%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG007^1 : 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 : n009.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 0.23s 0.34s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 29
% Syntax : Number of formulae : 247 ( 121 unt; 0 typ; 10 def)
% Number of atoms : 1772 ( 289 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3463 ( 269 ~; 245 |; 193 &;2276 @)
% ( 10 <=>; 186 =>; 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 : 92 ( 87 usr; 23 con; 0-4 aty)
% ( 212 !!; 72 ??; 0 @@+; 0 @@-)
% Number of variables : 781 ( 22 sgn 168 !; 6 ?; 781 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_56,type,
vNOT: $o > $o ).
thf(func_def_59,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_60,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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_66,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_67,type,
sK4: reg ).
thf(func_def_68,type,
sK5: reg ).
thf(func_def_69,type,
sK6: reg > reg ).
thf(func_def_70,type,
sK7: reg > reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg > reg ).
thf(func_def_73,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_75,type,
sK12: reg > reg ).
thf(func_def_76,type,
sK13: reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: reg > 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,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(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,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f36,axiom,
( eq
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f41,axiom,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ 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] :
~ ( eq @ catalunya @ paris ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
~ ( eq @ catalunya @ paris ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f53,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
~ ( eq @ catalunya @ paris ) ) ),
inference(rectify,[],[f50]) ).
thf(f54,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
~ ( eq @ catalunya @ paris ) ) )
!= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f46]) ).
thf(f56,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f58,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f60,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f70,plain,
( eq
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f71,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f72,plain,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f43]) ).
thf(f73,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f76,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f77,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f78,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f79,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
inference(rectify,[],[f33]) ).
thf(f81,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
=> ( ( c @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f80]) ).
thf(f82,plain,
( tpp
= ( ^ [X0: reg,X1: reg] :
( ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f83,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f89,plain,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
inference(rectify,[],[f37]) ).
thf(f90,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f92,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f97,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f98,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f108,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f109,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f110,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f111,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f110]) ).
thf(f128,plain,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
inference(rectify,[],[f47]) ).
thf(f129,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) )
= $true ),
inference(fool_elimination,[],[f128]) ).
thf(f130,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f131,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f132,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f133,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f132]) ).
thf(f134,plain,
( ( ^ [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
& ~ ( o @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f135,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
~ ( eq @ catalunya @ paris ) ) )
!= $true ),
inference(flattening,[],[f54]) ).
thf(f139,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f81]) ).
thf(f140,plain,
( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f73]) ).
thf(f143,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f144,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f131]) ).
thf(f148,plain,
( ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f129]) ).
thf(f149,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f133]) ).
thf(f152,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f159,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( o @ Y0 @ Y1 )
& ( c @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f160,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f163,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f164,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f165,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f166,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f168,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f169,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
~ ( eq @ catalunya @ paris ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f171,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
!= $true )
| ( ( c @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f173,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f180,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f184,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f187,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f192,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f187,f143,f166]) ).
thf(f200,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f164,f144,f144]) ).
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,[],[f173,f144,f144]) ).
thf(f203,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,[],[f159,f201]) ).
thf(f204,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f180,f144,f144]) ).
thf(f205,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f184,f204,f203,f203]) ).
thf(f206,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 )
& ( c @ Y3 @ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f160,f204,f203,f203]) ).
thf(f207,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] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ fool
@ Y0 )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f140,f163,f149,f192,f168]) ).
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,[],[f148,f163,f168,f203]) ).
thf(f209,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y1
@ Y2 )
& ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y2 ) ) ) )
@ catalunya
@ spain ) ) )
= $true ),
inference(definition_unfolding,[],[f152,f163,f168,f205]) ).
thf(f211,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 )
& ( c @ Y4 @ Y5 ) )
@ Y3
@ Y1 ) ) ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f165,f163,f168,f206]) ).
thf(f212,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
~ ( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y1
@ Y2 ) )
@ catalunya
@ paris ) ) )
!= $true ),
inference(definition_unfolding,[],[f169,f163,f168,f200]) ).
thf(f231,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f232,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ sK1 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
( ( ^ [Y0: $i] :
( ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ sK1 @ Y0 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) )
| ~ ( a @ sK1 @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
( ( ~ ( a @ sK1 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( $false
= ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f238,plain,
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) ) )
= $true ),
inference(and_proxy_clausification,[],[f238]) ).
thf(f244,plain,
! [X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ paris ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f245,plain,
! [X1: reg] :
( $true
= ( ( c @ X1 @ catalunya )
=> ( c @ X1 @ paris ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X1: reg] :
( ( ( c @ X1 @ paris )
= $true )
| ( ( c @ X1 @ catalunya )
= $false ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( a @ sK1 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f248,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( fool @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f249,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( fool @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( fool @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( Y0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( fool @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) ) ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( X2 @ Y0 )
| ~ ( fool @ X1 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( ( ( X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( fool @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ~ ( fool @ X1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f259,plain,
! [X2: $i > $o,X1: $i] :
( ( ( fool @ X1 @ ( sK3 @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f260,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ spain ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f261,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ spain ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ spain ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ spain ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
& ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ spain ) ) ) )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f268,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f266]) ).
thf(f269,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f276,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f277,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( $true
= ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) ) ) ),
inference(beta-eta_normalization,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f277]) ).
thf(f338,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(f339,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,[],[f338]) ).
thf(f340,plain,
! [X1: $i] :
( ( !! @ $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 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $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 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f342,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,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( fool @ X1 @ X2 ) ) )
| ( $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 ) ) ) ),
inference(or_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $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 ) ) ) ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f346,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 ) ) ) ) ) ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f344]) ).
thf(f347,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 )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f348,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(pi_proxy_clausification,[],[f347]) ).
thf(f349,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,[],[f348]) ).
thf(f350,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK11 @ X3 ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK11 @ X3 ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK12 @ X3 ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ( c @ ( sK12 @ X3 ) @ X3 )
=> ( c @ ( sK12 @ X3 ) @ france ) ) )
| ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( ( c @ ( sK11 @ X3 ) @ X3 )
=> ( c @ ( sK11 @ X3 ) @ spain ) ) ) ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f354,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ( c @ ( sK11 @ X3 ) @ X3 )
=> ( c @ ( sK11 @ X3 ) @ spain ) ) )
| ( ( c @ ( sK12 @ X3 ) @ france )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ( c @ ( sK11 @ X3 ) @ X3 )
=> ( c @ ( sK11 @ X3 ) @ spain ) ) )
| ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f353]) ).
thf(f356,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK11 @ X3 ) @ spain )
= $false )
| ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f358,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK12 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK11 @ X3 ) @ spain )
= $false ) ),
inference(imp_proxy_clausification,[],[f354]) ).
thf(f359,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK12 @ X3 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f354]) ).
thf(f360,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f361,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) ) )
| ~ ( a @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f368,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f366]) ).
thf(f369,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
= $true )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f368]) ).
thf(f376,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f369]) ).
thf(f377,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f376]) ).
thf(f378,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( a @ X1 @ X2 ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) ),
inference(imp_proxy_clausification,[],[f377]) ).
thf(f416,definition,
( spl16_1
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f417,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f416]) ).
thf(f429,definition,
( spl16_4
<=> ! [X3: reg] :
( ( $false
= ( c @ X3 @ catalunya ) )
| ( ( c @ X3 @ spain )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f430,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ spain )
= $true )
| ( $false
= ( c @ X3 @ catalunya ) ) )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f431,plain,
( spl16_1
| spl16_4 ),
inference(avatar_split_clause,[],[f278,f429,f416]) ).
thf(f475,definition,
( spl16_15
<=> ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f476,plain,
( ! [X3: reg] :
( ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f475]) ).
thf(f478,definition,
( spl16_16
<=> ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f479,plain,
( ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f478]) ).
thf(f480,plain,
( spl16_15
| spl16_16 ),
inference(avatar_split_clause,[],[f357,f478,f475]) ).
thf(f482,definition,
( spl16_17
<=> ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ spain )
= $false )
| ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
thf(f483,plain,
( ! [X3: reg] :
( ( ( c @ ( sK12 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK11 @ X3 ) @ spain )
= $false ) )
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f482]) ).
thf(f484,plain,
( spl16_16
| spl16_17 ),
inference(avatar_split_clause,[],[f356,f482,f478]) ).
thf(f486,definition,
( spl16_18
<=> ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK12 @ X3 ) @ france )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl16_18])],[avatar_definition]) ).
thf(f487,plain,
( ! [X3: reg] :
( ( ( c @ ( sK11 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK12 @ X3 ) @ france )
= $false ) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f486]) ).
thf(f488,plain,
( spl16_18
| spl16_16 ),
inference(avatar_split_clause,[],[f359,f478,f486]) ).
thf(f490,definition,
( spl16_19
<=> ! [X3: reg] :
( ( ( c @ ( sK12 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK11 @ X3 ) @ spain )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
thf(f491,plain,
( ! [X3: reg] :
( ( ( c @ ( sK12 @ X3 ) @ france )
= $false )
| ( ( c @ ( sK11 @ X3 ) @ spain )
= $false ) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f490]) ).
thf(f492,plain,
( spl16_19
| spl16_16 ),
inference(avatar_split_clause,[],[f358,f478,f490]) ).
thf(f509,definition,
( spl16_23
<=> ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_23])],[avatar_definition]) ).
thf(f510,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f509]) ).
thf(f511,plain,
( spl16_23
| spl16_1 ),
inference(avatar_split_clause,[],[f378,f416,f509]) ).
thf(f585,plain,
( ! [X0: reg] :
( ( $true != $true )
| ( ( c @ spain @ X0 )
= $true )
| ( ( c @ X0 @ catalunya )
= $false ) )
| ~ spl16_4 ),
inference(constrained_superposition,[],[f171,f430]) ).
thf(f586,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ catalunya )
= $false )
| ( ( c @ spain @ X0 )
= $true ) )
| ~ spl16_4 ),
inference(trivial_inequality_removal,[],[f585]) ).
thf(f594,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ france )
= $true )
| ( $true = $false )
| ( ( c @ X0 @ catalunya )
= $false ) )
| ~ spl16_23 ),
inference(constrained_superposition,[],[f246,f510]) ).
thf(f598,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ france )
= $true )
| ( ( c @ X0 @ catalunya )
= $false ) )
| ~ spl16_23 ),
inference(trivial_inequality_removal,[],[f594]) ).
thf(f616,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ catalunya )
= $false )
| ( ( c @ france @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl16_23 ),
inference(constrained_superposition,[],[f171,f598]) ).
thf(f617,plain,
( ! [X0: reg] :
( ( ( c @ france @ X0 )
= $true )
| ( ( c @ X0 @ catalunya )
= $false ) )
| ~ spl16_23 ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f725,plain,
! [X0: $i] :
( ( $true
= ( fool @ X0 @ X0 ) )
| ( $true = $false )
| ( $true
= ( fool @ X0 @ X0 ) ) ),
inference(constrained_superposition,[],[f258,f259]) ).
thf(f726,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( fool @ X0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f725]) ).
thf(f727,plain,
! [X0: $i] :
( $true
= ( fool @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f726]) ).
thf(f732,plain,
( ( $true = $false )
| ~ spl16_16 ),
inference(forward_demodulation,[],[f727,f479]) ).
thf(f733,plain,
( $false
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f732]) ).
thf(f734,plain,
~ spl16_16,
inference(avatar_contradiction_clause,[],[f733]) ).
thf(f789,definition,
( spl16_28
<=> ( ( c @ ( sK11 @ catalunya ) @ catalunya )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_28])],[avatar_definition]) ).
thf(f790,plain,
( ( ( c @ ( sK11 @ catalunya ) @ catalunya )
!= $true )
| spl16_28 ),
inference(avatar_component_clause,[],[f789]) ).
thf(f791,plain,
( ( ( c @ ( sK11 @ catalunya ) @ catalunya )
= $true )
| ~ spl16_28 ),
inference(avatar_component_clause,[],[f789]) ).
thf(f808,definition,
( spl16_32
<=> ( $true
= ( c @ france @ ( sK12 @ catalunya ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_32])],[avatar_definition]) ).
thf(f810,plain,
( ( $true
= ( c @ france @ ( sK12 @ catalunya ) ) )
| ~ spl16_32 ),
inference(avatar_component_clause,[],[f808]) ).
thf(f826,plain,
( ( ( c @ spain @ ( sK11 @ catalunya ) )
= $true )
| ( $true = $false )
| ~ spl16_4
| ~ spl16_28 ),
inference(constrained_superposition,[],[f791,f586]) ).
thf(f833,plain,
( ( ( c @ spain @ ( sK11 @ catalunya ) )
= $true )
| ~ spl16_4
| ~ spl16_28 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f840,plain,
( ( $true
= ( c @ ( sK11 @ catalunya ) @ spain ) )
| ( $true != $true )
| ~ spl16_4
| ~ spl16_28 ),
inference(constrained_superposition,[],[f171,f833]) ).
thf(f841,plain,
( ( $true
= ( c @ ( sK11 @ catalunya ) @ spain ) )
| ~ spl16_4
| ~ spl16_28 ),
inference(trivial_inequality_removal,[],[f840]) ).
thf(f899,plain,
( ( $true
= ( c @ france @ ( sK12 @ catalunya ) ) )
| ( $true = $false )
| ( ( c @ ( sK11 @ catalunya ) @ spain )
= $false )
| ~ spl16_17
| ~ spl16_23 ),
inference(constrained_superposition,[],[f483,f617]) ).
thf(f914,plain,
( ( $true
= ( c @ france @ ( sK12 @ catalunya ) ) )
| ( ( c @ ( sK11 @ catalunya ) @ spain )
= $false )
| ~ spl16_17
| ~ spl16_23 ),
inference(trivial_inequality_removal,[],[f899]) ).
thf(f928,plain,
( ( $true = $false )
| ( $true
= ( c @ france @ ( sK12 @ catalunya ) ) )
| ~ spl16_4
| ~ spl16_17
| ~ spl16_23
| ~ spl16_28 ),
inference(forward_demodulation,[],[f914,f841]) ).
thf(f929,plain,
( ( $true
= ( c @ france @ ( sK12 @ catalunya ) ) )
| ~ spl16_4
| ~ spl16_17
| ~ spl16_23
| ~ spl16_28 ),
inference(trivial_inequality_removal,[],[f928]) ).
thf(f944,plain,
( spl16_32
| ~ spl16_4
| ~ spl16_17
| ~ spl16_23
| ~ spl16_28 ),
inference(avatar_split_clause,[],[f929,f789,f509,f482,f429,f808]) ).
thf(f995,plain,
( ( $true = $false )
| ~ spl16_1 ),
inference(constrained_superposition,[],[f247,f417]) ).
thf(f1001,plain,
( $false
| ~ spl16_1 ),
inference(trivial_inequality_removal,[],[f995]) ).
thf(f1002,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f1001]) ).
thf(f1027,plain,
( ( $true
= ( c @ ( sK11 @ catalunya ) @ spain ) )
| ~ spl16_4
| ~ spl16_28 ),
inference(trivial_inequality_removal,[],[f840]) ).
thf(f1108,plain,
( ( ( c @ ( sK12 @ catalunya ) @ france )
= $true )
| ( $true != $true )
| ~ spl16_32 ),
inference(constrained_superposition,[],[f171,f810]) ).
thf(f1109,plain,
( ( ( c @ ( sK12 @ catalunya ) @ france )
= $true )
| ~ spl16_32 ),
inference(trivial_inequality_removal,[],[f1108]) ).
thf(f1331,plain,
( ! [X0: reg] :
( ( $true
= ( c @ ( sK11 @ X0 ) @ X0 ) )
| ( $true = $false )
| ( ( c @ ( sK12 @ X0 ) @ catalunya )
= $false ) )
| ~ spl16_18
| ~ spl16_23 ),
inference(constrained_superposition,[],[f598,f487]) ).
thf(f1339,plain,
( ! [X0: reg] :
( ( ( c @ ( sK12 @ X0 ) @ catalunya )
= $false )
| ( $true
= ( c @ ( sK11 @ X0 ) @ X0 ) ) )
| ~ spl16_18
| ~ spl16_23 ),
inference(trivial_inequality_removal,[],[f1331]) ).
thf(f1355,plain,
( ( ( c @ ( sK11 @ catalunya ) @ catalunya )
= $true )
| ( ( c @ ( sK11 @ catalunya ) @ catalunya )
= $true )
| ( $true = $false )
| ~ spl16_15
| ~ spl16_18
| ~ spl16_23 ),
inference(constrained_superposition,[],[f476,f1339]) ).
thf(f1368,plain,
( ( $true = $false )
| ( ( c @ ( sK11 @ catalunya ) @ catalunya )
= $true )
| ~ spl16_15
| ~ spl16_18
| ~ spl16_23 ),
inference(duplicate_literal_removal,[],[f1355]) ).
thf(f1369,plain,
( ( ( c @ ( sK11 @ catalunya ) @ catalunya )
= $true )
| ~ spl16_15
| ~ spl16_18
| ~ spl16_23 ),
inference(trivial_inequality_removal,[],[f1368]) ).
thf(f1396,plain,
( ( ( c @ ( sK11 @ catalunya ) @ spain )
= $false )
| ( $true = $false )
| ~ spl16_19
| ~ spl16_32 ),
inference(constrained_superposition,[],[f491,f1109]) ).
thf(f1411,plain,
( ( ( c @ ( sK11 @ catalunya ) @ spain )
= $false )
| ~ spl16_19
| ~ spl16_32 ),
inference(trivial_inequality_removal,[],[f1396]) ).
thf(f1422,plain,
( ( $true = $false )
| ~ spl16_4
| ~ spl16_19
| ~ spl16_28
| ~ spl16_32 ),
inference(forward_demodulation,[],[f1411,f1027]) ).
thf(f1423,plain,
( $false
| ~ spl16_4
| ~ spl16_19
| ~ spl16_28
| ~ spl16_32 ),
inference(trivial_inequality_removal,[],[f1422]) ).
thf(f1424,plain,
( ~ spl16_4
| ~ spl16_19
| ~ spl16_28
| ~ spl16_32 ),
inference(avatar_contradiction_clause,[],[f1423]) ).
thf(f1440,plain,
( $false
| ~ spl16_15
| ~ spl16_18
| ~ spl16_23
| spl16_28 ),
inference(forward_subsumption_resolution,[],[f1369,f790]) ).
thf(f1441,plain,
( ~ spl16_15
| ~ spl16_18
| ~ spl16_23
| spl16_28 ),
inference(avatar_contradiction_clause,[],[f1440]) ).
cnf(s3,plain,
( spl16_1
| spl16_4 ),
inference(sat_conversion,[],[f431]) ).
cnf(s14,plain,
( spl16_15
| spl16_16 ),
inference(sat_conversion,[],[f480]) ).
cnf(s15,plain,
( spl16_16
| spl16_17 ),
inference(sat_conversion,[],[f484]) ).
cnf(s16,plain,
( spl16_16
| spl16_18 ),
inference(sat_conversion,[],[f488]) ).
cnf(s17,plain,
( spl16_16
| spl16_19 ),
inference(sat_conversion,[],[f492]) ).
cnf(s21,plain,
( spl16_1
| spl16_23 ),
inference(sat_conversion,[],[f511]) ).
cnf(s28,plain,
~ spl16_16,
inference(sat_conversion,[],[f734]) ).
cnf(s43,plain,
( ~ spl16_4
| ~ spl16_17
| ~ spl16_23
| ~ spl16_28
| spl16_32 ),
inference(sat_conversion,[],[f944]) ).
cnf(s58,plain,
~ spl16_1,
inference(sat_conversion,[],[f1002]) ).
cnf(s70,plain,
( ~ spl16_4
| ~ spl16_19
| ~ spl16_28
| ~ spl16_32 ),
inference(sat_conversion,[],[f1424]) ).
cnf(s86,plain,
( ~ spl16_15
| ~ spl16_18
| ~ spl16_23
| spl16_28 ),
inference(sat_conversion,[],[f1441]) ).
cnf(s92,plain,
spl16_23,
inference(rat,[],[s21,s58]) ).
cnf(s96,plain,
spl16_19,
inference(rat,[],[s17,s28]) ).
cnf(s97,plain,
spl16_18,
inference(rat,[],[s16,s28]) ).
cnf(s98,plain,
spl16_17,
inference(rat,[],[s15,s28]) ).
cnf(s99,plain,
spl16_15,
inference(rat,[],[s14,s28]) ).
cnf(s100,plain,
spl16_28,
inference(rat,[],[s86,s97,s92,s99]) ).
cnf(s111,plain,
spl16_4,
inference(rat,[],[s3,s58]) ).
cnf(s112,plain,
~ spl16_32,
inference(rat,[],[s70,s100,s96,s111]) ).
cnf(s113,plain,
$false,
inference(rat,[],[s43,s100,s98,s92,s112,s111]) ).
thf(f1443,plain,
$false,
inference(avatar_sat_refutation,[],[s113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG007^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 18:34:00 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.23/0.34 % (190127)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.34 % (190147)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2974895218:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.34 % (190148)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.34 % (190148)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
% 0.23/0.34 % (190142)lrs+10_16_si=on:nwc=1.5:random_seed=3645424254:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.34 % (190144)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=331323944:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.34 % (190146)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=649622026:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.34 % (190141)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=262903036:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.34 % (190145)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=3534186123: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)
% 0.23/0.34 % (190148)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=1084070073:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.34 % (190144)Instruction limit reached!
% 0.23/0.34 % (190144)------------------------------
% 0.23/0.34 % (190144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190144)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190144)Termination reason: Instruction limit
% 0.23/0.34 % (190144)Termination phase: Property scanning
% 0.23/0.34 % (190144)Time elapsed: 0.002 s
% 0.23/0.34 % (190144)Peak memory usage: 10 MB
% 0.23/0.34 % (190144)Instructions burned: 4 (million)
% 0.23/0.34 % (190142)Instruction limit reached!
% 0.23/0.34 % (190142)------------------------------
% 0.23/0.34 % (190142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190142)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190142)Termination reason: Instruction limit
% 0.23/0.34 % (190142)Termination phase: Saturation
% 0.23/0.34 % (190142)Time elapsed: 0.009 s
% 0.23/0.34 % (190142)Peak memory usage: 11 MB
% 0.23/0.34 % (190142)Instructions burned: 19 (million)
% 0.23/0.34 % (190147)Instruction limit reached!
% 0.23/0.34 % (190147)------------------------------
% 0.23/0.34 % (190147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190147)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190147)Termination reason: Instruction limit
% 0.23/0.34 % (190147)Termination phase: Saturation
% 0.23/0.34 % (190147)Time elapsed: 0.021 s
% 0.23/0.34 % (190147)Peak memory usage: 13 MB
% 0.23/0.34 % (190147)Instructions burned: 76 (million)
% 0.23/0.34 % (190146)Instruction limit reached!
% 0.23/0.34 % (190146)------------------------------
% 0.23/0.34 % (190146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190146)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190146)Termination reason: Instruction limit
% 0.23/0.34 % (190146)Termination phase: Saturation
% 0.23/0.34 % (190146)Time elapsed: 0.013 s
% 0.23/0.34 % (190146)Peak memory usage: 11 MB
% 0.23/0.34 % (190146)Instructions burned: 24 (million)
% 0.23/0.34 % (190162)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3260576927:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.34 % (190167)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.34 % (190167)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=722186630:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.34 % (190162)Instruction limit reached!
% 0.23/0.34 % (190162)------------------------------
% 0.23/0.34 % (190162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190162)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190162)Termination reason: Instruction limit
% 0.23/0.34 % (190162)Termination phase: Property scanning
% 0.23/0.34 % (190162)Time elapsed: 0.002 s
% 0.23/0.34 % (190162)Peak memory usage: 10 MB
% 0.23/0.34 % (190162)Instructions burned: 4 (million)
% 0.23/0.34 % (190167)Instruction limit reached!
% 0.23/0.34 % (190167)------------------------------
% 0.23/0.34 % (190167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190167)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190167)Termination reason: Instruction limit
% 0.23/0.34 % (190167)Termination phase: Function definition elimination
% 0.23/0.34 % (190167)Time elapsed: 0.002 s
% 0.23/0.34 % (190167)Peak memory usage: 10 MB
% 0.23/0.34 % (190167)Instructions burned: 10 (million)
% 0.23/0.34 % (190164)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=704048076:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.34 % (190164)Instruction limit reached!
% 0.23/0.34 % (190164)------------------------------
% 0.23/0.34 % (190164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190164)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190164)Termination reason: Instruction limit
% 0.23/0.34 % (190164)Termination phase: Property scanning
% 0.23/0.34 % (190164)Time elapsed: 0.003 s
% 0.23/0.34 % (190164)Peak memory usage: 10 MB
% 0.23/0.34 % (190164)Instructions burned: 7 (million)
% 0.23/0.34 % (190168)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2292881913:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.34 % (190180)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1430710741:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.34 % (190168)Instruction limit reached!
% 0.23/0.34 % (190168)------------------------------
% 0.23/0.34 % (190168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190168)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190168)Termination reason: Instruction limit
% 0.23/0.34 % (190168)Termination phase: Property scanning
% 0.23/0.34 % (190168)Time elapsed: 0.006 s
% 0.23/0.34 % (190168)Peak memory usage: 10 MB
% 0.23/0.34 % (190168)Instructions burned: 14 (million)
% 0.23/0.34 % (190178)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
% 0.23/0.34 % (190178)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.34 % (190148) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-190127-190148"...
% 0.23/0.34 % (190141) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-190127-190141"...
% 0.23/0.34 % (190178)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3101044314:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.34 % (190186)lrs+10_1_si=on:cs=on:random_seed=2326304971:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.23/0.34 % (190148)...printing done.
% 0.23/0.34 % (190141)...printing done.
% 0.23/0.34 % (190141)Refutation found. Thanks to Tanya!
% 0.23/0.34 % SZS status Theorem for theBenchmark
% 0.23/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.34 % (190141)------------------------------
% 0.23/0.34 % (190141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (190141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (190141)CaDiCaL version: 2.1.3
% 0.23/0.34 % (190141)Termination reason: Refutation
% 0.23/0.34 % (190141)Time elapsed: 0.051 s
% 0.23/0.34 % (190141)Peak memory usage: 13 MB
% 0.23/0.34 % (190141)Instructions burned: 101 (million)
% 0.23/0.34 % (190127)Success in time 0.091 s
% 0.23/0.34 % Vampire exiting
%------------------------------------------------------------------------------