%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG005^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:25 AM UTC 2026
% Result : Theorem 0.18s 0.31s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 29
% Syntax : Number of formulae : 250 ( 127 unt; 0 typ; 10 def)
% Number of atoms : 1794 ( 283 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3606 ( 284 ~; 231 |; 203 &;2373 @)
% ( 10 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 90 usr; 26 con; 0-4 aty)
% ( 226 !!; 76 ??; 0 @@+; 0 @@-)
% Number of variables : 810 ( 22 sgn 164 !; 6 ?; 810 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_53,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vNOT: $o > $o ).
thf(func_def_58,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
vOR: $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 ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_69,type,
sK6: reg ).
thf(func_def_70,type,
sK7: reg ).
thf(func_def_71,type,
sK8: reg ).
thf(func_def_72,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_75,type,
sK12: $i > ( $i > $o ) > $i ).
thf(func_def_76,type,
sK13: reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > reg ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: reg > reg ).
thf(func_def_81,type,
sK18: reg ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f33,axiom,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).
thf(f35,axiom,
( ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) )
= p ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f38,axiom,
( po
= ( ^ [X0: reg,X1: reg] :
( ( o @ X0 @ X1 )
& ~ ( p @ X1 @ X0 )
& ~ ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',po) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f43,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_axiom_for_fool) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f47,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
~ ( po @ catalunya @ paris ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
~ ( po @ catalunya @ paris ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f58,plain,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f43]) ).
thf(f59,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f58]) ).
thf(f63,plain,
( ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) )
= p ),
inference(rectify,[],[f35]) ).
thf(f64,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f70,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f72,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f75,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f76,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f81,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f82,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f85,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f86,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f91,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f92,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f95,plain,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
inference(rectify,[],[f47]) ).
thf(f96,plain,
( $true
= ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f103,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f104,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f106,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f109,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f110,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( po
= ( ^ [X0: reg,X1: reg] :
( ( o @ X0 @ X1 )
& ~ ( p @ X1 @ X0 )
& ~ ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f112,plain,
( po
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 )
& ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f114,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f115,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f114]) ).
thf(f116,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f117,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f116]) ).
thf(f130,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
~ ( po @ catalunya @ paris ) ) ),
inference(rectify,[],[f50]) ).
thf(f131,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
~ ( po @ catalunya @ paris ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f134,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f135,plain,
! [X1: reg,X0: reg] :
( ( ( c @ X0 @ X1 )
= $true )
=> ( ( c @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f134]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
~ ( po @ catalunya @ paris ) ) ) ),
inference(flattening,[],[f131]) ).
thf(f139,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f135]) ).
thf(f140,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f145,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f146,plain,
( $true
= ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f148,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f152,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f153,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f157,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f115]) ).
thf(f158,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f170,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f171,plain,
( po
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 )
& ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f174,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
~ ( po @ catalunya @ paris ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f176,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f178,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f181,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f184,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f185,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f186,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f187,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
!= $true )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f188,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f117]) ).
thf(f192,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f158,f170,f145]) ).
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
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f178,f148,f148]) ).
thf(f202,plain,
( po
= ( ^ [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 )
& ( ^ [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 ) ) ) ),
inference(definition_unfolding,[],[f171,f148,f148,f201]) ).
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
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f181,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,[],[f186,f148,f148]) ).
thf(f205,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ 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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 ) ) )
& ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f176,f203,f203,f204]) ).
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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f188,f204,f203,f203]) ).
thf(f208,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ fool
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( c @ Y1 @ Y2 )
& ~ ( ^ [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 ) )
@ spain
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f146,f184,f185,f203]) ).
thf(f209,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 ) ) )
& ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 ) )
@ catalunya
@ spain ) ) )
= $true ),
inference(definition_unfolding,[],[f152,f184,f185,f205]) ).
thf(f210,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ fool
@ Y0 )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f153,f184,f140,f192,f185]) ).
thf(f211,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 ) ) ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f157,f184,f185,f206]) ).
thf(f212,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
~ ( ^ [Y1: reg,Y2: reg] :
( ~ ( ^ [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 )
& ( ^ [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 ) )
@ catalunya
@ paris ) ) )
!= $true ),
inference(definition_unfolding,[],[f174,f184,f185,f202]) ).
thf(f214,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( fool @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f215,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( fool @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ( Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ( Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ( X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ ( sK0 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ~ ( fool @ X1 @ ( sK0 @ X1 @ X2 ) )
| ( X2 @ ( sK0 @ X1 @ X2 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2 @ ( sK0 @ X1 @ X2 ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ~ ( fool @ X1 @ ( sK0 @ X1 @ X2 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f225,plain,
! [X2: $i > $o,X1: $i] :
( ( ( fool @ X1 @ ( sK0 @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,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 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f227,plain,
! [X1: $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 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( !! @ $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 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $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 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( ~ ( 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 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( a @ X1 @ X2 ) ) )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ X3 @ france )
= $true )
| ( $false
= ( a @ X1 @ X2 ) )
| ( $false
= ( c @ X3 @ paris ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f283,plain,
( ( !! @ $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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f284,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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK4 @ 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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
( ( ^ [Y0: $i] :
( ~ ( a @ sK4 @ 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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( ~ ( a @ sK4 @ sK5 )
| ~ ( ~ ( !! @ 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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f288,plain,
( ( ~ ( ~ ( !! @ 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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f289,plain,
( $false
= ( ~ ( a @ sK4 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f290,plain,
( ( a @ sK4 @ sK5 )
= $true ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( ~ ( !! @ 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 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f292,plain,
( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f291]) ).
thf(f306,plain,
( $true
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ catalunya ) ) ) )
@ sK8 ) ),
inference(sigma_proxy_clausification,[],[f292]) ).
thf(f307,plain,
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK8 )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK8 )
=> ( c @ Y0 @ catalunya ) ) ) ) ),
inference(beta-eta_normalization,[],[f306]) ).
thf(f308,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK8 )
=> ( c @ Y0 @ catalunya ) ) )
= $true ),
inference(and_proxy_clausification,[],[f307]) ).
thf(f309,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ sK8 )
=> ( c @ Y0 @ paris ) ) )
= $true ),
inference(and_proxy_clausification,[],[f307]) ).
thf(f310,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ sK8 )
=> ( c @ Y0 @ paris ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK8 )
=> ( c @ X1 @ paris ) )
= $true ),
inference(beta-eta_normalization,[],[f310]) ).
thf(f312,plain,
! [X1: reg] :
( ( $false
= ( c @ X1 @ sK8 ) )
| ( ( c @ X1 @ paris )
= $true ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ sK8 )
=> ( c @ Y0 @ catalunya ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f314,plain,
! [X1: reg] :
( ( ( c @ X1 @ sK8 )
=> ( c @ X1 @ catalunya ) )
= $true ),
inference(beta-eta_normalization,[],[f313]) ).
thf(f315,plain,
! [X1: reg] :
( ( $false
= ( c @ X1 @ sK8 ) )
| ( ( c @ X1 @ catalunya )
= $true ) ),
inference(imp_proxy_clausification,[],[f314]) ).
thf(f341,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ Y0 @ Y1 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f342,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ Y0 @ Y1 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( ( c @ spain @ france )
& ~ ( ?? @ 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,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( fool @ X1 @ X2 )
| ( ( c @ spain @ france )
& ~ ( ?? @ 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,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X1: $i] :
( ( ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( fool @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( fool @ X1 @ X2 ) ) )
| ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f346]) ).
thf(f350,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 ) ) ) ) ) )
= $true )
| ( $false
= ( fool @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f347]) ).
thf(f351,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) ) )
@ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f354,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK10 @ X3 ) ) )
| ( $false
= ( fool @ X1 @ X2 ) )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK10 @ X3 ) ) )
| ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK11 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ( c @ ( sK10 @ X3 ) @ X3 )
=> ( c @ ( sK10 @ X3 ) @ spain ) ) )
| ( $false
= ( ( c @ ( sK11 @ X3 ) @ X3 )
=> ( c @ ( sK11 @ X3 ) @ france ) ) )
| ( $false
= ( fool @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ( c @ ( sK11 @ X3 ) @ X3 )
=> ( c @ ( sK11 @ X3 ) @ france ) ) )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) )
| ( $false
= ( fool @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true )
| ( $false
= ( ( c @ ( sK11 @ X3 ) @ X3 )
=> ( c @ ( sK11 @ X3 ) @ france ) ) )
| ( $false
= ( fool @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f357]) ).
thf(f360,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true )
| ( $false
= ( fool @ X1 @ X2 ) )
| ( $false
= ( c @ ( sK11 @ X3 ) @ france ) ) ),
inference(imp_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true )
| ( $false
= ( fool @ X1 @ X2 ) )
| ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f359]) ).
thf(f362,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( $false
= ( c @ ( sK11 @ X3 ) @ france ) )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f358]) ).
thf(f363,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( fool @ X1 @ X2 ) )
| ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f358]) ).
thf(f381,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f382,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f381]) ).
thf(f383,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X1: $i] :
( ( ~ ( a @ X1 @ X2 )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X1: $i] :
( ( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) ) )
= $true )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f385]) ).
thf(f387,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,[],[f386]) ).
thf(f425,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f387]) ).
thf(f426,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ~ ( a @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f425]) ).
thf(f427,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,[],[f426]) ).
thf(f428,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) )
= $true ) ),
inference(beta-eta_normalization,[],[f427]) ).
thf(f429,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f428]) ).
thf(f437,definition,
( spl19_1
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
thf(f438,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f437]) ).
thf(f440,definition,
( spl19_2
<=> ! [X3: reg] :
( ( ( c @ X3 @ france )
= $true )
| ( $false
= ( c @ X3 @ paris ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
thf(f441,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ paris ) )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f440]) ).
thf(f442,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f239,f440,f437]) ).
thf(f470,definition,
( spl19_9
<=> ! [X2: $i,X1: $i] :
( $false
= ( fool @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
thf(f471,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( fool @ X1 @ X2 ) )
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f470]) ).
thf(f478,definition,
( spl19_11
<=> ! [X3: reg] :
( ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
thf(f479,plain,
( ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true ) )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f478]) ).
thf(f480,plain,
( spl19_11
| spl19_9 ),
inference(avatar_split_clause,[],[f361,f470,f478]) ).
thf(f482,definition,
( spl19_12
<=> ! [X3: reg] :
( ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true )
| ( $false
= ( c @ ( sK11 @ X3 ) @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_12])],[avatar_definition]) ).
thf(f483,plain,
( ! [X3: reg] :
( ( ( c @ ( sK10 @ X3 ) @ X3 )
= $true )
| ( $false
= ( c @ ( sK11 @ X3 ) @ france ) ) )
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f482]) ).
thf(f484,plain,
( spl19_9
| spl19_12 ),
inference(avatar_split_clause,[],[f360,f482,f470]) ).
thf(f486,definition,
( spl19_13
<=> ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition]) ).
thf(f487,plain,
( ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) ) )
| ~ spl19_13 ),
inference(avatar_component_clause,[],[f486]) ).
thf(f488,plain,
( spl19_9
| spl19_13 ),
inference(avatar_split_clause,[],[f363,f486,f470]) ).
thf(f490,definition,
( spl19_14
<=> ! [X3: reg] :
( ( $false
= ( c @ ( sK11 @ X3 ) @ france ) )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_14])],[avatar_definition]) ).
thf(f491,plain,
( ! [X3: reg] :
( ( $false
= ( c @ ( sK11 @ X3 ) @ france ) )
| ( $false
= ( c @ ( sK10 @ X3 ) @ spain ) ) )
| ~ spl19_14 ),
inference(avatar_component_clause,[],[f490]) ).
thf(f492,plain,
( spl19_9
| spl19_14 ),
inference(avatar_split_clause,[],[f362,f490,f470]) ).
thf(f536,definition,
( spl19_25
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_25])],[avatar_definition]) ).
thf(f537,plain,
( ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true ) )
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f536]) ).
thf(f538,plain,
( spl19_1
| spl19_25 ),
inference(avatar_split_clause,[],[f429,f536,f437]) ).
thf(f725,plain,
( ( $false = $true )
| ~ spl19_1 ),
inference(constrained_superposition,[],[f438,f290]) ).
thf(f729,plain,
( $false
| ~ spl19_1 ),
inference(trivial_inequality_removal,[],[f725]) ).
thf(f730,plain,
~ spl19_1,
inference(avatar_contradiction_clause,[],[f729]) ).
thf(f817,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( fool @ X0 @ X0 )
= $true )
| ( ( fool @ X0 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f225,f223]) ).
thf(f820,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( fool @ X0 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f817]) ).
thf(f821,plain,
! [X0: $i] :
( ( fool @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f820]) ).
thf(f826,plain,
( ( $false = $true )
| ~ spl19_9 ),
inference(forward_demodulation,[],[f821,f471]) ).
thf(f827,plain,
( $false
| ~ spl19_9 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f828,plain,
~ spl19_9,
inference(avatar_contradiction_clause,[],[f827]) ).
thf(f832,plain,
( ( $false = $true )
| ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ( ( c @ ( sK10 @ sK8 ) @ sK8 )
= $true )
| ~ spl19_11 ),
inference(constrained_superposition,[],[f479,f312]) ).
thf(f844,plain,
( ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ( ( c @ ( sK10 @ sK8 ) @ sK8 )
= $true )
| ~ spl19_11 ),
inference(trivial_inequality_removal,[],[f832]) ).
thf(f848,definition,
( spl19_28
<=> ( ( c @ ( sK10 @ sK8 ) @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_28])],[avatar_definition]) ).
thf(f850,plain,
( ( ( c @ ( sK10 @ sK8 ) @ sK8 )
= $true )
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f848]) ).
thf(f868,definition,
( spl19_32
<=> ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl19_32])],[avatar_definition]) ).
thf(f870,plain,
( ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ~ spl19_32 ),
inference(avatar_component_clause,[],[f868]) ).
thf(f872,plain,
( spl19_28
| spl19_32
| ~ spl19_11 ),
inference(avatar_split_clause,[],[f844,f478,f868,f848]) ).
thf(f891,plain,
( ( ( c @ ( sK11 @ sK8 ) @ france )
= $true )
| ( $false = $true )
| ~ spl19_2
| ~ spl19_32 ),
inference(constrained_superposition,[],[f441,f870]) ).
thf(f892,plain,
( ( ( c @ ( sK11 @ sK8 ) @ france )
= $true )
| ~ spl19_2
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f891]) ).
thf(f899,plain,
( ( $true != $true )
| ( $true
= ( c @ france @ ( sK11 @ sK8 ) ) )
| ~ spl19_2
| ~ spl19_32 ),
inference(constrained_superposition,[],[f187,f892]) ).
thf(f900,plain,
( ( $true
= ( c @ france @ ( sK11 @ sK8 ) ) )
| ~ spl19_2
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f899]) ).
thf(f905,plain,
( ( ( c @ ( sK11 @ sK8 ) @ france )
= $true )
| ( $true != $true )
| ~ spl19_2
| ~ spl19_32 ),
inference(constrained_superposition,[],[f187,f900]) ).
thf(f916,plain,
( ( ( c @ ( sK10 @ sK8 ) @ sK8 )
= $true )
| ( $false = $true )
| ~ spl19_2
| ~ spl19_12
| ~ spl19_32 ),
inference(constrained_superposition,[],[f483,f892]) ).
thf(f926,plain,
( ( ( c @ ( sK10 @ sK8 ) @ sK8 )
= $true )
| ~ spl19_2
| ~ spl19_12
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f916]) ).
thf(f933,plain,
( spl19_28
| ~ spl19_2
| ~ spl19_12
| ~ spl19_32 ),
inference(avatar_split_clause,[],[f926,f868,f482,f440,f848]) ).
thf(f937,plain,
( ( ( c @ ( sK10 @ sK8 ) @ catalunya )
= $true )
| ( $false = $true )
| ~ spl19_28 ),
inference(constrained_superposition,[],[f315,f850]) ).
thf(f942,plain,
( ( ( c @ ( sK10 @ sK8 ) @ catalunya )
= $true )
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f937]) ).
thf(f954,plain,
( ( ( c @ ( sK10 @ sK8 ) @ spain )
= $true )
| ( $false = $true )
| ~ spl19_25
| ~ spl19_28 ),
inference(constrained_superposition,[],[f537,f942]) ).
thf(f956,plain,
( ( ( c @ ( sK10 @ sK8 ) @ spain )
= $true )
| ~ spl19_25
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f954]) ).
thf(f1020,plain,
( ( $false
= ( c @ ( sK10 @ sK8 ) @ spain ) )
| ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ( $false = $true )
| ~ spl19_13 ),
inference(constrained_superposition,[],[f487,f312]) ).
thf(f1032,plain,
( ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ( $false
= ( c @ ( sK10 @ sK8 ) @ spain ) )
| ~ spl19_13 ),
inference(trivial_inequality_removal,[],[f1020]) ).
thf(f1039,plain,
( ( $false = $true )
| ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ~ spl19_13
| ~ spl19_25
| ~ spl19_28 ),
inference(forward_demodulation,[],[f1032,f956]) ).
thf(f1040,plain,
( ( ( c @ ( sK11 @ sK8 ) @ paris )
= $true )
| ~ spl19_13
| ~ spl19_25
| ~ spl19_28 ),
inference(trivial_inequality_removal,[],[f1039]) ).
thf(f1043,plain,
( spl19_32
| ~ spl19_13
| ~ spl19_25
| ~ spl19_28 ),
inference(avatar_split_clause,[],[f1040,f848,f536,f486,f868]) ).
thf(f1044,plain,
( ( ( c @ ( sK11 @ sK8 ) @ france )
= $true )
| ~ spl19_2
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f905]) ).
thf(f1074,plain,
( ( $false
= ( c @ ( sK10 @ sK8 ) @ spain ) )
| ( $false = $true )
| ~ spl19_2
| ~ spl19_14
| ~ spl19_32 ),
inference(constrained_superposition,[],[f1044,f491]) ).
thf(f1083,plain,
( ( $false
= ( c @ ( sK10 @ sK8 ) @ spain ) )
| ~ spl19_2
| ~ spl19_14
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f1074]) ).
thf(f1088,plain,
( ( $false = $true )
| ~ spl19_2
| ~ spl19_14
| ~ spl19_25
| ~ spl19_28
| ~ spl19_32 ),
inference(forward_demodulation,[],[f1083,f956]) ).
thf(f1089,plain,
( $false
| ~ spl19_2
| ~ spl19_14
| ~ spl19_25
| ~ spl19_28
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f1088]) ).
thf(f1090,plain,
( ~ spl19_2
| ~ spl19_14
| ~ spl19_25
| ~ spl19_28
| ~ spl19_32 ),
inference(avatar_contradiction_clause,[],[f1089]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f442]) ).
cnf(s9,plain,
( spl19_9
| spl19_11 ),
inference(sat_conversion,[],[f480]) ).
cnf(s10,plain,
( spl19_9
| spl19_12 ),
inference(sat_conversion,[],[f484]) ).
cnf(s11,plain,
( spl19_9
| spl19_13 ),
inference(sat_conversion,[],[f488]) ).
cnf(s12,plain,
( spl19_9
| spl19_14 ),
inference(sat_conversion,[],[f492]) ).
cnf(s23,plain,
( spl19_1
| spl19_25 ),
inference(sat_conversion,[],[f538]) ).
cnf(s29,plain,
~ spl19_1,
inference(sat_conversion,[],[f730]) ).
cnf(s30,plain,
~ spl19_9,
inference(sat_conversion,[],[f828]) ).
cnf(s36,plain,
( ~ spl19_11
| spl19_28
| spl19_32 ),
inference(sat_conversion,[],[f872]) ).
cnf(s41,plain,
( ~ spl19_2
| ~ spl19_12
| spl19_28
| ~ spl19_32 ),
inference(sat_conversion,[],[f933]) ).
cnf(s43,plain,
( ~ spl19_13
| ~ spl19_25
| ~ spl19_28
| spl19_32 ),
inference(sat_conversion,[],[f1043]) ).
cnf(s46,plain,
( ~ spl19_2
| ~ spl19_14
| ~ spl19_25
| ~ spl19_28
| ~ spl19_32 ),
inference(sat_conversion,[],[f1090]) ).
cnf(s49,plain,
spl19_25,
inference(rat,[],[s23,s29]) ).
cnf(s60,plain,
spl19_14,
inference(rat,[],[s12,s30]) ).
cnf(s61,plain,
spl19_13,
inference(rat,[],[s11,s30]) ).
cnf(s62,plain,
spl19_12,
inference(rat,[],[s10,s30]) ).
cnf(s63,plain,
spl19_11,
inference(rat,[],[s9,s30]) ).
cnf(s71,plain,
spl19_2,
inference(rat,[],[s1,s29]) ).
cnf(s72,plain,
spl19_28,
inference(rat,[],[s41,s36,s62,s71,s63]) ).
cnf(s73,plain,
spl19_32,
inference(rat,[],[s43,s61,s49,s72]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s46,s71,s60,s49,s73,s72]) ).
thf(f1091,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG005^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n002.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 18:36:38 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.06/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.31 % (1681663)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.31 % (1681677)lrs+10_16_si=on:nwc=1.5:random_seed=604933341:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.31 % (1681682)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.31 % (1681682)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
% 0.18/0.31 % (1681677)Instruction limit reached!
% 0.18/0.31 % (1681677)------------------------------
% 0.18/0.31 % (1681677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681677)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681677)Termination reason: Instruction limit
% 0.18/0.31 % (1681677)Termination phase: Saturation
% 0.18/0.31 % (1681677)Time elapsed: 0.005 s
% 0.18/0.31 % (1681677)Peak memory usage: 11 MB
% 0.18/0.31 % (1681677)Instructions burned: 21 (million)
% 0.18/0.31 % (1681676)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1492526774:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.31 % (1681680)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=411303496:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.31 % (1681678)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=73479598:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.31 % (1681679)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=1113595245: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)
% 0.18/0.31 % (1681681)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2647924294:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.31 % (1681682)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=1905013700:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.31 % (1681678)Instruction limit reached!
% 0.18/0.31 % (1681678)------------------------------
% 0.18/0.31 % (1681678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681678)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681678)Termination reason: Instruction limit
% 0.18/0.31 % (1681678)Termination phase: Property scanning
% 0.18/0.31 % (1681678)Time elapsed: 0.002 s
% 0.18/0.31 % (1681678)Peak memory usage: 10 MB
% 0.18/0.31 % (1681678)Instructions burned: 4 (million)
% 0.18/0.31 % (1681690)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3694173115:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.18/0.31 % (1681690)Instruction limit reached!
% 0.18/0.31 % (1681690)------------------------------
% 0.18/0.31 % (1681690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681690)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681690)Termination reason: Instruction limit
% 0.18/0.31 % (1681690)Termination phase: Property scanning
% 0.18/0.31 % (1681690)Time elapsed: 0.001 s
% 0.18/0.31 % (1681690)Peak memory usage: 10 MB
% 0.18/0.31 % (1681690)Instructions burned: 4 (million)
% 0.18/0.31 % (1681680)Instruction limit reached!
% 0.18/0.31 % (1681680)------------------------------
% 0.18/0.31 % (1681680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681680)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681680)Termination reason: Instruction limit
% 0.18/0.31 % (1681680)Termination phase: Saturation
% 0.18/0.31 % (1681680)Time elapsed: 0.014 s
% 0.18/0.31 % (1681680)Peak memory usage: 11 MB
% 0.18/0.31 % (1681680)Instructions burned: 25 (million)
% 0.18/0.31 % (1681704)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.18/0.31 % (1681704)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1690096195:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.18/0.31 % (1681699)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1352532202:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.18/0.31 % (1681704)Instruction limit reached!
% 0.18/0.31 % (1681704)------------------------------
% 0.18/0.31 % (1681704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681704)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681704)Termination reason: Instruction limit
% 0.18/0.31 % (1681704)Termination phase: Function definition elimination
% 0.18/0.31 % (1681704)Time elapsed: 0.002 s
% 0.18/0.31 % (1681704)Peak memory usage: 10 MB
% 0.18/0.31 % (1681704)Instructions burned: 9 (million)
% 0.18/0.31 % (1681699)Instruction limit reached!
% 0.18/0.31 % (1681699)------------------------------
% 0.18/0.31 % (1681699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681699)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681699)Termination reason: Instruction limit
% 0.18/0.31 % (1681699)Termination phase: Property scanning
% 0.18/0.31 % (1681699)Time elapsed: 0.003 s
% 0.18/0.31 % (1681699)Peak memory usage: 10 MB
% 0.18/0.31 % (1681699)Instructions burned: 6 (million)
% 0.18/0.31 % (1681676) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1681663-1681676"...
% 0.18/0.31 % (1681715)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
% 0.18/0.31 % (1681715)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.18/0.31 % (1681707)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3371882811:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.18/0.31 % (1681715)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1677786710:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.18/0.31 % (1681707)Instruction limit reached!
% 0.18/0.31 % (1681707)------------------------------
% 0.18/0.31 % (1681707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681707)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681707)Termination reason: Instruction limit
% 0.18/0.31 % (1681707)Termination phase: Property scanning
% 0.18/0.31 % (1681707)Time elapsed: 0.006 s
% 0.18/0.31 % (1681707)Peak memory usage: 10 MB
% 0.18/0.31 % (1681707)Instructions burned: 14 (million)
% 0.18/0.31 % (1681681)Instruction limit reached!
% 0.18/0.31 % (1681681)------------------------------
% 0.18/0.31 % (1681681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681681)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681681)Termination reason: Instruction limit
% 0.18/0.31 % (1681681)Termination phase: Saturation
% 0.18/0.31 % (1681681)Time elapsed: 0.039 s
% 0.18/0.31 % (1681681)Peak memory usage: 12 MB
% 0.18/0.31 % (1681681)Instructions burned: 76 (million)
% 0.18/0.31 % (1681676)...printing done.
% 0.18/0.31 % (1681715)Instruction limit reached!
% 0.18/0.31 % (1681715)------------------------------
% 0.18/0.31 % (1681715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.31 % (1681715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.31 % (1681715)CaDiCaL version: 2.1.3
% 0.18/0.31 % (1681715)Termination reason: Instruction limit
% 0.18/0.31 % (1681715)Termination phase: Saturation
% 0.18/0.31 % (1681715)Time elapsed: 0.007 s
% 0.18/0.31 % (1681715)Peak memory usage: 11 MB
% 0.18/0.31 % (1681715)Instructions burned: 30 (million)
% 0.18/0.31 % (1681676)Refutation found. Thanks to Tanya!
% 0.18/0.31 % SZS status Theorem for theBenchmark
% 0.18/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.32 % (1681676)------------------------------
% 0.18/0.32 % (1681676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.32 % (1681676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.32 % (1681676)CaDiCaL version: 2.1.3
% 0.18/0.32 % (1681676)Termination reason: Refutation
% 0.18/0.32 % (1681676)Time elapsed: 0.041 s
% 0.18/0.32 % (1681676)Peak memory usage: 13 MB
% 0.18/0.32 % (1681676)Instructions burned: 78 (million)
% 0.18/0.32 % (1681663)Success in time 0.087 s
% 0.18/0.32 % Vampire exiting
%------------------------------------------------------------------------------