,[],[f816]) ).
cnf(s47,plain,
( ~ spl19_12
| spl19_28
| ~ spl19_29 ),
inference(sat_conversion,[],[f980]) ).
cnf(s54,plain,
( ~ spl19_11
| ~ spl19_28
| spl19_29 ),
inference(sat_conversion,[],[f1039]) ).
cnf(s57,plain,
( ~ spl19_13
| ~ spl19_28
| ~ spl19_29 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s59,plain,
spl19_13,
inference(rat,[],[s11,s27]) ).
cnf(s60,plain,
spl19_12,
inference(rat,[],[s10,s27]) ).
cnf(s61,plain,
spl19_11,
inference(rat,[],[s9,s27]) ).
cnf(s62,plain,
spl19_10,
inference(rat,[],[s8,s27]) ).
cnf(s63,plain,
spl19_28,
inference(rat,[],[s36,s47,s62,s60]) ).
cnf(s64,plain,
~ spl19_29,
inference(rat,[],[s57,s59,s63]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s54,s61,s64,s63]) ).
thf(f1122,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG016^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n014.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 18:34:15 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.30 % (3042866)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (3042875)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=84148504:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (3042873)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1839890735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (3042871)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2376658270:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (3042872)lrs+10_16_si=on:nwc=1.5:random_seed=2784103846:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (3042874)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=937496214:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.30 % (3042875)Instruction limit reached!
% 0.20/0.30 % (3042875)------------------------------
% 0.20/0.30 % (3042875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042875)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042875)Termination reason: Instruction limit
% 0.20/0.30 % (3042875)Termination phase: Saturation
% 0.20/0.30 % (3042875)Time elapsed: 0.008 s
% 0.20/0.30 % (3042875)Peak memory usage: 11 MB
% 0.20/0.30 % (3042875)Instructions burned: 27 (million)
% 0.20/0.30 % (3042873)Instruction limit reached!
% 0.20/0.30 % (3042873)------------------------------
% 0.20/0.30 % (3042873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042873)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042873)Termination reason: Instruction limit
% 0.20/0.30 % (3042873)Termination phase: Property scanning
% 0.20/0.30 % (3042873)Time elapsed: 0.003 s
% 0.20/0.30 % (3042873)Peak memory usage: 10 MB
% 0.20/0.30 % (3042873)Instructions burned: 7 (million)
% 0.20/0.30 % (3042877)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (3042877)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.30 % (3042872)Instruction limit reached!
% 0.20/0.30 % (3042872)------------------------------
% 0.20/0.30 % (3042872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042872)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042872)Termination reason: Instruction limit
% 0.20/0.30 % (3042872)Termination phase: Saturation
% 0.20/0.30 % (3042872)Time elapsed: 0.009 s
% 0.20/0.30 % (3042872)Peak memory usage: 11 MB
% 0.20/0.30 % (3042872)Instructions burned: 18 (million)
% 0.20/0.30 % (3042877)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=261178235:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (3042876)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3725374102:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (3042883)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2350226266:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (3042883)Instruction limit reached!
% 0.20/0.30 % (3042883)------------------------------
% 0.20/0.30 % (3042883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042883)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042883)Termination reason: Instruction limit
% 0.20/0.30 % (3042883)Termination phase: Property scanning
% 0.20/0.30 % (3042883)Time elapsed: 0.001 s
% 0.20/0.30 % (3042883)Peak memory usage: 10 MB
% 0.20/0.30 % (3042883)Instructions burned: 4 (million)
% 0.20/0.30 % (3042884)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2925562293:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.30 % (3042885)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (3042889)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4097812674:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.30 % (3042884)Instruction limit reached!
% 0.20/0.30 % (3042884)------------------------------
% 0.20/0.30 % (3042884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042884)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042884)Termination reason: Instruction limit
% 0.20/0.30 % (3042884)Termination phase: Property scanning
% 0.20/0.30 % (3042884)Time elapsed: 0.003 s
% 0.20/0.30 % (3042884)Peak memory usage: 10 MB
% 0.20/0.30 % (3042884)Instructions burned: 6 (million)
% 0.20/0.30 % (3042885)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2586128414:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.30 % (3042889)Instruction limit reached!
% 0.20/0.30 % (3042889)------------------------------
% 0.20/0.30 % (3042889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042889)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042889)Termination reason: Instruction limit
% 0.20/0.30 % (3042889)Termination phase: Saturation
% 0.20/0.30 % (3042889)Time elapsed: 0.004 s
% 0.20/0.30 % (3042889)Peak memory usage: 11 MB
% 0.20/0.30 % (3042889)Instructions burned: 15 (million)
% 0.20/0.30 % (3042871) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3042866-3042871"...
% 0.20/0.30 % (3042885)Instruction limit reached!
% 0.20/0.30 % (3042885)------------------------------
% 0.20/0.30 % (3042885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042885)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042885)Termination reason: Instruction limit
% 0.20/0.30 % (3042885)Termination phase: Property scanning
% 0.20/0.30 % (3042885)Time elapsed: 0.003 s
% 0.20/0.30 % (3042885)Peak memory usage: 10 MB
% 0.20/0.30 % (3042885)Instructions burned: 7 (million)
% 0.20/0.30 % (3042871)...printing done.
% 0.20/0.30 % (3042871)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (3042871)------------------------------
% 0.20/0.30 % (3042871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3042871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3042871)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3042871)Termination reason: Refutation
% 0.20/0.30 % (3042871)Time elapsed: 0.037 s
% 0.20/0.30 % (3042871)Peak memory usage: 13 MB
% 0.20/0.30 % (3042871)Instructions burned: 71 (million)
% 0.20/0.30 % (3042866)Success in time 0.075 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------