%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG013^1 : 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 07:49:26 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 76 unt; 0 typ; 2 def)
% Number of atoms : 732 ( 97 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1591 ( 106 ~; 37 |; 105 &;1078 @)
% ( 2 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 79 usr; 15 con; 0-4 aty)
% ( 109 !!; 55 ??; 0 @@+; 0 @@-)
% Number of variables : 407 ( 12 sgn 61 !; 10 ?; 407 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vAND: $o > $o > $o ).
thf(func_def_58,type,
vNOT: $o > $o ).
thf(func_def_59,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_60,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_62,type,
vOR: $o > $o > $o ).
thf(func_def_63,type,
sK0: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK1: reg > reg ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg ).
thf(func_def_67,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_70,type,
sK7: reg ).
thf(func_def_71,type,
sK8: reg ).
thf(func_def_72,type,
sK9: reg > reg ).
thf(func_def_73,type,
sK10: reg > reg ).
thf(func_def_74,type,
sK11: reg > reg ).
thf(func_def_75,type,
sK12: reg > reg ).
thf(func_def_76,type,
sK13: reg > reg ).
thf(func_def_77,type,
sK14: reg > reg ).
thf(func_def_78,type,
sK15: $i > ( $i > $o ) > $i ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
! [X0: reg] : ( c @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',c_reflexive) ).
thf(f35,axiom,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f36,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) )
= eq ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f42,axiom,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ntpp) ).
thf(f48,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f49,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X2: reg,X1: reg] :
~ ( eq @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X2: reg,X1: reg] :
~ ( eq @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f59,plain,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) )
= eq ),
inference(rectify,[],[f36]) ).
thf(f60,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f68,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f69,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f72,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f73,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f83,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f84,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f99,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f100,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f106,plain,
! [X0: reg] : ( c @ X0 @ X0 ),
inference(rectify,[],[f32]) ).
thf(f107,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f106]) ).
thf(f110,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ( pp @ X0 @ X1 )
& ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f111,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f110]) ).
thf(f117,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f118,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f121,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f122,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f130,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg,X2: reg] :
~ ( eq @ X2 @ X1 ) ) ),
inference(rectify,[],[f50]) ).
thf(f131,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( eq @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f136,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f137,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( eq @ Y1 @ Y2 ) ) ) ) ) ),
inference(flattening,[],[f131]) ).
thf(f142,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f145,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f107]) ).
thf(f156,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f157,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) )
& ( pp @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f161,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f165,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f181,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f182,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f184,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f187,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( eq @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f188,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f201,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f182,f165,f165]) ).
thf(f202,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f161,f165,f165]) ).
thf(f204,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f181,f202]) ).
thf(f205,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f156,f165,f165]) ).
thf(f207,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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ 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
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 ) ) )
& ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f157,f204,f204,f205]) ).
thf(f208,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ 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
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 ) ) )
& ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f142,f184,f188,f207]) ).
thf(f214,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f187,f184,f188,f201]) ).
thf(f227,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f228,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) ) )
| ~ ( a @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
| ~ ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) )
@ sK3 ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( c @ sK3 @ france )
=> ( c @ sK3 @ paris ) ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( c @ sK3 @ paris ) )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f280]) ).
thf(f308,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f309,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) )
| ~ ( a @ Y0 @ Y1 ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) )
| ~ ( a @ sK5 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
( ( ^ [Y0: $i] :
( ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) )
| ~ ( a @ sK5 @ Y0 ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f310]) ).
thf(f312,plain,
( $false
= ( ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) )
| ~ ( a @ sK5 @ sK6 ) ) ),
inference(beta-eta_normalization,[],[f311]) ).
thf(f313,plain,
( $false
= ( ~ ( a @ sK5 @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f314,plain,
( ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f315,plain,
! [X1: reg] :
( $false
= ( ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X1: reg] :
( ( ?? @ reg
@ ^ [Y0: reg] :
~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f315]) ).
thf(f317,plain,
! [X2: reg,X1: reg] :
( $false
= ( ^ [Y0: reg] :
~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: reg,X1: reg] :
( $false
= ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f319,plain,
! [X2: reg,X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f318]) ).
thf(f321,plain,
! [X2: reg,X1: reg] :
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f319]) ).
thf(f322,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f324,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f323]) ).
thf(f328,plain,
( $true
= ( a @ sK5 @ sK6 ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f422,definition,
( spl16_1
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f423,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f422]) ).
thf(f450,definition,
( spl16_8
<=> ( $false
= ( c @ sK3 @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f452,plain,
( ( $false
= ( c @ sK3 @ paris ) )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f450]) ).
thf(f453,plain,
( spl16_1
| spl16_8 ),
inference(avatar_split_clause,[],[f281,f450,f422]) ).
thf(f535,plain,
! [X0: reg,X1: reg] :
( ( ( c @ X0 @ X1 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f145,f324]) ).
thf(f537,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
= $true ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f548,plain,
( ! [X0: reg] :
( ( $false = $true )
| ( $false
= ( c @ sK3 @ X0 ) ) )
| ~ spl16_8 ),
inference(constrained_superposition,[],[f452,f324]) ).
thf(f556,plain,
( ! [X0: reg] :
( $false
= ( c @ sK3 @ X0 ) )
| ~ spl16_8 ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f560,plain,
( ( $false = $true )
| ~ spl16_8 ),
inference(forward_demodulation,[],[f556,f537]) ).
thf(f561,plain,
( $false
| ~ spl16_8 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f562,plain,
~ spl16_8,
inference(avatar_contradiction_clause,[],[f561]) ).
thf(f565,plain,
( ( $false = $true )
| ~ spl16_1 ),
inference(constrained_superposition,[],[f328,f423]) ).
thf(f568,plain,
( $false
| ~ spl16_1 ),
inference(trivial_inequality_removal,[],[f565]) ).
thf(f569,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f568]) ).
cnf(s7,plain,
( spl16_1
| spl16_8 ),
inference(sat_conversion,[],[f453]) ).
cnf(s28,plain,
~ spl16_8,
inference(sat_conversion,[],[f562]) ).
cnf(s30,plain,
~ spl16_1,
inference(sat_conversion,[],[f569]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s7,s28,s30]) ).
thf(f570,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG013^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:36:26 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.31 % (470277)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (470285)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=2299700758:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.31 % (470283)lrs+10_16_si=on:nwc=1.5:random_seed=2368593628:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (470282)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2211316069:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (470286)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2720573171:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (470284)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3432840649:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (470287)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3896790528:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (470284)Instruction limit reached!
% 0.20/0.31 % (470284)------------------------------
% 0.20/0.31 % (470284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (470284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (470284)CaDiCaL version: 2.1.3
% 0.20/0.31 % (470284)Termination reason: Instruction limit
% 0.20/0.31 % (470284)Termination phase: Property scanning
% 0.20/0.31 % (470284)Time elapsed: 0.004 s
% 0.20/0.31 % (470284)Peak memory usage: 10 MB
% 0.20/0.31 % (470284)Instructions burned: 8 (million)
% 0.20/0.31 % (470283)Instruction limit reached!
% 0.20/0.31 % (470283)------------------------------
% 0.20/0.31 % (470283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (470283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (470283)CaDiCaL version: 2.1.3
% 0.20/0.31 % (470283)Termination reason: Instruction limit
% 0.20/0.31 % (470283)Termination phase: Saturation
% 0.20/0.31 % (470283)Time elapsed: 0.009 s
% 0.20/0.31 % (470283)Peak memory usage: 11 MB
% 0.20/0.31 % (470283)Instructions burned: 19 (million)
% 0.20/0.31 % (470288)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (470288)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.31 % (470286)Instruction limit reached!
% 0.20/0.31 % (470286)------------------------------
% 0.20/0.31 % (470286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (470286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (470286)CaDiCaL version: 2.1.3
% 0.20/0.31 % (470286)Termination reason: Instruction limit
% 0.20/0.31 % (470286)Termination phase: Saturation
% 0.20/0.31 % (470286)Time elapsed: 0.014 s
% 0.20/0.31 % (470286)Peak memory usage: 11 MB
% 0.20/0.31 % (470286)Instructions burned: 25 (million)
% 0.20/0.31 % (470282) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-470277-470282"...
% 0.20/0.31 % (470288)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=2131787530:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (470287) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-470277-470287"...
% 0.20/0.31 % (470282)...printing done.
% 0.20/0.31 % (470282)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.31 % (470282)------------------------------
% 0.20/0.31 % (470282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (470282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (470282)CaDiCaL version: 2.1.3
% 0.20/0.31 % (470282)Termination reason: Refutation
% 0.20/0.31 % (470282)Time elapsed: 0.020 s
% 0.20/0.31 % (470282)Peak memory usage: 13 MB
% 0.20/0.31 % (470282)Instructions burned: 39 (million)
% 0.20/0.31 % (470277)Success in time 0.067 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------