%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n007.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 07:49:29 AM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 101 ( 76 unt; 0 typ; 2 def)
% Number of atoms : 700 ( 94 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1520 ( 104 ~; 34 |; 98 &;1033 @)
% ( 2 <=>; 94 =>; 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)
% ( 103 !!; 52 ??; 0 @@+; 0 @@-)
% Number of variables : 397 ( 12 sgn 59 !; 10 ?; 397 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
reg: $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
c: reg > reg > $o ).
thf(func_def_33,type,
dc: reg > reg > $o ).
thf(func_def_34,type,
p: reg > reg > $o ).
thf(func_def_35,type,
eq: reg > reg > $o ).
thf(func_def_36,type,
o: reg > reg > $o ).
thf(func_def_37,type,
po: reg > reg > $o ).
thf(func_def_38,type,
ec: reg > reg > $o ).
thf(func_def_39,type,
pp: reg > reg > $o ).
thf(func_def_40,type,
tpp: reg > reg > $o ).
thf(func_def_41,type,
ntpp: reg > reg > $o ).
thf(func_def_42,type,
catalunya: reg ).
thf(func_def_43,type,
france: reg ).
thf(func_def_44,type,
spain: reg ).
thf(func_def_45,type,
paris: reg ).
thf(func_def_46,type,
a: $i > $i > $o ).
thf(func_def_47,type,
fool: $i > $i > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vOR: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_58,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
sK2: reg ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_67,type,
sK4: reg > reg ).
thf(func_def_68,type,
sK5: reg > reg ).
thf(func_def_69,type,
sK6: reg > reg ).
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: $i > ( $i > $o ) > $i ).
thf(func_def_77,type,
sK14: $i > ( $i > $o ) > $i ).
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] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(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,
( eq
= ( ^ [X0: reg,X1: reg] :
( ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
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,
( 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] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
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] :
? [X1: reg,X2: reg] :
~ ( eq @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg,X2: reg] :
~ ( eq @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f71,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f72,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f94,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f102,plain,
! [X0: reg] : ( c @ X0 @ X0 ),
inference(rectify,[],[f32]) ).
thf(f103,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f102]) ).
thf(f108,plain,
( p
= ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f109,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f110,plain,
( eq
= ( ^ [X0: reg,X1: reg] :
( ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f111,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f110]) ).
thf(f112,plain,
( o
= ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X1 )
& ( p @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f113,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f112]) ).
thf(f116,plain,
( ec
= ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f117,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f116]) ).
thf(f118,plain,
( pp
= ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f119,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f122,plain,
( ntpp
= ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X1 )
& ( ec @ X2 @ X0 ) )
& ( pp @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f123,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f134,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f135,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f136,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg,X2: reg] :
~ ( eq @ X1 @ X2 ) ) ),
inference(rectify,[],[f50]) ).
thf(f137,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( eq @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f138,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( eq @ Y2 @ Y1 ) ) ) ) ) ),
inference(flattening,[],[f137]) ).
thf(f155,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f167,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f171,plain,
! [X0: reg] :
( ( c @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f103]) ).
thf(f174,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f175,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f176,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y0 )
& ( p @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f113]) ).
thf(f178,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f117]) ).
thf(f179,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f181,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y0 )
& ( ec @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f187,plain,
( $true
= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f188,plain,
( $true
!= ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( eq @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f200,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,[],[f175,f174,f174]) ).
thf(f201,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y0 )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f176,f174,f174]) ).
thf(f203,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( ?? @ reg
@ ^ [Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y2 )
& ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f178,f201]) ).
thf(f204,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 )
& ~ ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f179,f174,f174]) ).
thf(f206,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ 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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f181,f204,f203,f203]) ).
thf(f212,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] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ 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 ) ) ) )
@ paris
@ france ) ) ) ),
inference(definition_unfolding,[],[f187,f167,f155,f206]) ).
thf(f213,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] :
( ?? @ 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 ) )
@ Y2
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f188,f167,f155,f200]) ).
thf(f214,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( a @ sK0 @ Y0 )
| ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 )
| ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( $false
= ( ~ ( a @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( $true
= ( a @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: reg] :
( $false
= ( ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f223,plain,
! [X1: reg] :
( $false
= ( ?? @ reg
@ ^ [Y0: reg] :
~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: reg,X1: reg] :
( $false
= ( ^ [Y0: reg] :
~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: reg,X1: reg] :
( $false
= ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: reg,X1: reg] :
( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f228,plain,
! [X2: reg,X1: reg] :
( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f229,plain,
! [X2: reg,X3: reg,X1: reg] :
( $true
= ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: reg,X3: reg,X1: reg] :
( $true
= ( ( c @ X3 @ X2 )
=> ( c @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $false
= ( c @ X3 @ X2 ) )
| ( $true
= ( c @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f235,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ 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 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f236,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ 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 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ 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 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ 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 ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ 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 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ 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 ) ) ) ),
inference(or_proxy_clausification,[],[f239]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f240]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) )
@ sK2 ) )
| ( $true
= ( ~ ( a @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) )
@ sK2 ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( c @ sK2 @ france )
=> ( c @ sK2 @ paris ) ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( c @ sK2 @ paris ) )
| ( $false
= ( a @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f421,definition,
( spl16_1
<=> ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f422,plain,
( ! [X2: $i,X1: $i] :
( $false
= ( a @ X1 @ X2 ) )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f421]) ).
thf(f429,definition,
( spl16_3
<=> ( $false
= ( c @ sK2 @ paris ) ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f431,plain,
( ( $false
= ( c @ sK2 @ paris ) )
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f432,plain,
( spl16_1
| spl16_3 ),
inference(avatar_split_clause,[],[f253,f429,f421]) ).
thf(f524,plain,
! [X0: reg,X1: reg] :
( ( $true = $false )
| ( ( c @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f231,f171]) ).
thf(f525,plain,
! [X0: reg,X1: reg] :
( ( c @ X0 @ X1 )
= $true ),
inference(trivial_inequality_removal,[],[f524]) ).
thf(f534,plain,
( ( $true = $false )
| ~ spl16_3 ),
inference(constrained_superposition,[],[f431,f525]) ).
thf(f540,plain,
( $false
| ~ spl16_3 ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f541,plain,
~ spl16_3,
inference(avatar_contradiction_clause,[],[f540]) ).
thf(f542,plain,
( ( $true = $false )
| ~ spl16_1 ),
inference(constrained_superposition,[],[f422,f221]) ).
thf(f548,plain,
( $false
| ~ spl16_1 ),
inference(trivial_inequality_removal,[],[f542]) ).
thf(f549,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f548]) ).
cnf(s2,plain,
( spl16_1
| spl16_3 ),
inference(sat_conversion,[],[f432]) ).
cnf(s22,plain,
~ spl16_3,
inference(sat_conversion,[],[f541]) ).
cnf(s24,plain,
~ spl16_1,
inference(sat_conversion,[],[f549]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s2,s22,s24]) ).
thf(f550,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEG013^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 % Computer : n007.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 18:32:11 UTC 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.33 Running first-order model finding
% 0.26/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.38 % (3754919)Will run a generic schedule for satisfiability detection.
% 0.26/0.38 % (3754930)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=884351876:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.38 % (3754925)% WARNING: option uhcvi not known.
% 0.26/0.38 % (3754926)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=760006848:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.38 % (3754928)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3164990566:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.38 % (3754925)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2308868784:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.26/0.38 % (3754927)dis+10_1_sil=32000:sp=arity:random_seed=3915131275:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.38 % (3754929)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3117359734:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.38 % (3754924)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=41744565_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.38 % (3754930) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3754919-3754930"...
% 0.26/0.38 % (3754928)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.38 % (3754925)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.38 % (3754930)...printing done.
% 0.26/0.38 % (3754930)Refutation found. Thanks to Tanya!
% 0.26/0.38 % SZS status Theorem for theBenchmark
% 0.26/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.55/0.38 % (3754930)------------------------------
% 0.55/0.38 % (3754930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.38 % (3754930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.38 % (3754930)CaDiCaL version: 2.1.3
% 0.55/0.38 % (3754930)Termination reason: Refutation
% 0.55/0.38 % (3754930)Time elapsed: 0.018 s
% 0.55/0.38 % (3754930)Peak memory usage: 13 MB
% 0.55/0.38 % (3754930)Instructions burned: 36 (million)
% 0.55/0.38 % (3754919)Success in time 0.045 s
% 0.55/0.38 % Vampire exiting
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