%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG003^1 : 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 : n018.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 07:49:24 AM UTC 2026
% Result : Theorem 6.00s 1.18s
% Output : Refutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 45
% Syntax : Number of formulae : 432 ( 127 unt; 0 typ; 26 def)
% Number of atoms : 4255 ( 896 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 6860 ( 655 ~;1121 |; 235 &;4207 @)
% ( 26 <=>; 255 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 106 ( 101 usr; 39 con; 0-4 aty)
% ( 268 !!; 93 ??; 0 @@+; 0 @@-)
% Number of variables : 1154 ( 23 sgn 451 !; 6 ?;1154 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_52,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
vIMP: $o > $o > $o ).
thf(func_def_54,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vNOT: $o > $o ).
thf(func_def_58,type,
vAND: $o > $o > $o ).
thf(func_def_59,type,
db3:
!>[X0: $tType] : X0 ).
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: reg ).
thf(func_def_64,type,
sK1: reg > reg ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_67,type,
sK4: reg > reg ).
thf(func_def_68,type,
sK5: 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(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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,
( ( ^ [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,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f33,axiom,
! [X1: reg,X0: reg] :
( ( c @ X0 @ X1 )
=> ( c @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_symmetric) ).
thf(f34,axiom,
( dc
= ( ^ [X0: reg,X1: reg] :
~ ( c @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',dc) ).
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(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ 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,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= tpp ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',tpp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) )
= ntpp ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f43,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ ( mbox @ a @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).
thf(f44,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f45,axiom,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f46,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f47,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( dc @ spain @ paris )
& ( dc @ catalunya @ paris ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f48,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( dc @ spain @ paris )
& ( dc @ catalunya @ paris ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
thf(f53,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f46]) ).
thf(f54,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( dc
= ( ^ [X0: reg,X1: reg] :
~ ( c @ X0 @ X1 ) ) ),
inference(rectify,[],[f34]) ).
thf(f56,plain,
( dc
= ( ^ [Y0: reg,Y1: reg] :
~ ( c @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f61,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f62,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f67,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f68,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f74,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( tpp @ catalunya @ spain ) ) ),
inference(rectify,[],[f44]) ).
thf(f75,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f78,plain,
( mvalid
@ ( mbox @ fool
@ ^ [X0: $i] : ( ec @ spain @ france ) ) ),
inference(rectify,[],[f45]) ).
thf(f79,plain,
( $true
= ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f82,plain,
( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] : ( mimplies @ ( mbox @ fool @ X0 ) @ ( mbox @ a @ X0 ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f83,plain,
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ ( mbox @ a @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f84,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f85,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f86,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) ) ) )
= tpp ),
inference(rectify,[],[f41]) ).
thf(f87,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f91,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f92,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f99,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ~ ( p @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f100,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f102,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f101]) ).
thf(f103,plain,
( ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f104,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f109,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f110,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) )
= mforall_prop ),
inference(rectify,[],[f11]) ).
thf(f112,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f113,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f121,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f122,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f126,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
( ( dc @ spain @ paris )
& ( dc @ catalunya @ paris ) ) ) ),
inference(rectify,[],[f48]) ).
thf(f127,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ) ),
inference(fool_elimination,[],[f126]) ).
thf(f129,plain,
! [X0: reg,X1: reg] :
( ( c @ X1 @ X0 )
=> ( c @ X0 @ X1 ) ),
inference(rectify,[],[f33]) ).
thf(f130,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
= $true )
=> ( ( c @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f129]) ).
thf(f132,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ) ),
inference(flattening,[],[f127]) ).
thf(f133,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f130]) ).
thf(f134,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f135,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f136,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f138,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f139,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f141,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( tpp @ catalunya @ spain ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f142,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f144,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f145,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f146,plain,
( tpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f147,plain,
( dc
= ( ^ [Y0: reg,Y1: reg] :
~ ( c @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f148,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f151,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f152,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f153,plain,
( $true
= ( mvalid
@ ( mbox @ fool
@ ^ [Y0: $i] : ( ec @ spain @ france ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f154,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f157,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
!= $true )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f133]) ).
thf(f158,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ) ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f159,plain,
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ fool @ Y0 ) @ ( mbox @ a @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f162,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f144,f134,f134]) ).
thf(f164,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f138,f162]) ).
thf(f165,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,[],[f139,f134,f134]) ).
thf(f167,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,[],[f145,f142,f136]) ).
thf(f170,plain,
( ntpp
= ( ^ [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
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) )
& ( ^ [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 ) ) ) ),
inference(definition_unfolding,[],[f135,f164,f164,f165]) ).
thf(f171,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
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ 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
@ Y5 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 ) ) )
& ( ^ [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 ) ) ) ),
inference(definition_unfolding,[],[f146,f164,f164,f165]) ).
thf(f173,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ 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
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 ) ) )
& ( ^ [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 ) )
@ catalunya
@ spain ) ) ) ),
inference(definition_unfolding,[],[f141,f154,f151,f171]) ).
thf(f174,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
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) )
& ( ^ [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 ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f148,f154,f151,f170]) ).
thf(f175,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
@ Y3 )
& ( ^ [Y6: reg,Y7: reg] :
( !! @ reg
@ ^ [Y8: reg] :
( ( c @ Y8 @ Y6 )
=> ( c @ Y8 @ Y7 ) ) )
@ Y5
@ Y4 ) ) )
@ Y1
@ Y2 ) )
@ spain
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f153,f154,f151,f164]) ).
thf(f176,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ( ^ [Y1: reg,Y2: reg] :
~ ( c @ Y1 @ Y2 )
@ catalunya
@ paris )
& ( ^ [Y1: reg,Y2: reg] :
~ ( c @ Y1 @ Y2 )
@ spain
@ paris ) ) ) ) ),
inference(definition_unfolding,[],[f158,f154,f151,f147,f147]) ).
thf(f177,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] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ fool
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ a
@ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f159,f154,f152,f167,f151,f151]) ).
thf(f178,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 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f179,plain,
! [X1: $i] :
( $true
= ( ^ [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 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ spain ) ) ) ) )
& ( c @ Y2 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ spain )
=> ( c @ Y2 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ catalunya )
=> ( c @ Y2 @ spain ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,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 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,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 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) ) ) )
& ( c @ Y1 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ spain )
=> ( c @ Y1 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ catalunya )
=> ( c @ Y1 @ spain ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,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 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( a @ X1 @ X2 ) ) )
| ( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) ) ) )
& ( c @ Y0 @ catalunya )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ catalunya ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ spain )
=> ( c @ Y0 @ catalunya ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f184]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) ) ) ) ),
inference(and_proxy_clausification,[],[f185]) ).
thf(f228,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ catalunya )
=> ( c @ Y0 @ spain ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f229,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ( c @ X3 @ catalunya )
=> ( c @ X3 @ spain ) )
= $true ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( c @ X3 @ spain ) )
| ( ( c @ X3 @ catalunya )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f232,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ) )
@ sK6 ) ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK6 @ Y0 )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
( ( ^ [Y0: $i] :
( ~ ( a @ sK6 @ Y0 )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) )
@ sK7 )
= $false ),
inference(sigma_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( $false
= ( ~ ( a @ sK6 @ sK7 )
| ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
( $false
= ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( ~ ( a @ sK6 @ sK7 ) )
= $false ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f238,plain,
( ( a @ sK6 @ sK7 )
= $true ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( ( ~ ( c @ catalunya @ paris ) )
= $false )
| ( ( ~ ( c @ spain @ paris ) )
= $false ) ),
inference(and_proxy_clausification,[],[f236]) ).
thf(f240,plain,
( ( $true
= ( c @ catalunya @ paris ) )
| ( ( ~ ( c @ spain @ paris ) )
= $false ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( $true
= ( c @ catalunya @ paris ) )
| ( $true
= ( c @ spain @ paris ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ Y0 @ Y1 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f243,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 @ spain ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ spain ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( fool @ X1 @ X2 )
| ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( fool @ X1 @ X2 ) )
= $true )
| ( $true
= ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( c @ spain @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( ( ( c @ spain @ france )
= $true )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f248]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f252,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ spain ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) ) ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK8 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ spain ) )
@ ( sK9 @ X3 ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X3 )
=> ( c @ Y0 @ france ) )
@ ( sK8 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ ( sK9 @ X3 ) @ X3 )
=> ( c @ ( sK9 @ X3 ) @ spain ) )
= $false )
| ( ( ( c @ ( sK8 @ X3 ) @ X3 )
=> ( c @ ( sK8 @ X3 ) @ france ) )
= $false )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) )
| ( ( ( c @ ( sK8 @ X3 ) @ X3 )
=> ( c @ ( sK8 @ X3 ) @ france ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true )
| ( ( fool @ X1 @ X2 )
= $false )
| ( ( ( c @ ( sK8 @ X3 ) @ X3 )
=> ( c @ ( sK8 @ X3 ) @ france ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f260,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true )
| ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( c @ ( sK8 @ X3 ) @ france ) ) ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true )
| ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f262,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( fool @ X1 @ X2 )
= $false )
| ( $false
= ( c @ ( sK8 @ X3 ) @ france ) )
| ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) ) ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f263,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) )
| ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) )
| ( ( fool @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f264,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( fool @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f265,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( a @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( fool @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( fool @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f269,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( fool @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ ( sK10 @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X3 )
| ( X2 @ X3 ) )
= $true )
| ( ( ~ ( fool @ X1 @ ( sK10 @ X1 @ X2 ) )
| ( X2 @ ( sK10 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( ~ ( fool @ X1 @ ( sK10 @ X1 @ X2 ) )
| ( X2 @ ( sK10 @ X1 @ X2 ) ) )
= $false )
| ( ( ~ ( a @ X1 @ X3 ) )
= $true )
| ( ( X2 @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f273]) ).
thf(f276,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $false
= ( ~ ( fool @ X1 @ ( sK10 @ X1 @ X2 ) ) ) )
| ( ( ~ ( a @ X1 @ X3 ) )
= $true )
| ( ( X2 @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f277,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( fool @ X1 @ ( sK10 @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X3 )
= $true )
| ( ( ~ ( a @ X1 @ X3 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( fool @ X1 @ ( sK10 @ X1 @ X2 ) )
= $true )
| ( ( X2 @ X3 )
= $true )
| ( ( a @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f280,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f281,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( ( ~ ( a @ X1 @ X2 )
| ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( a @ X1 @ X2 ) ) )
| ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f286]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) ) )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) ) ) ) )
@ X3 )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ paris )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) )
& ( c @ X3 @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ paris )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) )
= $false )
| ( ( ( c @ X3 @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false )
| ( ( ( c @ X3 @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ france )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) )
= $false )
| ( $true
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ ( sK11 @ X3 ) ) )
| ( $false
= ( c @ X3 @ france ) ) ),
inference(sigma_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ paris ) ) ) )
@ ( sK12 @ X3 ) )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( $true
= ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) ) )
@ ( sK11 @ X3 ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) ) ) )
= $true )
| ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) ) )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(and_proxy_clausification,[],[f299]) ).
thf(f302,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) ) ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) ) ),
inference(and_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( $false
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f301]) ).
thf(f304,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) )
@ X4 )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) )
@ X5 )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) )
@ X4 )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( ( c @ X4 @ ( sK12 @ X3 ) )
=> ( c @ X4 @ X3 ) )
= $true )
| ( ( ( c @ X5 @ ( sK11 @ X3 ) )
=> ( c @ X5 @ X3 ) )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( $false
= ( c @ X3 @ france ) )
| ( ( ( c @ X5 @ ( sK11 @ X3 ) )
=> ( c @ X5 @ X3 ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X4 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X4 @ X3 )
= $true )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X5 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg] :
( ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) )
@ X4 ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f302]) ).
thf(f310,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( $false
= ( c @ X3 @ france ) )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ X3 ) )
@ X5 ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( $true
= ( ( c @ X5 @ ( sK12 @ X3 ) )
=> ( c @ X5 @ X3 ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( ( c @ X4 @ ( sK11 @ X3 ) )
=> ( c @ X4 @ france ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) ) ),
inference(beta-eta_normalization,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X5 @ ( sK12 @ X3 ) )
= $false )
| ( ( ( c @ X4 @ ( sK11 @ X3 ) )
=> ( c @ X4 @ france ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X4 @ france )
= $true )
| ( ( c @ X4 @ ( sK11 @ X3 ) )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X5 @ ( sK12 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) ) )
= $true )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) ) ) )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(and_proxy_clausification,[],[f300]) ).
thf(f315,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) ) )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f300]) ).
thf(f316,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) ) )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) )
@ X4 )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) )
@ X4 )
= $true )
| ( ( c @ X3 @ paris )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ X3 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( ( c @ X5 @ ( sK11 @ X3 ) )
=> ( c @ X5 @ X3 ) )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( ( c @ X4 @ ( sK12 @ X3 ) )
=> ( c @ X4 @ paris ) )
= $true )
| ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( ( c @ X4 @ ( sK12 @ X3 ) )
=> ( c @ X4 @ paris ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( ( c @ X5 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X4 @ paris )
= $true )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( $false
= ( c @ X3 @ france ) ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) )
@ X4 )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) ) ) )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(pi_proxy_clausification,[],[f314]) ).
thf(f322,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK12 @ X3 ) )
=> ( c @ Y0 @ paris ) )
@ X4 )
= $true )
| ( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ ( sK11 @ X3 ) )
=> ( c @ Y0 @ france ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( ( c @ X4 @ ( sK12 @ X3 ) )
=> ( c @ X4 @ paris ) )
= $true )
| ( $true
= ( ( c @ X5 @ ( sK11 @ X3 ) )
=> ( c @ X5 @ france ) ) )
| ( $false
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( a @ X1 @ X2 )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X4 @ paris )
= $true )
| ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( ( c @ X5 @ ( sK11 @ X3 ) )
=> ( c @ X5 @ france ) ) ) ),
inference(imp_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X3: reg,X1: $i,X4: reg,X5: reg] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X4 @ paris )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( ( c @ X5 @ france )
= $true )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(imp_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f287]) ).
thf(f333,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) )
@ X3 )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f326]) ).
thf(f334,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( c @ X3 @ france ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f337,definition,
( spl14_1
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f338,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f337]) ).
thf(f392,definition,
( spl14_14
<=> ! [X3: reg] :
( ( $true
= ( c @ X3 @ spain ) )
| ( ( c @ X3 @ catalunya )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f393,plain,
( ! [X3: reg] :
( ( $true
= ( c @ X3 @ spain ) )
| ( ( c @ X3 @ catalunya )
= $false ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f394,plain,
( spl14_14
| spl14_1 ),
inference(avatar_split_clause,[],[f230,f337,f392]) ).
thf(f396,definition,
( spl14_15
<=> ( $true
= ( c @ spain @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f397,plain,
( ( $true
!= ( c @ spain @ paris ) )
| spl14_15 ),
inference(avatar_component_clause,[],[f396]) ).
thf(f398,plain,
( ( $true
= ( c @ spain @ paris ) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f396]) ).
thf(f400,definition,
( spl14_16
<=> ( $true
= ( c @ catalunya @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f402,plain,
( ( $true
= ( c @ catalunya @ paris ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f403,plain,
( spl14_15
| spl14_16 ),
inference(avatar_split_clause,[],[f241,f400,f396]) ).
thf(f405,definition,
( spl14_17
<=> ( ( c @ spain @ france )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f407,plain,
( ( ( c @ spain @ france )
= $true )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f405]) ).
thf(f409,definition,
( spl14_18
<=> ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f410,plain,
( ! [X2: $i,X1: $i] :
( ( fool @ X1 @ X2 )
= $false )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f411,plain,
( spl14_17
| spl14_18 ),
inference(avatar_split_clause,[],[f250,f409,f405]) ).
thf(f413,definition,
( spl14_19
<=> ! [X3: reg] :
( ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true )
| ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition]) ).
thf(f414,plain,
( ! [X3: reg] :
( ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) )
| ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true ) )
| ~ spl14_19 ),
inference(avatar_component_clause,[],[f413]) ).
thf(f415,plain,
( spl14_19
| spl14_18 ),
inference(avatar_split_clause,[],[f261,f409,f413]) ).
thf(f417,definition,
( spl14_20
<=> ! [X3: reg] :
( ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true )
| ( $false
= ( c @ ( sK8 @ X3 ) @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_20])],[avatar_definition]) ).
thf(f418,plain,
( ! [X3: reg] :
( ( $false
= ( c @ ( sK8 @ X3 ) @ france ) )
| ( ( c @ ( sK9 @ X3 ) @ X3 )
= $true ) )
| ~ spl14_20 ),
inference(avatar_component_clause,[],[f417]) ).
thf(f419,plain,
( spl14_20
| spl14_18 ),
inference(avatar_split_clause,[],[f260,f409,f417]) ).
thf(f421,definition,
( spl14_21
<=> ! [X3: reg] :
( ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) )
| ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_21])],[avatar_definition]) ).
thf(f422,plain,
( ! [X3: reg] :
( ( $true
= ( c @ ( sK8 @ X3 ) @ X3 ) )
| ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) ) )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f421]) ).
thf(f423,plain,
( spl14_21
| spl14_18 ),
inference(avatar_split_clause,[],[f263,f409,f421]) ).
thf(f425,definition,
( spl14_22
<=> ! [X3: reg] :
( ( $false
= ( c @ ( sK8 @ X3 ) @ france ) )
| ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_22])],[avatar_definition]) ).
thf(f426,plain,
( ! [X3: reg] :
( ( $false
= ( c @ ( sK9 @ X3 ) @ spain ) )
| ( $false
= ( c @ ( sK8 @ X3 ) @ france ) ) )
| ~ spl14_22 ),
inference(avatar_component_clause,[],[f425]) ).
thf(f427,plain,
( spl14_22
| spl14_18 ),
inference(avatar_split_clause,[],[f262,f409,f425]) ).
thf(f429,definition,
( spl14_23
<=> ! [X4: reg,X5: reg,X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X5 @ X3 )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( ( c @ X4 @ X3 )
= $true )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_23])],[avatar_definition]) ).
thf(f430,plain,
( ! [X3: reg,X4: reg,X5: reg] :
( ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( ( c @ X4 @ X3 )
= $true ) )
| ~ spl14_23 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f431,plain,
( spl14_23
| spl14_1 ),
inference(avatar_split_clause,[],[f308,f337,f429]) ).
thf(f433,definition,
( spl14_24
<=> ! [X4: reg,X5: reg,X3: reg] :
( ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X5 @ ( sK12 @ X3 ) )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X4 @ france )
= $true )
| ( ( c @ X4 @ ( sK11 @ X3 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_24])],[avatar_definition]) ).
thf(f434,plain,
( ! [X3: reg,X4: reg,X5: reg] :
( ( ( c @ X5 @ ( sK12 @ X3 ) )
= $false )
| ( ( c @ X4 @ ( sK11 @ X3 ) )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X4 @ france )
= $true )
| ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X3 @ paris )
= $false ) )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f435,plain,
( spl14_1
| spl14_24 ),
inference(avatar_split_clause,[],[f313,f433,f337]) ).
thf(f437,definition,
( spl14_25
<=> ! [X4: reg,X5: reg,X3: reg] :
( ( ( c @ X5 @ X3 )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X4 @ paris )
= $true )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
thf(f438,plain,
( ! [X3: reg,X4: reg,X5: reg] :
( ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X5 @ X3 )
= $true )
| ( ( c @ X4 @ paris )
= $true )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false ) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f437]) ).
thf(f439,plain,
( spl14_1
| spl14_25 ),
inference(avatar_split_clause,[],[f320,f437,f337]) ).
thf(f441,definition,
( spl14_26
<=> ! [X4: reg,X5: reg,X3: reg] :
( ( ( c @ X4 @ paris )
= $true )
| ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X5 @ france )
= $true )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( $false
= ( c @ X3 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_26])],[avatar_definition]) ).
thf(f442,plain,
( ! [X3: reg,X4: reg,X5: reg] :
( ( $false
= ( c @ X4 @ ( sK12 @ X3 ) ) )
| ( ( c @ X5 @ ( sK11 @ X3 ) )
= $false )
| ( ( c @ X3 @ paris )
= $false )
| ( $false
= ( c @ X3 @ france ) )
| ( ( c @ X4 @ paris )
= $true )
| ( ( c @ X5 @ france )
= $true ) )
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f441]) ).
thf(f443,plain,
( spl14_26
| spl14_1 ),
inference(avatar_split_clause,[],[f325,f337,f441]) ).
thf(f455,definition,
( spl14_29
<=> ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( $true
= ( c @ X3 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_29])],[avatar_definition]) ).
thf(f456,plain,
( ! [X3: reg] :
( ( $true
= ( c @ X3 @ france ) )
| ( ( c @ X3 @ paris )
= $false ) )
| ~ spl14_29 ),
inference(avatar_component_clause,[],[f455]) ).
thf(f457,plain,
( spl14_29
| spl14_1 ),
inference(avatar_split_clause,[],[f335,f337,f455]) ).
thf(f491,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( a @ X1 @ X3 )
= $false )
| ( ( X2 @ X3 )
= $true )
| ( $true = $false ) )
| ~ spl14_18 ),
inference(forward_demodulation,[],[f278,f410]) ).
thf(f492,plain,
( ! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( a @ X1 @ X3 )
= $false )
| ( ( X2 @ X3 )
= $true ) )
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f495,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ sK7 ) )
| ( $true = $false ) )
| ~ spl14_18 ),
inference(superposition,[],[f492,f238]) ).
thf(f499,plain,
( ! [X0: $i > $o] :
( $true
= ( X0 @ sK7 ) )
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f495]) ).
thf(f503,plain,
( ( ( ^ [Y0: $i] : $false
@ sK7 )
= $true )
| ~ spl14_18 ),
inference(primitive_instantiation,[],[f499]) ).
thf(f518,plain,
( ( $true = $false )
| ~ spl14_18 ),
inference(beta-eta_normalization,[],[f503]) ).
thf(f519,plain,
( $false
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f520,plain,
~ spl14_18,
inference(avatar_contradiction_clause,[],[f519]) ).
thf(f534,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ catalunya )
= $false )
| ( ( c @ spain @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl14_14 ),
inference(superposition,[],[f157,f393]) ).
thf(f535,plain,
( ! [X0: reg] :
( ( ( c @ spain @ X0 )
= $true )
| ( ( c @ X0 @ catalunya )
= $false ) )
| ~ spl14_14 ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f606,plain,
( ! [X0: reg] :
( ( ( c @ ( sK8 @ X0 ) @ paris )
= $false )
| ( $true = $false )
| ( ( c @ ( sK9 @ X0 ) @ X0 )
= $true ) )
| ~ spl14_20
| ~ spl14_29 ),
inference(superposition,[],[f456,f418]) ).
thf(f608,plain,
( ! [X0: reg] :
( ( ( c @ ( sK9 @ X0 ) @ X0 )
= $true )
| ( ( c @ ( sK8 @ X0 ) @ paris )
= $false ) )
| ~ spl14_20
| ~ spl14_29 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f768,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ X0 @ paris )
= $false )
| ( $true = $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $false
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ spain ) ) )
| ~ spl14_21
| ~ spl14_25 ),
inference(superposition,[],[f422,f438]) ).
thf(f769,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( $true
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ ( sK12 @ X0 ) ) )
| ( $true = $false ) )
| ~ spl14_19
| ~ spl14_25 ),
inference(superposition,[],[f414,f438]) ).
thf(f777,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ spain ) )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( ( c @ X1 @ X0 )
= $true ) )
| ~ spl14_21
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f768]) ).
thf(f782,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ ( sK12 @ X0 ) ) )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X1 @ X0 )
= $true )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( ( c @ X0 @ paris )
= $false ) )
| ~ spl14_19
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f769]) ).
thf(f799,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ X0 @ paris )
= $false )
| ( $true
= ( c @ X1 @ france ) )
| ( $true
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ ( sK12 @ X0 ) ) )
| ( $false
= ( c @ X0 @ france ) )
| ( $true = $false )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) ) )
| ~ spl14_19
| ~ spl14_26 ),
inference(superposition,[],[f442,f414]) ).
thf(f806,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ spain ) )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X0 @ france ) )
| ( $true = $false )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $true
= ( c @ X1 @ france ) ) )
| ~ spl14_21
| ~ spl14_26 ),
inference(superposition,[],[f422,f442]) ).
thf(f815,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( ( c @ X0 @ paris )
= $false )
| ( $true
= ( c @ X1 @ france ) )
| ( $false
= ( c @ X0 @ france ) )
| ( $false
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ spain ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) ) )
| ~ spl14_21
| ~ spl14_26 ),
inference(trivial_inequality_removal,[],[f806]) ).
thf(f818,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ ( sK12 @ X0 ) ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $true
= ( c @ X1 @ france ) )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X0 @ france ) ) )
| ~ spl14_19
| ~ spl14_26 ),
inference(trivial_inequality_removal,[],[f799]) ).
thf(f859,plain,
( ( $true = $false )
| ~ spl14_1 ),
inference(superposition,[],[f338,f238]) ).
thf(f867,plain,
( $false
| ~ spl14_1 ),
inference(trivial_inequality_removal,[],[f859]) ).
thf(f868,plain,
~ spl14_1,
inference(avatar_contradiction_clause,[],[f867]) ).
thf(f920,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris )
= $false )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $false
= ( c @ X0 @ france ) )
| ( $true = $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true ) )
| ~ spl14_20
| ~ spl14_23
| ~ spl14_29 ),
inference(superposition,[],[f608,f430]) ).
thf(f925,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris )
= $false )
| ( $true = $false )
| ( $false
= ( c @ X0 @ france ) )
| ( $true
= ( c @ X1 @ france ) )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true ) )
| ~ spl14_20
| ~ spl14_24
| ~ spl14_29 ),
inference(superposition,[],[f434,f608]) ).
thf(f928,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris )
= $false )
| ( $false
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( ( c @ X0 @ paris )
= $false )
| ( ( c @ X1 @ X0 )
= $true ) )
| ~ spl14_20
| ~ spl14_23
| ~ spl14_29 ),
inference(trivial_inequality_removal,[],[f920]) ).
thf(f931,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( $true
= ( c @ X1 @ france ) )
| ( ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris )
= $false )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) ) )
| ~ spl14_20
| ~ spl14_24
| ~ spl14_29 ),
inference(trivial_inequality_removal,[],[f925]) ).
thf(f1686,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X2 @ ( sK11 @ X0 ) )
= $false )
| ( ( c @ X0 @ paris )
= $false )
| ( ( c @ X2 @ X0 )
= $true )
| ( ( c @ X0 @ paris )
= $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( $true = $false ) )
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(superposition,[],[f430,f782]) ).
thf(f1690,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( ( c @ X2 @ X0 )
= $true )
| ( ( c @ X1 @ X0 )
= $true )
| ( $true = $false )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X2 @ ( sK11 @ X0 ) )
= $false ) )
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(duplicate_literal_removal,[],[f1686]) ).
thf(f1691,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X2 @ ( sK11 @ X0 ) )
= $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X2 @ X0 )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( ( c @ X0 @ paris )
= $false ) )
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f1690]) ).
thf(f1707,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $true
= ( c @ X1 @ france ) )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( $true = $false )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X2 @ ( sK11 @ X0 ) )
= $false )
| ( ( c @ X0 @ paris )
= $false )
| ( ( c @ X0 @ paris )
= $false )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X2 @ france )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true ) )
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26 ),
inference(superposition,[],[f818,f434]) ).
thf(f1716,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( ( c @ X2 @ ( sK11 @ X0 ) )
= $false )
| ( $true
= ( c @ X1 @ france ) )
| ( $true = $false )
| ( $false
= ( c @ X0 @ france ) )
| ( ( c @ X2 @ france )
= $true )
| ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( ( c @ X0 @ paris )
= $false ) )
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26 ),
inference(duplicate_literal_removal,[],[f1707]) ).
thf(f1717,plain,
( ! [X2: reg,X0: reg,X1: reg] :
( ( $true
= ( c @ ( sK8 @ ( sK12 @ X0 ) ) @ paris ) )
| ( ( c @ X2 @ ( sK11 @ X0 ) )
= $false )
| ( ( c @ ( sK9 @ ( sK12 @ X0 ) ) @ X0 )
= $true )
| ( $true
= ( c @ X1 @ france ) )
| ( ( c @ X2 @ france )
= $true )
| ( $false
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ X0 ) ) )
| ( ( c @ X0 @ paris )
= $false ) )
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26 ),
inference(trivial_inequality_removal,[],[f1716]) ).
thf(f2406,definition,
( spl14_66
<=> ( $false
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) ) ),
introduced(definition,[new_symbols(definition,[spl14_66])],[avatar_definition]) ).
thf(f2408,plain,
( ( $false
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ~ spl14_66 ),
inference(avatar_component_clause,[],[f2406]) ).
thf(f3010,plain,
( ! [X0: reg] :
( ( $true = $false )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ( ( c @ spain @ france )
= $false )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29 ),
inference(superposition,[],[f426,f928]) ).
thf(f3047,plain,
( ! [X0: reg] :
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ( ( c @ spain @ france )
= $false )
| ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29 ),
inference(trivial_inequality_removal,[],[f3010]) ).
thf(f3094,definition,
( spl14_72
<=> ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_72])],[avatar_definition]) ).
thf(f3095,plain,
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
!= $false )
| spl14_72 ),
inference(avatar_component_clause,[],[f3094]) ).
thf(f3096,plain,
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ~ spl14_72 ),
inference(avatar_component_clause,[],[f3094]) ).
thf(f3102,definition,
( spl14_74
<=> ! [X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ france ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_74])],[avatar_definition]) ).
thf(f3103,plain,
( ! [X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ france ) ) )
| ~ spl14_74 ),
inference(avatar_component_clause,[],[f3102]) ).
thf(f3105,definition,
( spl14_75
<=> ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_75])],[avatar_definition]) ).
thf(f3106,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( ( c @ X0 @ spain )
= $true ) )
| ~ spl14_75 ),
inference(avatar_component_clause,[],[f3105]) ).
thf(f3111,definition,
( spl14_76
<=> ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_76])],[avatar_definition]) ).
thf(f3113,plain,
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ~ spl14_76 ),
inference(avatar_component_clause,[],[f3111]) ).
thf(f3149,definition,
( spl14_77
<=> ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_77])],[avatar_definition]) ).
thf(f3151,plain,
( ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ~ spl14_77 ),
inference(avatar_component_clause,[],[f3149]) ).
thf(f3178,plain,
( ! [X0: reg] :
( ( ( c @ spain @ france )
= $false )
| ( $true
= ( c @ X0 @ france ) )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $true = $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29 ),
inference(superposition,[],[f426,f931]) ).
thf(f3213,plain,
( ! [X0: reg] :
( ( $false
= ( c @ spain @ paris ) )
| ( ( c @ spain @ france )
= $false )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $true
= ( c @ X0 @ france ) )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29 ),
inference(trivial_inequality_removal,[],[f3178]) ).
thf(f3236,plain,
( ! [X0: reg] :
( ( ( c @ spain @ france )
= $false )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) )
| ( $true
= ( c @ X0 @ france ) ) )
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29
| spl14_72 ),
inference(forward_subsumption_resolution,[],[f3213,f3095]) ).
thf(f3247,plain,
( ! [X0: reg] :
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true = $false ) )
| ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29
| spl14_72 ),
inference(forward_demodulation,[],[f3236,f407]) ).
thf(f3248,plain,
( ! [X0: reg] :
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29
| spl14_72 ),
inference(trivial_inequality_removal,[],[f3247]) ).
thf(f3299,definition,
( spl14_84
<=> ( $false
= ( c @ spain @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl14_84])],[avatar_definition]) ).
thf(f3301,plain,
( ( $false
= ( c @ spain @ paris ) )
| ~ spl14_84 ),
inference(avatar_component_clause,[],[f3299]) ).
thf(f3309,plain,
( ! [X0: reg] :
( ( ( c @ spain @ france )
= $false )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29
| spl14_72 ),
inference(forward_subsumption_resolution,[],[f3047,f3095]) ).
thf(f3313,plain,
( spl14_76
| spl14_74
| spl14_84
| ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29
| spl14_72 ),
inference(avatar_split_clause,[],[f3248,f3094,f455,f433,f425,f417,f405,f3299,f3102,f3111]) ).
thf(f3323,plain,
( ! [X0: reg] :
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false )
| ( ( c @ X0 @ spain )
= $true )
| ( $true = $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29
| spl14_72 ),
inference(forward_demodulation,[],[f3309,f407]) ).
thf(f3324,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) )
| ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ france )
= $false ) )
| ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29
| spl14_72 ),
inference(trivial_inequality_removal,[],[f3323]) ).
thf(f3330,plain,
( spl14_84
| spl14_75
| spl14_76
| ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29
| spl14_72 ),
inference(avatar_split_clause,[],[f3324,f3094,f455,f429,f425,f417,f405,f3111,f3105,f3299]) ).
thf(f3332,plain,
( ( $false
= ( c @ paris @ catalunya ) )
| ( $true != $true )
| ~ spl14_14
| spl14_15 ),
inference(superposition,[],[f397,f535]) ).
thf(f3337,plain,
( ( $false
= ( c @ paris @ catalunya ) )
| ~ spl14_14
| spl14_15 ),
inference(trivial_inequality_removal,[],[f3332]) ).
thf(f3339,plain,
( ( $true
= ( c @ paris @ catalunya ) )
| ( $true != $true )
| ~ spl14_16 ),
inference(superposition,[],[f157,f402]) ).
thf(f3340,plain,
( ( $true
= ( c @ paris @ catalunya ) )
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f3339]) ).
thf(f3346,plain,
( ( $true = $false )
| ~ spl14_14
| spl14_15
| ~ spl14_16 ),
inference(superposition,[],[f3340,f3337]) ).
thf(f3354,plain,
( $false
| ~ spl14_14
| spl14_15
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f3346]) ).
thf(f3355,plain,
( ~ spl14_14
| spl14_15
| ~ spl14_16 ),
inference(avatar_contradiction_clause,[],[f3354]) ).
thf(f3520,plain,
( ( $true = $false )
| ~ spl14_15
| ~ spl14_84 ),
inference(superposition,[],[f398,f3301]) ).
thf(f3529,plain,
( $false
| ~ spl14_15
| ~ spl14_84 ),
inference(trivial_inequality_removal,[],[f3520]) ).
thf(f3530,plain,
( ~ spl14_15
| ~ spl14_84 ),
inference(avatar_contradiction_clause,[],[f3529]) ).
thf(f3684,plain,
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ( $true = $false )
| ~ spl14_29
| ~ spl14_76 ),
inference(superposition,[],[f3113,f456]) ).
thf(f3694,plain,
( ( ( c @ ( sK8 @ ( sK12 @ spain ) ) @ paris )
= $false )
| ~ spl14_29
| ~ spl14_76 ),
inference(trivial_inequality_removal,[],[f3684]) ).
thf(f3713,plain,
( spl14_72
| ~ spl14_29
| ~ spl14_76 ),
inference(avatar_split_clause,[],[f3694,f3111,f455,f3094]) ).
thf(f3813,plain,
( ! [X0: reg] :
( ( $false
= ( c @ spain @ paris ) )
| ( $true = $false )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( ( c @ spain @ france )
= $false ) )
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(superposition,[],[f3096,f815]) ).
thf(f3814,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true = $false )
| ( ( c @ spain @ france )
= $false )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(superposition,[],[f3096,f777]) ).
thf(f3825,plain,
( ! [X0: reg] :
( ( ( c @ spain @ france )
= $false )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f3813]) ).
thf(f3827,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ spain @ france )
= $false )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false ) )
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f3814]) ).
thf(f3832,plain,
( ! [X0: reg] :
( ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( $true = $false )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_17
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(forward_demodulation,[],[f3825,f407]) ).
thf(f3833,plain,
( ! [X0: reg] :
( ( $true
= ( c @ X0 @ france ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_17
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f3832]) ).
thf(f3834,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( ( c @ spain @ france )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true = $false ) )
| ~ spl14_15
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(forward_demodulation,[],[f3827,f398]) ).
thf(f3835,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ spain @ france )
= $false )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false ) )
| ~ spl14_15
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f3834]) ).
thf(f3840,plain,
( ! [X0: reg] :
( ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true = $false )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(forward_demodulation,[],[f3833,f398]) ).
thf(f3841,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f3840]) ).
thf(f3842,plain,
( ! [X0: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true = $false )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(forward_demodulation,[],[f3835,f407]) ).
thf(f3843,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f3842]) ).
thf(f3846,plain,
( spl14_77
| spl14_74
| ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f3841,f3094,f441,f421,f405,f396,f3102,f3149]) ).
thf(f3847,plain,
( spl14_77
| spl14_75
| ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f3843,f3094,f437,f421,f405,f396,f3105,f3149]) ).
thf(f4273,definition,
( spl14_94
<=> ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_94])],[avatar_definition]) ).
thf(f4275,plain,
( ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain )
= $false )
| ~ spl14_94 ),
inference(avatar_component_clause,[],[f4273]) ).
thf(f4311,definition,
( spl14_102
<=> ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ ( sK11 @ spain ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_102])],[avatar_definition]) ).
thf(f4313,plain,
( ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ ( sK11 @ spain ) )
= $true )
| ~ spl14_102 ),
inference(avatar_component_clause,[],[f4311]) ).
thf(f4459,definition,
( spl14_122
<=> ( $true
= ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain ) ) ),
introduced(definition,[new_symbols(definition,[spl14_122])],[avatar_definition]) ).
thf(f4461,plain,
( ( $true
= ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain ) )
| ~ spl14_122 ),
inference(avatar_component_clause,[],[f4459]) ).
thf(f4474,definition,
( spl14_125
<=> ( $true
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) ) ),
introduced(definition,[new_symbols(definition,[spl14_125])],[avatar_definition]) ).
thf(f4476,plain,
( ( $true
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ~ spl14_125 ),
inference(avatar_component_clause,[],[f4474]) ).
thf(f5520,plain,
( ! [X0: reg,X1: reg] :
( ( $true = $false )
| ( $false
= ( c @ spain @ paris ) )
| ( ( c @ spain @ france )
= $false )
| ( $true
= ( c @ X1 @ spain ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) ) )
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72 ),
inference(superposition,[],[f1691,f3096]) ).
thf(f5530,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( ( c @ spain @ france )
= $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ spain @ paris ) )
| ( $true
= ( c @ X1 @ spain ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true ) )
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f5520]) ).
thf(f5541,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( $false
= ( c @ spain @ paris ) )
| ( $true = $false )
| ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ spain ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) ) )
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72 ),
inference(forward_demodulation,[],[f5530,f407]) ).
thf(f5542,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ spain @ paris ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( ( c @ X0 @ spain )
= $true )
| ( $true
= ( c @ X1 @ spain ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f5541]) ).
thf(f5548,plain,
( ! [X0: reg,X1: reg] :
( ( $true = $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( ( c @ X0 @ spain )
= $true )
| ( $true
= ( c @ X1 @ spain ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72 ),
inference(forward_demodulation,[],[f5542,f398]) ).
thf(f5549,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ spain ) )
| ( ( c @ X0 @ spain )
= $true )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f5548]) ).
thf(f5553,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ X1 @ spain ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true = $false )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( ( c @ X0 @ spain )
= $true ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72
| ~ spl14_77 ),
inference(forward_demodulation,[],[f5549,f3151]) ).
thf(f5554,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ X0 @ spain )
= $true )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ spain ) ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72
| ~ spl14_77 ),
inference(trivial_inequality_removal,[],[f5553]) ).
thf(f5556,plain,
( spl14_75
| spl14_75
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f5554,f3149,f3094,f437,f429,f413,f405,f396,f3105,f3105]) ).
thf(f5627,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( $true
= ( c @ X1 @ france ) )
| ( ( c @ spain @ france )
= $false )
| ( $true = $false ) )
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72 ),
inference(superposition,[],[f3096,f1717]) ).
thf(f5636,plain,
( ! [X0: reg,X1: reg] :
( ( ( c @ spain @ france )
= $false )
| ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( $true
= ( c @ X1 @ france ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f5627]) ).
thf(f5643,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ france ) )
| ( $true
= ( c @ X0 @ france ) )
| ( $true = $false )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( $false
= ( c @ spain @ paris ) ) )
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72 ),
inference(forward_demodulation,[],[f5636,f407]) ).
thf(f5644,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( ( c @ ( sK9 @ ( sK12 @ spain ) ) @ spain )
= $true )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) )
| ( $true
= ( c @ X1 @ france ) ) )
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72 ),
inference(trivial_inequality_removal,[],[f5643]) ).
thf(f5649,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ X1 @ france ) )
| ( $true = $false )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) ) )
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| ~ spl14_77 ),
inference(forward_demodulation,[],[f5644,f3151]) ).
thf(f5650,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ spain @ paris ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) ) )
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| ~ spl14_77 ),
inference(trivial_inequality_removal,[],[f5649]) ).
thf(f5653,plain,
( ! [X0: reg,X1: reg] :
( ( $true
= ( c @ X1 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true = $false ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| ~ spl14_77 ),
inference(forward_demodulation,[],[f5650,f398]) ).
thf(f5654,plain,
( ! [X0: reg,X1: reg] :
( ( $false
= ( c @ X0 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X0 @ france ) )
| ( $false
= ( c @ X1 @ ( sK11 @ spain ) ) )
| ( $true
= ( c @ X1 @ france ) ) )
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| ~ spl14_77 ),
inference(trivial_inequality_removal,[],[f5653]) ).
thf(f5656,plain,
( spl14_74
| spl14_74
| ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| ~ spl14_77 ),
inference(avatar_split_clause,[],[f5654,f3149,f3094,f441,f433,f413,f405,f396,f3102,f3102]) ).
thf(f5774,plain,
( ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain )
= $false )
| ( $true = $false )
| ( $true
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ~ spl14_21
| ~ spl14_74 ),
inference(superposition,[],[f3103,f422]) ).
thf(f5812,plain,
( ( $true
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ ( sK11 @ spain ) )
= $true )
| ( $true = $false )
| ~ spl14_19
| ~ spl14_74 ),
inference(superposition,[],[f414,f3103]) ).
thf(f5887,plain,
( ( $true
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain )
= $false )
| ~ spl14_21
| ~ spl14_74 ),
inference(trivial_inequality_removal,[],[f5774]) ).
thf(f5900,plain,
( ( $true
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ ( sK11 @ spain ) )
= $true )
| ~ spl14_19
| ~ spl14_74 ),
inference(trivial_inequality_removal,[],[f5812]) ).
thf(f5944,plain,
( spl14_125
| spl14_94
| ~ spl14_21
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f5887,f3102,f421,f4273,f4474]) ).
thf(f5949,plain,
( spl14_125
| spl14_102
| ~ spl14_19
| ~ spl14_74 ),
inference(avatar_split_clause,[],[f5900,f3102,f413,f4311,f4474]) ).
thf(f6899,plain,
( ( $true = $false )
| ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ ( sK11 @ spain ) )
= $true )
| ~ spl14_20
| ~ spl14_125 ),
inference(superposition,[],[f418,f4476]) ).
thf(f6901,plain,
( ( ( c @ ( sK9 @ ( sK11 @ spain ) ) @ ( sK11 @ spain ) )
= $true )
| ~ spl14_20
| ~ spl14_125 ),
inference(trivial_inequality_removal,[],[f6899]) ).
thf(f6906,plain,
( spl14_102
| ~ spl14_20
| ~ spl14_125 ),
inference(avatar_split_clause,[],[f6901,f4474,f417,f4311]) ).
thf(f7371,plain,
( ( $true = $false )
| ( $true
= ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain ) )
| ~ spl14_75
| ~ spl14_102 ),
inference(superposition,[],[f3106,f4313]) ).
thf(f7381,plain,
( ( $true
= ( c @ ( sK9 @ ( sK11 @ spain ) ) @ spain ) )
| ~ spl14_75
| ~ spl14_102 ),
inference(trivial_inequality_removal,[],[f7371]) ).
thf(f7400,plain,
( spl14_122
| ~ spl14_75
| ~ spl14_102 ),
inference(avatar_split_clause,[],[f7381,f4311,f3105,f4459]) ).
thf(f7446,plain,
( ( $false
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ( $true = $false )
| ~ spl14_22
| ~ spl14_122 ),
inference(superposition,[],[f426,f4461]) ).
thf(f7450,plain,
( ( $false
= ( c @ ( sK8 @ ( sK11 @ spain ) ) @ france ) )
| ~ spl14_22
| ~ spl14_122 ),
inference(trivial_inequality_removal,[],[f7446]) ).
thf(f7453,plain,
( spl14_66
| ~ spl14_22
| ~ spl14_122 ),
inference(avatar_split_clause,[],[f7450,f4459,f425,f2406]) ).
thf(f7454,plain,
( ( $true = $false )
| ~ spl14_66
| ~ spl14_125 ),
inference(superposition,[],[f2408,f4476]) ).
thf(f7470,plain,
( $false
| ~ spl14_66
| ~ spl14_125 ),
inference(trivial_inequality_removal,[],[f7454]) ).
thf(f7471,plain,
( ~ spl14_66
| ~ spl14_125 ),
inference(avatar_contradiction_clause,[],[f7470]) ).
thf(f7491,plain,
( ( $true = $false )
| ~ spl14_94
| ~ spl14_122 ),
inference(superposition,[],[f4461,f4275]) ).
thf(f7500,plain,
( $false
| ~ spl14_94
| ~ spl14_122 ),
inference(trivial_inequality_removal,[],[f7491]) ).
thf(f7501,plain,
( ~ spl14_94
| ~ spl14_122 ),
inference(avatar_contradiction_clause,[],[f7500]) ).
cnf(s13,plain,
( spl14_1
| spl14_14 ),
inference(sat_conversion,[],[f394]) ).
cnf(s14,plain,
( spl14_15
| spl14_16 ),
inference(sat_conversion,[],[f403]) ).
cnf(s15,plain,
( spl14_17
| spl14_18 ),
inference(sat_conversion,[],[f411]) ).
cnf(s16,plain,
( spl14_18
| spl14_19 ),
inference(sat_conversion,[],[f415]) ).
cnf(s17,plain,
( spl14_18
| spl14_20 ),
inference(sat_conversion,[],[f419]) ).
cnf(s18,plain,
( spl14_18
| spl14_21 ),
inference(sat_conversion,[],[f423]) ).
cnf(s19,plain,
( spl14_18
| spl14_22 ),
inference(sat_conversion,[],[f427]) ).
cnf(s20,plain,
( spl14_1
| spl14_23 ),
inference(sat_conversion,[],[f431]) ).
cnf(s21,plain,
( spl14_1
| spl14_24 ),
inference(sat_conversion,[],[f435]) ).
cnf(s22,plain,
( spl14_1
| spl14_25 ),
inference(sat_conversion,[],[f439]) ).
cnf(s23,plain,
( spl14_1
| spl14_26 ),
inference(sat_conversion,[],[f443]) ).
cnf(s26,plain,
( spl14_1
| spl14_29 ),
inference(sat_conversion,[],[f457]) ).
cnf(s29,plain,
~ spl14_18,
inference(sat_conversion,[],[f520]) ).
cnf(s39,plain,
~ spl14_1,
inference(sat_conversion,[],[f868]) ).
cnf(s134,plain,
( ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_24
| ~ spl14_29
| spl14_72
| spl14_74
| spl14_76
| spl14_84 ),
inference(sat_conversion,[],[f3313]) ).
cnf(s146,plain,
( ~ spl14_17
| ~ spl14_20
| ~ spl14_22
| ~ spl14_23
| ~ spl14_29
| spl14_72
| spl14_75
| spl14_76
| spl14_84 ),
inference(sat_conversion,[],[f3330]) ).
cnf(s150,plain,
( ~ spl14_14
| spl14_15
| ~ spl14_16 ),
inference(sat_conversion,[],[f3355]) ).
cnf(s175,plain,
( ~ spl14_15
| ~ spl14_84 ),
inference(sat_conversion,[],[f3530]) ).
cnf(s184,plain,
( ~ spl14_29
| spl14_72
| ~ spl14_76 ),
inference(sat_conversion,[],[f3713]) ).
cnf(s214,plain,
( ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_26
| ~ spl14_72
| spl14_74
| spl14_77 ),
inference(sat_conversion,[],[f3846]) ).
cnf(s215,plain,
( ~ spl14_15
| ~ spl14_17
| ~ spl14_21
| ~ spl14_25
| ~ spl14_72
| spl14_75
| spl14_77 ),
inference(sat_conversion,[],[f3847]) ).
cnf(s394,plain,
( spl14_75
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72
| ~ spl14_15
| spl14_75
| ~ spl14_77 ),
inference(sat_conversion,[],[f5556]) ).
cnf(s395,plain,
( ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_23
| ~ spl14_25
| ~ spl14_72
| spl14_75
| ~ spl14_77 ),
inference(rat,[],[s394]) ).
cnf(s405,plain,
( spl14_74
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| ~ spl14_15
| spl14_74
| ~ spl14_77 ),
inference(sat_conversion,[],[f5656]) ).
cnf(s406,plain,
( ~ spl14_15
| ~ spl14_17
| ~ spl14_19
| ~ spl14_24
| ~ spl14_26
| ~ spl14_72
| spl14_74
| ~ spl14_77 ),
inference(rat,[],[s405]) ).
cnf(s432,plain,
( ~ spl14_21
| ~ spl14_74
| spl14_94
| spl14_125 ),
inference(sat_conversion,[],[f5944]) ).
cnf(s437,plain,
( ~ spl14_19
| ~ spl14_74
| spl14_102
| spl14_125 ),
inference(sat_conversion,[],[f5949]) ).
cnf(s588,plain,
( ~ spl14_20
| spl14_102
| ~ spl14_125 ),
inference(sat_conversion,[],[f6906]) ).
cnf(s611,plain,
( ~ spl14_75
| ~ spl14_102
| spl14_122 ),
inference(sat_conversion,[],[f7400]) ).
cnf(s617,plain,
( ~ spl14_22
| spl14_66
| ~ spl14_122 ),
inference(sat_conversion,[],[f7453]) ).
cnf(s620,plain,
( ~ spl14_66
| ~ spl14_125 ),
inference(sat_conversion,[],[f7471]) ).
cnf(s621,plain,
( ~ spl14_94
| ~ spl14_122 ),
inference(sat_conversion,[],[f7501]) ).
cnf(s623,plain,
spl14_29,
inference(rat,[],[s26,s39]) ).
cnf(s626,plain,
spl14_26,
inference(rat,[],[s23,s39]) ).
cnf(s627,plain,
spl14_25,
inference(rat,[],[s22,s39]) ).
cnf(s628,plain,
spl14_24,
inference(rat,[],[s21,s39]) ).
cnf(s629,plain,
spl14_23,
inference(rat,[],[s20,s39]) ).
cnf(s630,plain,
spl14_22,
inference(rat,[],[s19,s29]) ).
cnf(s631,plain,
spl14_21,
inference(rat,[],[s18,s29]) ).
cnf(s632,plain,
spl14_20,
inference(rat,[],[s17,s29]) ).
cnf(s633,plain,
spl14_19,
inference(rat,[],[s16,s29]) ).
cnf(s636,plain,
spl14_17,
inference(rat,[],[s15,s29]) ).
cnf(s637,plain,
spl14_14,
inference(rat,[],[s13,s39]) ).
cnf(s654,plain,
spl14_15,
inference(rat,[],[s14,s150,s637]) ).
cnf(s655,plain,
~ spl14_84,
inference(rat,[],[s175,s654]) ).
cnf(s657,plain,
( spl14_75
| ~ spl14_72 ),
inference(rat,[],[s215,s395,s629,s633,s654,s636,s627,s631]) ).
cnf(s658,plain,
( spl14_74
| ~ spl14_72 ),
inference(rat,[],[s214,s406,s628,s633,s654,s636,s626,s631]) ).
cnf(s661,plain,
( ~ spl14_72
| spl14_125 ),
inference(rat,[],[s621,s611,s432,s437,s658,s657,s631,s633]) ).
cnf(s662,plain,
spl14_125,
inference(rat,[],[s621,s611,s432,s437,s146,s134,s184,s661,s631,s633,s630,s629,s623,s632,s636,s655,s628]) ).
cnf(s663,plain,
~ spl14_66,
inference(rat,[],[s620,s662]) ).
cnf(s664,plain,
spl14_102,
inference(rat,[],[s588,s632,s662]) ).
cnf(s665,plain,
~ spl14_122,
inference(rat,[],[s617,s630,s663]) ).
cnf(s666,plain,
~ spl14_75,
inference(rat,[],[s611,s664,s665]) ).
cnf(s667,plain,
~ spl14_72,
inference(rat,[],[s657,s666]) ).
cnf(s668,plain,
~ spl14_76,
inference(rat,[],[s184,s623,s667]) ).
cnf(s669,plain,
$false,
inference(rat,[],[s146,s655,s666,s636,s632,s623,s629,s630,s667,s668]) ).
thf(f7513,plain,
$false,
inference(avatar_sat_refutation,[],[s669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG003^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 18:36:11 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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
% 0.18/0.35 % (469689)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.35 % (469696)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1609531873:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.35 % (469696)Instruction limit reached!
% 0.18/0.35 % (469696)------------------------------
% 0.18/0.35 % (469696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (469696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (469696)CaDiCaL version: 2.1.3
% 0.18/0.35 % (469696)Termination reason: Instruction limit
% 0.18/0.35 % (469696)Termination phase: Property scanning
% 0.18/0.35 % (469696)Time elapsed: 0.002 s
% 0.18/0.35 % (469696)Peak memory usage: 10 MB
% 0.18/0.35 % (469696)Instructions burned: 10 (million)
% 0.18/0.35 % (469695)lrs+10_16_si=on:nwc=1.5:random_seed=2379006058:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.35 % (469694)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2183271417:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.35 % (469700)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.35 % (469700)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
% 0.18/0.35 % (469700)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=1170279022:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.35 % (469702)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4204761566:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.18/0.35 % (469702)Instruction limit reached!
% 0.18/0.35 % (469702)------------------------------
% 0.18/0.35 % (469702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (469702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (469702)CaDiCaL version: 2.1.3
% 0.18/0.35 % (469702)Termination reason: Instruction limit
% 0.18/0.35 % (469702)Termination phase: Property scanning
% 0.18/0.35 % (469702)Time elapsed: 0.001 s
% 0.18/0.35 % (469702)Peak memory usage: 10 MB
% 0.18/0.35 % (469702)Instructions burned: 4 (million)
% 0.18/0.35 % (469695)Instruction limit reached!
% 0.18/0.35 % (469695)------------------------------
% 0.18/0.35 % (469695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (469695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (469695)CaDiCaL version: 2.1.3
% 0.18/0.35 % (469695)Termination reason: Instruction limit
% 0.18/0.35 % (469695)Termination phase: Saturation
% 0.18/0.35 % (469695)Time elapsed: 0.008 s
% 0.18/0.35 % (469695)Peak memory usage: 11 MB
% 0.18/0.35 % (469695)Instructions burned: 18 (million)
% 0.18/0.35 % (469698)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=867165644:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.35 % (469697)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=3307047997: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)
% 0.18/0.35 % (469699)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=64580371:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.35 % (469707)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3409891391:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.18/0.35 % (469707)Instruction limit reached!
% 0.18/0.35 % (469707)------------------------------
% 0.18/0.35 % (469707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.35 % (469707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.35 % (469707)CaDiCaL version: 2.1.3
% 0.18/0.35 % (469707)Termination reason: Instruction limit
% 0.18/0.35 % (469707)Termination phase: Function definition elimination
% 0.18/0.35 % (469707)Time elapsed: 0.002 s
% 0.18/0.35 % (469707)Peak memory usage: 10 MB
% 0.18/0.35 % (469707)Instructions burned: 8 (million)
% 0.96/0.39 % (469708)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.96/0.39 % (469698)Instruction limit reached!
% 0.96/0.39 % (469698)------------------------------
% 0.96/0.39 % (469698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (469698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (469698)CaDiCaL version: 2.1.3
% 0.96/0.39 % (469698)Termination reason: Instruction limit
% 0.96/0.39 % (469698)Termination phase: Saturation
% 0.96/0.39 % (469698)Time elapsed: 0.019 s
% 0.96/0.39 % (469698)Peak memory usage: 11 MB
% 0.96/0.39 % (469698)Instructions burned: 24 (million)
% 0.96/0.39 % (469713)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3788793557:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.96/0.39 % (469708)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3263388431:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.96/0.39 % (469713)Instruction limit reached!
% 0.96/0.39 % (469713)------------------------------
% 0.96/0.39 % (469713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (469713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (469713)CaDiCaL version: 2.1.3
% 0.96/0.39 % (469713)Termination reason: Instruction limit
% 0.96/0.39 % (469713)Termination phase: Saturation
% 0.96/0.39 % (469713)Time elapsed: 0.003 s
% 0.96/0.39 % (469713)Peak memory usage: 11 MB
% 0.96/0.39 % (469713)Instructions burned: 13 (million)
% 0.96/0.39 % (469708)Instruction limit reached!
% 0.96/0.39 % (469708)------------------------------
% 0.96/0.39 % (469708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (469708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (469708)CaDiCaL version: 2.1.3
% 0.96/0.39 % (469708)Termination reason: Instruction limit
% 0.96/0.39 % (469708)Termination phase: Property scanning
% 0.96/0.39 % (469708)Time elapsed: 0.005 s
% 0.96/0.39 % (469708)Peak memory usage: 10 MB
% 0.96/0.39 % (469708)Instructions burned: 7 (million)
% 0.96/0.39 % (469717)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=548550996:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.96/0.39 % (469715)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
% 0.96/0.39 % (469715)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.96/0.39 % (469715)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=275019566:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.96/0.39 % (469694)Instruction limit reached!
% 0.96/0.39 % (469694)------------------------------
% 0.96/0.39 % (469694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (469694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (469694)CaDiCaL version: 2.1.3
% 0.96/0.39 % (469694)Termination reason: Instruction limit
% 0.96/0.39 % (469694)Termination phase: Saturation
% 0.96/0.39 % (469694)Time elapsed: 0.050 s
% 0.96/0.39 % (469694)Peak memory usage: 12 MB
% 0.96/0.39 % (469694)Instructions burned: 87 (million)
% 0.96/0.39 % (469718)lrs+10_1_si=on:cs=on:random_seed=2504602905:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.96/0.39 % (469718)Instruction limit reached!
% 0.96/0.39 % (469718)------------------------------
% 0.96/0.39 % (469718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (469718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (469718)CaDiCaL version: 2.1.3
% 0.96/0.39 % (469718)Termination reason: Instruction limit
% 0.96/0.39 % (469718)Termination phase: Function definition elimination
% 0.96/0.39 % (469718)Time elapsed: 0.004 s
% 0.96/0.39 % (469718)Peak memory usage: 10 MB
% 0.96/0.39 % (469718)Instructions burned: 9 (million)
% 0.96/0.39 % (469715)Instruction limit reached!
% 0.96/0.39 % (469715)------------------------------
% 0.96/0.43 % (469715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469715)CaDiCaL version: 2.1.3
% 0.96/0.43 % (469715)Termination reason: Instruction limit
% 0.96/0.43 % (469715)Termination phase: Saturation
% 0.96/0.43 % (469715)Time elapsed: 0.014 s
% 0.96/0.43 % (469715)Peak memory usage: 12 MB
% 0.96/0.43 % (469715)Instructions burned: 30 (million)
% 0.96/0.43 % (469721)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.96/0.43 % (469717)Instruction limit reached!
% 0.96/0.43 % (469717)------------------------------
% 0.96/0.43 % (469717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469717)CaDiCaL version: 2.1.3
% 0.96/0.43 % (469717)Termination reason: Instruction limit
% 0.96/0.43 % (469717)Termination phase: Saturation
% 0.96/0.43 % (469717)Time elapsed: 0.023 s
% 0.96/0.43 % (469717)Peak memory usage: 13 MB
% 0.96/0.43 % (469717)Instructions burned: 86 (million)
% 0.96/0.43 % (469721)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2411142120:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.96/0.43 % (469721)Instruction limit reached!
% 0.96/0.43 % (469721)------------------------------
% 0.96/0.43 % (469721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469721)CaDiCaL version: 2.1.3
% 0.96/0.43 % (469721)Termination reason: Instruction limit
% 0.96/0.43 % (469721)Termination phase: Property scanning
% 0.96/0.43 % (469721)Time elapsed: 0.003 s
% 0.96/0.43 % (469721)Peak memory usage: 10 MB
% 0.96/0.43 % (469721)Instructions burned: 6 (million)
% 0.96/0.43 % (469726)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2067104355:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.96/0.43 % (469723)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1013366026:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.96/0.43 % (469699)Instruction limit reached!
% 0.96/0.43 % (469699)------------------------------
% 0.96/0.43 % (469699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469699)CaDiCaL version: 2.1.3
% 0.96/0.43 % (469699)Termination reason: Instruction limit
% 0.96/0.43 % (469699)Termination phase: Saturation
% 0.96/0.43 % (469699)Time elapsed: 0.067 s
% 0.96/0.43 % (469699)Peak memory usage: 12 MB
% 0.96/0.43 % (469699)Instructions burned: 75 (million)
% 0.96/0.43 % (469700)Instruction limit reached!
% 0.96/0.43 % (469700)------------------------------
% 0.96/0.43 % (469700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469700)CaDiCaL version: 2.1.3
% 0.96/0.43 % (469700)Termination reason: Instruction limit
% 0.96/0.43 % (469700)Termination phase: Saturation
% 0.96/0.43 % (469700)Time elapsed: 0.080 s
% 0.96/0.43 % (469700)Peak memory usage: 13 MB
% 0.96/0.43 % (469700)Instructions burned: 158 (million)
% 0.96/0.43 % (469723)Refutation not found, incomplete strategy
% 0.96/0.43 % (469723)------------------------------
% 0.96/0.43 % (469723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469723)CaDiCaL version: 2.1.3
% 0.96/0.43 % (469723)Termination reason: Refutation not found, incomplete strategy
% 0.96/0.43 % (469723)Time elapsed: 0.006 s
% 0.96/0.43 % (469723)Peak memory usage: 12 MB
% 0.96/0.43 % (469723)Instructions burned: 12 (million)
% 0.96/0.43 % (469723)------------------------------
% 0.96/0.43 % (469723)------------------------------
% 0.96/0.43 % (469726)Instruction limit reached!
% 0.96/0.43 % (469726)------------------------------
% 0.96/0.43 % (469726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.43 % (469726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.43 % (469726)CaDiCaL version: 2.1.3
% 0.96/0.48 % (469726)Termination reason: Instruction limit
% 0.96/0.48 % (469726)Termination phase: Saturation
% 0.96/0.48 % (469726)Time elapsed: 0.009 s
% 0.96/0.48 % (469726)Peak memory usage: 12 MB
% 0.96/0.48 % (469726)Instructions burned: 29 (million)
% 0.96/0.48 % (469727)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2703156714:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.96/0.48 % (469732)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1064867840:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.96/0.48 % (469724)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2690079912:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.96/0.48 % (469732)Instruction limit reached!
% 0.96/0.48 % (469732)------------------------------
% 0.96/0.48 % (469732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.48 % (469732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.48 % (469732)CaDiCaL version: 2.1.3
% 0.96/0.48 % (469732)Termination reason: Instruction limit
% 0.96/0.48 % (469732)Termination phase: shuffling
% 0.96/0.48 % (469732)Time elapsed: 0.0000 s
% 0.96/0.48 % (469732)Peak memory usage: 9 MB
% 0.96/0.48 % (469732)Instructions burned: 2 (million)
% 0.96/0.48 % (469727)Instruction limit reached!
% 0.96/0.48 % (469727)------------------------------
% 0.96/0.48 % (469727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.48 % (469727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.48 % (469727)CaDiCaL version: 2.1.3
% 0.96/0.48 % (469727)Termination reason: Instruction limit
% 0.96/0.48 % (469727)Termination phase: Saturation
% 0.96/0.48 % (469727)Time elapsed: 0.012 s
% 0.96/0.48 % (469727)Peak memory usage: 11 MB
% 0.96/0.48 % (469727)Instructions burned: 14 (million)
% 0.96/0.48 % (469730)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1007622436:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.96/0.48 % (469724)Refutation not found, incomplete strategy
% 0.96/0.48 % (469724)------------------------------
% 0.96/0.48 % (469724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.48 % (469724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.48 % (469724)CaDiCaL version: 2.1.3
% 0.96/0.48 % (469724)Termination reason: Refutation not found, incomplete strategy
% 0.96/0.48 % (469724)Time elapsed: 0.009 s
% 0.96/0.48 % (469724)Peak memory usage: 12 MB
% 0.96/0.48 % (469724)Instructions burned: 9 (million)
% 0.96/0.48 % (469724)------------------------------
% 0.96/0.48 % (469724)------------------------------
% 0.96/0.48 % (469731)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2348488352:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.96/0.48 % (469737)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=114074879:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.96/0.48 % (469733)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2982361846:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.96/0.48 % (469739)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2201693986:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.96/0.48 % (469731)Instruction limit reached!
% 0.96/0.48 % (469731)------------------------------
% 0.96/0.48 % (469731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.48 % (469731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.48 % (469731)CaDiCaL version: 2.1.3
% 0.96/0.48 % (469731)Termination reason: Instruction limit
% 0.96/0.48 % (469731)Termination phase: Saturation
% 0.96/0.48 % (469731)Time elapsed: 0.010 s
% 0.96/0.48 % (469731)Peak memory usage: 12 MB
% 0.96/0.48 % (469731)Instructions burned: 15 (million)
% 0.96/0.48 % (469737)Instruction limit reached!
% 0.96/0.48 % (469737)------------------------------
% 0.96/0.48 % (469737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.48 % (469737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.48 % (469737)CaDiCaL version: 2.1.3
% 0.96/0.48 % (469737)Termination reason: Instruction limit
% 1.74/0.52 % (469737)Termination phase: Saturation
% 1.74/0.52 % (469737)Time elapsed: 0.013 s
% 1.74/0.52 % (469737)Peak memory usage: 11 MB
% 1.74/0.52 % (469737)Instructions burned: 23 (million)
% 1.74/0.52 % (469745)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.74/0.52 % (469740)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.74/0.52 % (469740)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.74/0.52 % (469745)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1405003184:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.74/0.52 % (469745)Instruction limit reached!
% 1.74/0.52 % (469745)------------------------------
% 1.74/0.52 % (469745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.52 % (469745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.52 % (469745)CaDiCaL version: 2.1.3
% 1.74/0.52 % (469745)Termination reason: Instruction limit
% 1.74/0.52 % (469745)Termination phase: Saturation
% 1.74/0.52 % (469745)Time elapsed: 0.003 s
% 1.74/0.52 % (469745)Peak memory usage: 11 MB
% 1.74/0.52 % (469745)Instructions burned: 15 (million)
% 1.74/0.52 % (469740)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=4043943551:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.74/0.52 % (469733)Instruction limit reached!
% 1.74/0.52 % (469733)------------------------------
% 1.74/0.52 % (469733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.52 % (469733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.52 % (469733)CaDiCaL version: 2.1.3
% 1.74/0.52 % (469733)Termination reason: Instruction limit
% 1.74/0.52 % (469733)Termination phase: Saturation
% 1.74/0.52 % (469733)Time elapsed: 0.023 s
% 1.74/0.52 % (469733)Peak memory usage: 12 MB
% 1.74/0.52 % (469733)Instructions burned: 26 (million)
% 1.74/0.52 % (469748)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3774540989:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.74/0.52 % (469748)Instruction limit reached!
% 1.74/0.52 % (469748)------------------------------
% 1.74/0.52 % (469748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.52 % (469748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.52 % (469748)CaDiCaL version: 2.1.3
% 1.74/0.52 % (469748)Termination reason: Instruction limit
% 1.74/0.52 % (469748)Termination phase: Property scanning
% 1.74/0.52 % (469748)Time elapsed: 0.002 s
% 1.74/0.52 % (469748)Peak memory usage: 10 MB
% 1.74/0.52 % (469748)Instructions burned: 10 (million)
% 1.74/0.52 % (469740)Instruction limit reached!
% 1.74/0.52 % (469740)------------------------------
% 1.74/0.52 % (469740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.52 % (469740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.52 % (469740)CaDiCaL version: 2.1.3
% 1.74/0.52 % (469740)Termination reason: Instruction limit
% 1.74/0.52 % (469740)Termination phase: Saturation
% 1.74/0.52 % (469740)Time elapsed: 0.012 s
% 1.74/0.52 % (469740)Peak memory usage: 11 MB
% 1.74/0.52 % (469740)Instructions burned: 14 (million)
% 1.74/0.52 % (469739)Instruction limit reached!
% 1.74/0.52 % (469739)------------------------------
% 1.74/0.52 % (469739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.74/0.52 % (469739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.74/0.52 % (469739)CaDiCaL version: 2.1.3
% 1.74/0.52 % (469739)Termination reason: Instruction limit
% 1.74/0.52 % (469739)Termination phase: Saturation
% 1.74/0.52 % (469739)Time elapsed: 0.034 s
% 1.74/0.52 % (469739)Peak memory usage: 12 MB
% 1.74/0.52 % (469739)Instructions burned: 62 (million)
% 1.74/0.52 % (469746)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=4160236830:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.74/0.52 % (469752)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3650912880:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.39/0.60 % (469750)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3615490875:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.39/0.60 % (469752)Instruction limit reached!
% 2.39/0.60 % (469752)------------------------------
% 2.39/0.60 % (469752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.60 % (469752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.60 % (469752)CaDiCaL version: 2.1.3
% 2.39/0.60 % (469752)Termination reason: Instruction limit
% 2.39/0.60 % (469752)Termination phase: Saturation
% 2.39/0.60 % (469752)Time elapsed: 0.006 s
% 2.39/0.60 % (469752)Peak memory usage: 12 MB
% 2.39/0.60 % (469752)Instructions burned: 22 (million)
% 2.39/0.60 % (469754)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=955316266:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.39/0.60 % (469759)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2447576855:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.39/0.60 % (469746)Instruction limit reached!
% 2.39/0.60 % (469746)------------------------------
% 2.39/0.60 % (469746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.60 % (469746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.60 % (469746)CaDiCaL version: 2.1.3
% 2.39/0.60 % (469746)Termination reason: Instruction limit
% 2.39/0.60 % (469746)Termination phase: Saturation
% 2.39/0.60 % (469746)Time elapsed: 0.025 s
% 2.39/0.60 % (469746)Peak memory usage: 12 MB
% 2.39/0.60 % (469746)Instructions burned: 31 (million)
% 2.39/0.60 % (469750)Instruction limit reached!
% 2.39/0.60 % (469750)------------------------------
% 2.39/0.60 % (469750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.60 % (469750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.60 % (469750)CaDiCaL version: 2.1.3
% 2.39/0.60 % (469750)Termination reason: Instruction limit
% 2.39/0.60 % (469750)Termination phase: Saturation
% 2.39/0.60 % (469750)Time elapsed: 0.014 s
% 2.39/0.60 % (469750)Peak memory usage: 11 MB
% 2.39/0.60 % (469750)Instructions burned: 24 (million)
% 2.39/0.60 % (469759)Refutation not found, incomplete strategy
% 2.39/0.60 % (469759)------------------------------
% 2.39/0.60 % (469759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.60 % (469759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.60 % (469759)CaDiCaL version: 2.1.3
% 2.39/0.60 % (469759)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.60 % (469759)Time elapsed: 0.004 s
% 2.39/0.60 % (469753)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1830920709:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.39/0.60 % (469759)Peak memory usage: 12 MB
% 2.39/0.60 % (469759)Instructions burned: 14 (million)
% 2.39/0.60 % (469759)------------------------------
% 2.39/0.60 % (469759)------------------------------
% 2.39/0.60 % (469765)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1279844029:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.39/0.60 % (469765)Refutation not found, incomplete strategy
% 2.39/0.60 % (469765)------------------------------
% 2.39/0.60 % (469765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.60 % (469765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.60 % (469765)CaDiCaL version: 2.1.3
% 2.39/0.60 % (469765)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.60 % (469765)Time elapsed: 0.004 s
% 2.39/0.60 % (469765)Peak memory usage: 12 MB
% 2.39/0.60 % (469765)Instructions burned: 12 (million)
% 2.39/0.60 % (469765)------------------------------
% 2.39/0.60 % (469765)------------------------------
% 2.39/0.60 % (469762)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2166098089:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.39/0.60 % (469763)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.39/0.60 % (469767)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1794990430:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.72/0.69 % (469763)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4056112249:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.72/0.69 % (469767)Refutation not found, incomplete strategy
% 2.72/0.69 % (469767)------------------------------
% 2.72/0.69 % (469767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.69 % (469767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.69 % (469767)CaDiCaL version: 2.1.3
% 2.72/0.69 % (469767)Termination reason: Refutation not found, incomplete strategy
% 2.72/0.69 % (469767)Time elapsed: 0.005 s
% 2.72/0.69 % (469767)Peak memory usage: 12 MB
% 2.72/0.69 % (469767)Instructions burned: 17 (million)
% 2.72/0.69 % (469767)------------------------------
% 2.72/0.69 % (469767)------------------------------
% 2.72/0.69 % (469763)Instruction limit reached!
% 2.72/0.69 % (469763)------------------------------
% 2.72/0.69 % (469763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.69 % (469763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.69 % (469763)CaDiCaL version: 2.1.3
% 2.72/0.69 % (469763)Termination reason: Instruction limit
% 2.72/0.69 % (469763)Termination phase: Property scanning
% 2.72/0.69 % (469763)Time elapsed: 0.005 s
% 2.72/0.69 % (469763)Peak memory usage: 10 MB
% 2.72/0.69 % (469763)Instructions burned: 7 (million)
% 2.72/0.69 % (469762)Instruction limit reached!
% 2.72/0.69 % (469762)------------------------------
% 2.72/0.69 % (469762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.69 % (469762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.69 % (469762)CaDiCaL version: 2.1.3
% 2.72/0.69 % (469762)Termination reason: Instruction limit
% 2.72/0.69 % (469762)Termination phase: Saturation
% 2.72/0.69 % (469762)Time elapsed: 0.021 s
% 2.72/0.69 % (469762)Peak memory usage: 12 MB
% 2.72/0.69 % (469762)Instructions burned: 43 (million)
% 2.72/0.69 % (469771)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.72/0.69 % (469771)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=465118856:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.72/0.69 % (469771)Instruction limit reached!
% 2.72/0.69 % (469771)------------------------------
% 2.72/0.69 % (469771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.69 % (469771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.69 % (469771)CaDiCaL version: 2.1.3
% 2.72/0.69 % (469771)Termination reason: Instruction limit
% 2.72/0.69 % (469771)Termination phase: Function definition elimination
% 2.72/0.69 % (469771)Time elapsed: 0.002 s
% 2.72/0.69 % (469771)Peak memory usage: 10 MB
% 2.72/0.69 % (469771)Instructions burned: 9 (million)
% 2.72/0.69 % (469772)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3165850513:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.72/0.69 % (469775)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3219867387:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.72/0.69 % (469773)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3677069630:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.72/0.69 % (469772)Instruction limit reached!
% 2.72/0.69 % (469772)------------------------------
% 2.72/0.69 % (469772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.69 % (469772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.69 % (469772)CaDiCaL version: 2.1.3
% 2.72/0.69 % (469772)Termination reason: Instruction limit
% 2.72/0.69 % (469772)Termination phase: Saturation
% 2.72/0.69 % (469772)Time elapsed: 0.011 s
% 2.72/0.69 % (469772)Peak memory usage: 12 MB
% 2.72/0.69 % (469772)Instructions burned: 23 (million)
% 2.72/0.69 % (469773)Refutation not found, incomplete strategy
% 2.72/0.69 % (469773)------------------------------
% 2.72/0.69 % (469773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.77 % (469773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.77 % (469773)CaDiCaL version: 2.1.3
% 3.04/0.77 % (469773)Termination reason: Refutation not found, incomplete strategy
% 3.04/0.77 % (469773)Time elapsed: 0.011 s
% 3.04/0.77 % (469773)Peak memory usage: 12 MB
% 3.04/0.77 % (469773)Instructions burned: 18 (million)
% 3.04/0.77 % (469773)------------------------------
% 3.04/0.77 % (469773)------------------------------
% 3.04/0.77 % (469730)Instruction limit reached!
% 3.04/0.77 % (469730)------------------------------
% 3.04/0.77 % (469730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.77 % (469730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.77 % (469730)CaDiCaL version: 2.1.3
% 3.04/0.77 % (469730)Termination reason: Instruction limit
% 3.04/0.77 % (469730)Termination phase: Saturation
% 3.04/0.77 % (469730)Time elapsed: 0.162 s
% 3.04/0.77 % (469730)Peak memory usage: 13 MB
% 3.04/0.77 % (469730)Instructions burned: 328 (million)
% 3.04/0.77 % (469780)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=648155397:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 3.04/0.77 % (469781)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2633334911:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 3.04/0.77 % (469782)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2855735955:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.04/0.77 % (469782)Refutation not found, incomplete strategy
% 3.04/0.77 % (469782)------------------------------
% 3.04/0.77 % (469782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.77 % (469782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.77 % (469782)CaDiCaL version: 2.1.3
% 3.04/0.77 % (469782)Termination reason: Refutation not found, incomplete strategy
% 3.04/0.77 % (469782)Time elapsed: 0.006 s
% 3.04/0.77 % (469782)Peak memory usage: 12 MB
% 3.04/0.77 % (469782)Instructions burned: 11 (million)
% 3.04/0.77 % (469782)------------------------------
% 3.04/0.77 % (469782)------------------------------
% 3.04/0.77 % (469781)Instruction limit reached!
% 3.04/0.77 % (469781)------------------------------
% 3.04/0.77 % (469781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.77 % (469781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.77 % (469781)CaDiCaL version: 2.1.3
% 3.04/0.77 % (469781)Termination reason: Instruction limit
% 3.04/0.77 % (469781)Termination phase: Saturation
% 3.04/0.77 % (469781)Time elapsed: 0.025 s
% 3.04/0.77 % (469781)Peak memory usage: 12 MB
% 3.04/0.77 % (469781)Instructions burned: 46 (million)
% 3.04/0.77 % (469754)Instruction limit reached!
% 3.04/0.77 % (469754)------------------------------
% 3.04/0.77 % (469754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.77 % (469754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.77 % (469754)CaDiCaL version: 2.1.3
% 3.04/0.77 % (469754)Termination reason: Instruction limit
% 3.04/0.77 % (469754)Termination phase: Saturation
% 3.04/0.77 % (469754)Time elapsed: 0.134 s
% 3.04/0.77 % (469754)Peak memory usage: 13 MB
% 3.04/0.77 % (469754)Instructions burned: 144 (million)
% 3.04/0.77 % (469786)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2082441391:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.04/0.77 % (469787)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.04/0.77 % (469787)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1168298962:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.04/0.77 % (469786)Instruction limit reached!
% 3.04/0.77 % (469786)------------------------------
% 3.04/0.77 % (469786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.77 % (469786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.92 % (469786)CaDiCaL version: 2.1.3
% 4.20/0.92 % (469786)Termination reason: Instruction limit
% 4.20/0.92 % (469786)Termination phase: Saturation
% 4.20/0.92 % (469786)Time elapsed: 0.015 s
% 4.20/0.92 % (469786)Peak memory usage: 12 MB
% 4.20/0.92 % (469786)Instructions burned: 21 (million)
% 4.20/0.92 % (469788)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3248877133:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 4.20/0.92 % (469775)Instruction limit reached!
% 4.20/0.92 % (469775)------------------------------
% 4.20/0.92 % (469775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.92 % (469775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.92 % (469775)CaDiCaL version: 2.1.3
% 4.20/0.92 % (469775)Termination reason: Instruction limit
% 4.20/0.92 % (469775)Termination phase: Saturation
% 4.20/0.92 % (469775)Time elapsed: 0.095 s
% 4.20/0.92 % (469775)Peak memory usage: 14 MB
% 4.20/0.92 % (469775)Instructions burned: 317 (million)
% 4.20/0.92 % (469788)Instruction limit reached!
% 4.20/0.92 % (469788)------------------------------
% 4.20/0.92 % (469788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.92 % (469788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.92 % (469788)CaDiCaL version: 2.1.3
% 4.20/0.92 % (469788)Termination reason: Instruction limit
% 4.20/0.92 % (469788)Termination phase: Saturation
% 4.20/0.92 % (469788)Time elapsed: 0.007 s
% 4.20/0.92 % (469788)Peak memory usage: 12 MB
% 4.20/0.92 % (469788)Instructions burned: 13 (million)
% 4.20/0.92 % (469793)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3502278860:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 4.20/0.92 % (469793)Refutation not found, incomplete strategy
% 4.20/0.92 % (469793)------------------------------
% 4.20/0.92 % (469793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.92 % (469793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.92 % (469793)CaDiCaL version: 2.1.3
% 4.20/0.92 % (469793)Termination reason: Refutation not found, incomplete strategy
% 4.20/0.92 % (469793)Time elapsed: 0.004 s
% 4.20/0.92 % (469793)Peak memory usage: 12 MB
% 4.20/0.92 % (469793)Instructions burned: 18 (million)
% 4.20/0.92 % (469793)------------------------------
% 4.20/0.92 % (469793)------------------------------
% 4.20/0.92 % (469791)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1233433984:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 4.20/0.92 % (469796)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2985794879:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 4.20/0.92 % (469794)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=964104782:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 4.20/0.92 % (469796)Instruction limit reached!
% 4.20/0.92 % (469796)------------------------------
% 4.20/0.92 % (469796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.92 % (469796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.92 % (469796)CaDiCaL version: 2.1.3
% 4.20/0.92 % (469796)Termination reason: Instruction limit
% 4.20/0.92 % (469796)Termination phase: Saturation
% 4.20/0.92 % (469796)Time elapsed: 0.041 s
% 4.20/0.92 % (469796)Peak memory usage: 13 MB
% 4.20/0.92 % (469796)Instructions burned: 142 (million)
% 4.20/0.92 % (469794)Instruction limit reached!
% 4.20/0.92 % (469794)------------------------------
% 4.20/0.92 % (469794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.92 % (469794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.92 % (469794)CaDiCaL version: 2.1.3
% 4.20/0.92 % (469794)Termination reason: Instruction limit
% 4.20/0.92 % (469794)Termination phase: Saturation
% 4.20/0.92 % (469794)Time elapsed: 0.025 s
% 4.20/0.92 % (469794)Peak memory usage: 12 MB
% 4.20/0.92 % (469794)Instructions burned: 31 (million)
% 4.20/0.92 % (469800)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=881635573:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.20/0.92 % (469791)Instruction limit reached!
% 4.20/0.92 % (469791)------------------------------
% 5.33/1.06 % (469791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.33/1.06 % (469791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.06 % (469791)CaDiCaL version: 2.1.3
% 5.33/1.06 % (469791)Termination reason: Instruction limit
% 5.33/1.06 % (469791)Termination phase: Saturation
% 5.33/1.06 % (469791)Time elapsed: 0.067 s
% 5.33/1.06 % (469791)Peak memory usage: 13 MB
% 5.33/1.06 % (469791)Instructions burned: 66 (million)
% 5.33/1.06 % (469800)Instruction limit reached!
% 5.33/1.06 % (469800)------------------------------
% 5.33/1.06 % (469800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.33/1.06 % (469800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.06 % (469800)CaDiCaL version: 2.1.3
% 5.33/1.06 % (469800)Termination reason: Instruction limit
% 5.33/1.06 % (469800)Termination phase: Saturation
% 5.33/1.06 % (469800)Time elapsed: 0.010 s
% 5.33/1.06 % (469800)Peak memory usage: 12 MB
% 5.33/1.06 % (469800)Instructions burned: 37 (million)
% 5.33/1.06 % (469801)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3073504594:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.33/1.06 % (469804)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.33/1.06 % (469804)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3463079075:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.33/1.06 % (469801)Refutation not found, incomplete strategy
% 5.33/1.06 % (469801)------------------------------
% 5.33/1.06 % (469801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.33/1.06 % (469801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.06 % (469801)CaDiCaL version: 2.1.3
% 5.33/1.06 % (469801)Termination reason: Refutation not found, incomplete strategy
% 5.33/1.06 % (469801)Time elapsed: 0.010 s
% 5.33/1.06 % (469801)Peak memory usage: 12 MB
% 5.33/1.06 % (469801)Instructions burned: 18 (million)
% 5.33/1.06 % (469801)------------------------------
% 5.33/1.06 % (469801)------------------------------
% 5.33/1.06 % (469807)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3284973841:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 5.33/1.06 % (469805)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3702689931:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 5.33/1.06 % (469805)Refutation not found, incomplete strategy
% 5.33/1.06 % (469805)------------------------------
% 5.33/1.06 % (469805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.33/1.06 % (469805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.06 % (469805)CaDiCaL version: 2.1.3
% 5.33/1.06 % (469805)Termination reason: Refutation not found, incomplete strategy
% 5.33/1.06 % (469805)Time elapsed: 0.016 s
% 5.33/1.06 % (469805)Peak memory usage: 12 MB
% 5.33/1.06 % (469805)Instructions burned: 17 (million)
% 5.33/1.06 % (469805)------------------------------
% 5.33/1.06 % (469805)------------------------------
% 5.33/1.06 % (469804)Instruction limit reached!
% 5.33/1.06 % (469804)------------------------------
% 5.33/1.06 % (469804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.33/1.06 % (469804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.06 % (469804)CaDiCaL version: 2.1.3
% 5.33/1.06 % (469804)Termination reason: Instruction limit
% 5.33/1.06 % (469804)Termination phase: Saturation
% 5.33/1.06 % (469804)Time elapsed: 0.047 s
% 5.33/1.06 % (469804)Peak memory usage: 13 MB
% 5.33/1.06 % (469804)Instructions burned: 182 (million)
% 5.33/1.06 % (469811)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1728073780:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.33/1.06 % (469787)Instruction limit reached!
% 5.33/1.06 % (469787)------------------------------
% 5.33/1.06 % (469787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.33/1.06 % (469787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.06 % (469787)CaDiCaL version: 2.1.3
% 5.33/1.06 % (469787)Termination reason: Instruction limit
% 5.33/1.06 % (469787)Termination phase: Saturation
% 5.33/1.06 % (469787)Time elapsed: 0.183 s
% 5.33/1.06 % (469787)Peak memory usage: 12 MB
% 5.33/1.06 % (469787)Instructions burned: 201 (million)
% 6.00/1.18 % (469813)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=4199397480:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 6.00/1.18 % (469810)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4200913315:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 6.00/1.18 % (469810)Refutation not found, incomplete strategy
% 6.00/1.18 % (469810)------------------------------
% 6.00/1.18 % (469810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469810)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469810)Termination reason: Refutation not found, incomplete strategy
% 6.00/1.18 % (469810)Time elapsed: 0.013 s
% 6.00/1.18 % (469810)Peak memory usage: 12 MB
% 6.00/1.18 % (469810)Instructions burned: 7 (million)
% 6.00/1.18 % (469810)------------------------------
% 6.00/1.18 % (469810)------------------------------
% 6.00/1.18 % (469807)Instruction limit reached!
% 6.00/1.18 % (469807)------------------------------
% 6.00/1.18 % (469807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469807)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469807)Termination reason: Instruction limit
% 6.00/1.18 % (469807)Termination phase: Saturation
% 6.00/1.18 % (469807)Time elapsed: 0.096 s
% 6.00/1.18 % (469807)Peak memory usage: 12 MB
% 6.00/1.18 % (469807)Instructions burned: 96 (million)
% 6.00/1.18 % (469816)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3334327436:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 6.00/1.18 % (469817)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=112712369:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 6.00/1.18 % (469697)Instruction limit reached!
% 6.00/1.18 % (469697)------------------------------
% 6.00/1.18 % (469697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469697)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469697)Termination reason: Instruction limit
% 6.00/1.18 % (469697)Termination phase: Saturation
% 6.00/1.18 % (469697)Time elapsed: 0.580 s
% 6.00/1.18 % (469697)Peak memory usage: 15 MB
% 6.00/1.18 % (469697)Instructions burned: 634 (million)
% 6.00/1.18 % (469820)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2113380777:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 6.00/1.18 % (469820)Refutation not found, incomplete strategy
% 6.00/1.18 % (469820)------------------------------
% 6.00/1.18 % (469820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469820)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469820)Termination reason: Refutation not found, incomplete strategy
% 6.00/1.18 % (469820)Time elapsed: 0.006 s
% 6.00/1.18 % (469820)Peak memory usage: 12 MB
% 6.00/1.18 % (469820)Instructions burned: 12 (million)
% 6.00/1.18 % (469820)------------------------------
% 6.00/1.18 % (469820)------------------------------
% 6.00/1.18 % (469817)Instruction limit reached!
% 6.00/1.18 % (469817)------------------------------
% 6.00/1.18 % (469817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469817)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469817)Termination reason: Instruction limit
% 6.00/1.18 % (469817)Termination phase: Saturation
% 6.00/1.18 % (469817)Time elapsed: 0.041 s
% 6.00/1.18 % (469817)Peak memory usage: 12 MB
% 6.00/1.18 % (469817)Instructions burned: 44 (million)
% 6.00/1.18 % (469822)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3459766638:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.00/1.18 % (469813)Instruction limit reached!
% 6.00/1.18 % (469813)------------------------------
% 6.00/1.18 % (469813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469813)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469813)Termination reason: Instruction limit
% 6.00/1.18 % (469813)Termination phase: Saturation
% 6.00/1.18 % (469813)Time elapsed: 0.140 s
% 6.00/1.18 % (469813)Peak memory usage: 14 MB
% 6.00/1.18 % (469813)Instructions burned: 518 (million)
% 6.00/1.18 % (469823)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=544639845:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 6.00/1.18 % (469816)Instruction limit reached!
% 6.00/1.18 % (469816)------------------------------
% 6.00/1.18 % (469816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469816)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469816)Termination reason: Instruction limit
% 6.00/1.18 % (469816)Termination phase: Saturation
% 6.00/1.18 % (469816)Time elapsed: 0.098 s
% 6.00/1.18 % (469816)Peak memory usage: 13 MB
% 6.00/1.18 % (469816)Instructions burned: 130 (million)
% 6.00/1.18 % (469825)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=1819737182:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 6.00/1.18 % (469825)Instruction limit reached!
% 6.00/1.18 % (469825)------------------------------
% 6.00/1.18 % (469825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469825)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469825)Termination reason: Instruction limit
% 6.00/1.18 % (469825)Termination phase: Saturation
% 6.00/1.18 % (469825)Time elapsed: 0.019 s
% 6.00/1.18 % (469825)Peak memory usage: 12 MB
% 6.00/1.18 % (469825)Instructions burned: 66 (million)
% 6.00/1.18 % (469829)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3915024629:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 6.00/1.18 % (469828)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2232698118:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 6.00/1.18 % (469780)Instruction limit reached!
% 6.00/1.18 % (469780)------------------------------
% 6.00/1.18 % (469780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469780)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469780)Termination reason: Instruction limit
% 6.00/1.18 % (469780)Termination phase: Saturation
% 6.00/1.18 % (469780)Time elapsed: 0.431 s
% 6.00/1.18 % (469780)Peak memory usage: 14 MB
% 6.00/1.18 % (469780)Instructions burned: 853 (million)
% 6.00/1.18 % (469832)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=1999253754:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 6.00/1.18 % (469823)Instruction limit reached!
% 6.00/1.18 % (469823)------------------------------
% 6.00/1.18 % (469823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469823)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469823)Termination reason: Instruction limit
% 6.00/1.18 % (469823)Termination phase: Saturation
% 6.00/1.18 % (469823)Time elapsed: 0.082 s
% 6.00/1.18 % (469823)Peak memory usage: 12 MB
% 6.00/1.18 % (469823)Instructions burned: 95 (million)
% 6.00/1.18 % (469828)Instruction limit reached!
% 6.00/1.18 % (469828)------------------------------
% 6.00/1.18 % (469828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469828)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469828)Termination reason: Instruction limit
% 6.00/1.18 % (469828)Termination phase: Saturation
% 6.00/1.18 % (469828)Time elapsed: 0.067 s
% 6.00/1.18 % (469828)Peak memory usage: 13 MB
% 6.00/1.18 % (469828)Instructions burned: 105 (million)
% 6.00/1.18 % (469834)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2606460519:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.00/1.18 % (469835)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=368574472:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 6.00/1.18 % (469835)Instruction limit reached!
% 6.00/1.18 % (469835)------------------------------
% 6.00/1.18 % (469835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469835)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469835)Termination reason: Instruction limit
% 6.00/1.18 % (469835)Termination phase: Saturation
% 6.00/1.18 % (469835)Time elapsed: 0.019 s
% 6.00/1.18 % (469835)Peak memory usage: 12 MB
% 6.00/1.18 % (469835)Instructions burned: 34 (million)
% 6.00/1.18 % (469838)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4138740184:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/91Mi)
% 6.00/1.18 % (469838)Instruction limit reached!
% 6.00/1.18 % (469838)------------------------------
% 6.00/1.18 % (469838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469838)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469838)Termination reason: Instruction limit
% 6.00/1.18 % (469838)Termination phase: Saturation
% 6.00/1.18 % (469838)Time elapsed: 0.051 s
% 6.00/1.18 % (469838)Peak memory usage: 13 MB
% 6.00/1.18 % (469838)Instructions burned: 91 (million)
% 6.00/1.18 % (469811) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-469689-469811"...
% 6.00/1.18 % (469840)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=1271389539:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2990 on theBenchmark for (2990ds/66Mi)
% 6.00/1.18 % (469840)Refutation not found, incomplete strategy
% 6.00/1.18 % (469840)------------------------------
% 6.00/1.18 % (469840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469840)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469840)Termination reason: Refutation not found, incomplete strategy
% 6.00/1.18 % (469840)Time elapsed: 0.007 s
% 6.00/1.18 % (469840)Peak memory usage: 12 MB
% 6.00/1.18 % (469840)Instructions burned: 11 (million)
% 6.00/1.18 % (469840)------------------------------
% 6.00/1.18 % (469840)------------------------------
% 6.00/1.18 % (469811)...printing done.
% 6.00/1.18 % (469811)Refutation found. Thanks to Tanya!
% 6.00/1.18 % SZS status Theorem for theBenchmark
% 6.00/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 6.00/1.18 % (469811)------------------------------
% 6.00/1.18 % (469811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.00/1.18 % (469811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.18 % (469811)CaDiCaL version: 2.1.3
% 6.00/1.18 % (469811)Termination reason: Refutation
% 6.00/1.18 % (469811)Time elapsed: 0.405 s
% 6.00/1.18 % (469811)Peak memory usage: 15 MB
% 6.00/1.18 % (469811)Instructions burned: 819 (million)
% 6.00/1.18 % (469689)Success in time 0.952 s
% 6.00/1.18 % Vampire exiting
%------------------------------------------------------------------------------