%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG015^1 : 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 : n005.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 0.77s 0.48s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of formulae : 154 ( 72 unt; 0 typ; 8 def)
% Number of atoms : 1277 ( 213 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 2426 ( 143 ~; 163 |; 143 &;1614 @)
% ( 8 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 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 : 94 ( 89 usr; 21 con; 0-4 aty)
% ( 147 !!; 55 ??; 0 @@+; 0 @@-)
% Number of variables : 524 ( 12 sgn 130 !; 10 ?; 524 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
vNOT: $o > $o ).
thf(func_def_60,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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: $i > ( $i > $o ) > $i ).
thf(func_def_65,type,
sK2: reg > reg ).
thf(func_def_66,type,
sK3: reg > reg ).
thf(func_def_69,type,
sK6: reg > reg ).
thf(func_def_70,type,
sK7: reg > reg ).
thf(func_def_71,type,
sK8: reg > reg ).
thf(func_def_72,type,
sK9: reg > reg ).
thf(func_def_73,type,
sK10: 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: reg ).
thf(func_def_78,type,
sK15: reg ).
thf(func_def_79,type,
sK16: reg > reg ).
thf(func_def_80,type,
sK17: reg > reg ).
thf(func_def_81,type,
sK18: reg > reg ).
thf(func_def_82,type,
sK19: reg > reg ).
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(f35,axiom,
( ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) )
= p ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',p) ).
thf(f36,axiom,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',eq) ).
thf(f37,axiom,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',o) ).
thf(f39,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) )
= ec ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',ec) ).
thf(f40,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) )
= pp ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL014^0.ax',pp) ).
thf(f42,axiom,
( ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) )
= ntpp ),
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 )
& ( p @ X2 @ france )
& ( p @ X1 @ france ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f50,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg,X2: reg] :
( ~ ( eq @ X1 @ X2 )
& ( p @ X2 @ france )
& ( p @ X1 @ france ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f59,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ( p @ X1 @ X0 )
& ( p @ X0 @ X1 ) ) )
= pp ),
inference(rectify,[],[f40]) ).
thf(f60,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f67,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f68,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f74,plain,
( ( ^ [X0: reg,X1: reg] :
? [X2: reg] :
( ( p @ X2 @ X0 )
& ( p @ X2 @ X1 ) ) )
= o ),
inference(rectify,[],[f37]) ).
thf(f75,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f80,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ? [X2: reg] :
( ( ec @ X2 @ X0 )
& ( ec @ X2 @ X1 ) )
& ( pp @ X0 @ X1 ) ) )
= ntpp ),
inference(rectify,[],[f42]) ).
thf(f81,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f90,plain,
( mvalid
@ ( mbox @ a
@ ^ [X0: $i] : ( ntpp @ paris @ france ) ) ),
inference(rectify,[],[f48]) ).
thf(f91,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f102,plain,
( ( ^ [X0: reg,X1: reg] :
( ( p @ X0 @ X1 )
& ( p @ X1 @ X0 ) ) )
= eq ),
inference(rectify,[],[f36]) ).
thf(f103,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f106,plain,
~ ( mvalid
@ ( mbox @ a
@ ^ [X0: $i] :
? [X1: reg,X2: reg] :
( ~ ( eq @ X1 @ X2 )
& ( p @ X2 @ france )
& ( p @ X1 @ france ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f107,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ france )
& ( p @ Y1 @ france )
& ~ ( eq @ Y2 @ Y1 ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f106]) ).
thf(f108,plain,
( ( ^ [X0: reg,X1: reg] :
! [X2: reg] :
( ( c @ X2 @ X0 )
=> ( c @ X2 @ X1 ) ) )
= p ),
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(f114,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f115,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f114]) ).
thf(f126,plain,
( ( ^ [X0: reg,X1: reg] :
( ~ ( o @ X0 @ X1 )
& ( c @ X0 @ X1 ) ) )
= ec ),
inference(rectify,[],[f39]) ).
thf(f127,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f126]) ).
thf(f138,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ france )
& ( p @ Y1 @ france )
& ~ ( eq @ Y2 @ Y1 ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f107]) ).
thf(f141,plain,
( o
= ( ^ [Y0: reg,Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ Y1 )
& ( p @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f150,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] :
( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( p @ Y2 @ france )
& ( p @ Y1 @ france )
& ~ ( eq @ Y2 @ Y1 ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f138]) ).
thf(f153,plain,
( pp
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y0 @ Y1 )
& ~ ( p @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f154,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( p @ Y1 @ Y0 )
& ( p @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f156,plain,
( p
= ( ^ [Y0: reg,Y1: reg] :
( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f161,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f115]) ).
thf(f162,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f163,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( pp @ Y0 @ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ec @ Y2 @ Y1 )
& ( ec @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f164,plain,
( ( mvalid
@ ( mbox @ a
@ ^ [Y0: $i] : ( ntpp @ paris @ france ) ) )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f165,plain,
( ec
= ( ^ [Y0: reg,Y1: reg] :
( ( c @ Y0 @ Y1 )
& ~ ( o @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f127]) ).
thf(f169,plain,
( eq
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
& ( ^ [Y2: reg,Y3: reg] :
( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f154,f156,f156]) ).
thf(f170,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,[],[f141,f156,f156]) ).
thf(f172,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,[],[f165,f170]) ).
thf(f175,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,[],[f153,f156,f156]) ).
thf(f177,plain,
( ntpp
= ( ^ [Y0: reg,Y1: reg] :
( ( ^ [Y2: reg,Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y2
@ Y3 )
& ~ ( ^ [Y4: reg,Y5: reg] :
( !! @ reg
@ ^ [Y6: reg] :
( ( c @ Y6 @ Y4 )
=> ( c @ Y6 @ Y5 ) ) )
@ Y3
@ Y2 ) )
@ Y0
@ Y1 )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y1 )
& ( ^ [Y3: reg,Y4: reg] :
( ( c @ Y3 @ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( ?? @ reg
@ ^ [Y7: reg] :
( ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y6 )
& ( ^ [Y8: reg,Y9: reg] :
( !! @ reg
@ ^ [Y10: reg] :
( ( c @ Y10 @ Y8 )
=> ( c @ Y10 @ Y9 ) ) )
@ Y7
@ Y5 ) ) )
@ Y3
@ Y4 ) )
@ Y2
@ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f163,f175,f172,f172]) ).
thf(f182,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] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y2
@ france )
& ( ^ [Y3: reg,Y4: reg] :
( !! @ reg
@ ^ [Y5: reg] :
( ( c @ Y5 @ Y3 )
=> ( c @ Y5 @ Y4 ) ) )
@ Y1
@ france )
& ~ ( ^ [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 ) )
@ Y2
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f150,f162,f161,f156,f156,f169]) ).
thf(f185,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ a
@ ^ [Y0: $i] :
( ^ [Y1: reg,Y2: reg] :
( ( ^ [Y3: reg,Y4: reg] :
( ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y3
@ Y4 )
& ~ ( ^ [Y5: reg,Y6: reg] :
( !! @ reg
@ ^ [Y7: reg] :
( ( c @ Y7 @ Y5 )
=> ( c @ Y7 @ Y6 ) ) )
@ Y4
@ Y3 ) )
@ Y1
@ Y2 )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y2 )
& ( ^ [Y4: reg,Y5: reg] :
( ( c @ Y4 @ Y5 )
& ~ ( ^ [Y6: reg,Y7: reg] :
( ?? @ reg
@ ^ [Y8: reg] :
( ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y7 )
& ( ^ [Y9: reg,Y10: reg] :
( !! @ reg
@ ^ [Y11: reg] :
( ( c @ Y11 @ Y9 )
=> ( c @ Y11 @ Y10 ) ) )
@ Y8
@ Y6 ) ) )
@ Y4
@ Y5 ) )
@ Y3
@ Y1 ) ) ) )
@ paris
@ france ) ) )
= $true ),
inference(definition_unfolding,[],[f164,f162,f161,f177]) ).
thf(f247,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f248,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ?? @ reg
@ ^ [Y2: reg] :
( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y2 )
=> ( c @ Y4 @ Y3 ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a @ sK4 @ Y0 )
| ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
( ( ^ [Y0: $i] :
( ~ ( a @ sK4 @ Y0 )
| ( ?? @ reg
@ ^ [Y1: reg] :
( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y1 )
=> ( c @ Y3 @ Y2 ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( ( ~ ( a @ sK4 @ sK5 )
| ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f252,plain,
( ( ?? @ reg
@ ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f251]) ).
thf(f253,plain,
( ( ~ ( a @ sK4 @ sK5 ) )
= $false ),
inference(or_proxy_clausification,[],[f251]) ).
thf(f254,plain,
( ( a @ sK4 @ sK5 )
= $true ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X1: reg] :
( ( ^ [Y0: reg] :
( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y0 )
=> ( c @ Y2 @ Y1 ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f256,plain,
! [X1: reg] :
( ( ?? @ reg
@ ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: reg,X1: reg] :
( ( ^ [Y0: reg] :
( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ france ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ X1 )
=> ( c @ Y1 @ Y0 ) ) )
& ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ Y0 )
=> ( c @ Y1 @ X1 ) ) ) ) )
@ X2 )
= $false ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: reg,X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
& ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: reg,X1: reg] :
( ( ( ~ ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) ) )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: reg,X1: reg] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) ) )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: reg,X1: reg] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
& ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ X1 ) ) ) )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f260]) ).
thf(f263,plain,
! [X2: reg,X1: reg] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) ) )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f261]) ).
thf(f264,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) )
@ X3 )
= $true )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) )
@ X3 )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) )
@ ( sK6 @ X2 ) )
= $false )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X2 )
=> ( c @ Y0 @ france ) )
@ ( sK6 @ X2 ) )
= $false )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ X2 ) )
@ X3 )
= $true )
| ( ( ^ [Y0: reg] :
( ( c @ Y0 @ X1 )
=> ( c @ Y0 @ france ) )
@ ( sK7 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ( c @ ( sK7 @ X1 ) @ X1 )
=> ( c @ ( sK7 @ X1 ) @ france ) )
= $false )
| ( $true
= ( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) ) )
| ( ( ( c @ ( sK6 @ X2 ) @ X2 )
=> ( c @ ( sK6 @ X2 ) @ france ) )
= $false ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( ( c @ ( sK6 @ X2 ) @ X2 )
=> ( c @ ( sK6 @ X2 ) @ france ) )
= $false )
| ( $true
= ( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) ) )
| ( ( c @ ( sK7 @ X1 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $true
= ( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) ) )
| ( ( c @ ( sK7 @ X1 ) @ X1 )
= $true )
| ( ( ( c @ ( sK6 @ X2 ) @ X2 )
=> ( c @ ( sK6 @ X2 ) @ france ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f270,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ ( sK7 @ X1 ) @ X1 )
= $true )
| ( ( c @ X3 @ X1 )
= $false )
| ( ( ( c @ ( sK6 @ X2 ) @ X2 )
=> ( c @ ( sK6 @ X2 ) @ france ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ ( sK7 @ X1 ) @ X1 )
= $true )
| ( ( c @ ( sK6 @ X2 ) @ france )
= $false )
| ( ( c @ X3 @ X1 )
= $false )
| ( ( c @ X3 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ ( sK7 @ X1 ) @ X1 )
= $true )
| ( ( c @ ( sK6 @ X2 ) @ X2 )
= $true )
| ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f270]) ).
thf(f273,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ ( sK6 @ X2 ) @ france )
= $false )
| ( ( c @ ( sK7 @ X1 ) @ france )
= $false )
| ( $true
= ( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f274,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( $true
= ( ( c @ X3 @ X1 )
=> ( c @ X3 @ X2 ) ) )
| ( ( c @ ( sK6 @ X2 ) @ X2 )
= $true )
| ( ( c @ ( sK7 @ X1 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f275,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ ( sK7 @ X1 ) @ france )
= $false )
| ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ X3 @ X1 )
= $false )
| ( ( c @ ( sK6 @ X2 ) @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: reg,X3: reg,X1: reg] :
( ( ( c @ ( sK7 @ X1 ) @ france )
= $false )
| ( ( c @ X3 @ X1 )
= $false )
| ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ ( sK6 @ X2 ) @ france )
= $false ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f288,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f289,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a @ Y0 @ Y1 )
| ( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ paris )
=> ( c @ Y2 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
=> ( c @ Y2 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ france )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ france ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) )
& ( c @ Y2 @ paris )
& ~ ( ?? @ reg
@ ^ [Y3: reg] :
( ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ paris ) ) )
& ( !! @ reg
@ ^ [Y4: reg] :
( ( c @ Y4 @ Y3 )
=> ( c @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f288]) ).
thf(f290,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 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( a @ X1 @ Y0 )
| ( ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ paris )
=> ( c @ Y1 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
=> ( c @ Y1 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( c @ Y1 @ france )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ france ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) )
& ( c @ Y1 @ paris )
& ~ ( ?? @ reg
@ ^ [Y2: reg] :
( ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ paris ) ) )
& ( !! @ reg
@ ^ [Y3: reg] :
( ( c @ Y3 @ Y2 )
=> ( c @ Y3 @ Y1 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( ~ ( a @ X1 @ X2 )
| ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( a @ X1 @ X2 ) )
= $true )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
& ~ ( ?? @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ france ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) )
& ( c @ Y0 @ paris )
& ~ ( ?? @ reg
@ ^ [Y1: reg] :
( ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ paris ) ) )
& ( !! @ reg
@ ^ [Y2: reg] :
( ( c @ Y2 @ Y1 )
=> ( c @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) )
& ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f294]) ).
thf(f297,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) ) )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ paris )
=> ( c @ Y0 @ france ) ) ) ) ),
inference(and_proxy_clausification,[],[f296]) ).
thf(f299,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,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ( c @ X3 @ paris )
=> ( c @ X3 @ france ) )
= $true ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X3: reg,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ X3 @ france )
= $true )
| ( ( c @ X3 @ paris )
= $false ) ),
inference(imp_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ reg
@ ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) ) )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f303,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: reg] :
( ( c @ Y0 @ france )
=> ( c @ Y0 @ paris ) )
@ sK10 )
= $false )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( ( c @ sK10 @ france )
=> ( c @ sK10 @ paris ) )
= $false ) ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X1: $i] :
( ( ( a @ X1 @ X2 )
= $false )
| ( ( c @ sK10 @ paris )
= $false ) ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X1: $i] :
( ( ( c @ sK10 @ france )
= $true )
| ( ( a @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f438,definition,
( spl20_7
<=> ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f439,plain,
( ! [X2: $i,X1: $i] :
( ( a @ X1 @ X2 )
= $false )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f438]) ).
thf(f441,definition,
( spl20_8
<=> ! [X3: reg] :
( ( ( c @ X3 @ france )
= $true )
| ( ( c @ X3 @ paris )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f442,plain,
( ! [X3: reg] :
( ( ( c @ X3 @ paris )
= $false )
| ( ( c @ X3 @ france )
= $true ) )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f441]) ).
thf(f443,plain,
( spl20_7
| spl20_8 ),
inference(avatar_split_clause,[],[f301,f441,f438]) ).
thf(f445,definition,
( spl20_9
<=> ( ( c @ sK10 @ france )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
thf(f447,plain,
( ( ( c @ sK10 @ france )
= $true )
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f445]) ).
thf(f448,plain,
( spl20_9
| spl20_7 ),
inference(avatar_split_clause,[],[f306,f438,f445]) ).
thf(f450,definition,
( spl20_10
<=> ( ( c @ sK10 @ paris )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
thf(f452,plain,
( ( ( c @ sK10 @ paris )
= $false )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f450]) ).
thf(f453,plain,
( spl20_7
| spl20_10 ),
inference(avatar_split_clause,[],[f305,f450,f438]) ).
thf(f585,plain,
! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X2 @ X3 )
= $true )
| ( ( c @ X1 @ france )
= $false )
| ( $true = $false )
| ( ( c @ ( sK6 @ X3 ) @ X3 )
= $true )
| ( ( c @ ( sK6 @ X0 ) @ X0 )
= $true )
| ( ( c @ X2 @ france )
= $false ) ),
inference(superposition,[],[f272,f275]) ).
thf(f595,plain,
! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( ( c @ ( sK6 @ X0 ) @ X0 )
= $true )
| ( ( c @ ( sK6 @ X3 ) @ X3 )
= $true )
| ( ( c @ X1 @ france )
= $false )
| ( ( c @ X2 @ france )
= $false )
| ( ( c @ X1 @ X0 )
= $true )
| ( ( c @ X2 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f585]) ).
thf(f597,definition,
( spl20_28
<=> ! [X2: reg,X3: reg] :
( ( ( c @ ( sK6 @ X2 ) @ X2 )
= $true )
| ( ( c @ X3 @ france )
= $false )
| ( ( c @ X3 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
thf(f598,plain,
( ! [X2: reg,X3: reg] :
( ( ( c @ ( sK6 @ X2 ) @ X2 )
= $true )
| ( ( c @ X3 @ france )
= $false )
| ( ( c @ X3 @ X2 )
= $true ) )
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f601,definition,
( spl20_29
<=> ! [X2: reg,X3: reg] :
( ( ( c @ X3 @ france )
= $false )
| ( ( c @ ( sK6 @ X2 ) @ france )
= $false )
| ( ( c @ X3 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_29])],[avatar_definition]) ).
thf(f602,plain,
( ! [X2: reg,X3: reg] :
( ( ( c @ ( sK6 @ X2 ) @ france )
= $false )
| ( ( c @ X3 @ france )
= $false )
| ( ( c @ X3 @ X2 )
= $true ) )
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f601]) ).
thf(f613,plain,
( spl20_28
| spl20_28 ),
inference(avatar_split_clause,[],[f595,f597,f597]) ).
thf(f637,plain,
( ( $true = $false )
| ~ spl20_7 ),
inference(superposition,[],[f254,f439]) ).
thf(f640,plain,
( $false
| ~ spl20_7 ),
inference(trivial_inequality_removal,[],[f637]) ).
thf(f641,plain,
~ spl20_7,
inference(avatar_contradiction_clause,[],[f640]) ).
thf(f667,plain,
( ! [X0: reg] :
( ( ( c @ ( sK6 @ paris ) @ france )
= $true )
| ( $true = $false )
| ( ( c @ X0 @ france )
= $false )
| ( ( c @ X0 @ paris )
= $true ) )
| ~ spl20_8
| ~ spl20_28 ),
inference(superposition,[],[f598,f442]) ).
thf(f672,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ france )
= $false )
| ( ( c @ ( sK6 @ paris ) @ france )
= $true )
| ( ( c @ X0 @ paris )
= $true ) )
| ~ spl20_8
| ~ spl20_28 ),
inference(trivial_inequality_removal,[],[f667]) ).
thf(f689,definition,
( spl20_36
<=> ! [X0: reg] :
( ( ( c @ X0 @ paris )
= $true )
| ( ( c @ X0 @ france )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_36])],[avatar_definition]) ).
thf(f690,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ paris )
= $true )
| ( ( c @ X0 @ france )
= $false ) )
| ~ spl20_36 ),
inference(avatar_component_clause,[],[f689]) ).
thf(f692,definition,
( spl20_37
<=> ( ( c @ ( sK6 @ paris ) @ france )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_37])],[avatar_definition]) ).
thf(f694,plain,
( ( ( c @ ( sK6 @ paris ) @ france )
= $true )
| ~ spl20_37 ),
inference(avatar_component_clause,[],[f692]) ).
thf(f696,plain,
( spl20_37
| spl20_36
| ~ spl20_8
| ~ spl20_28 ),
inference(avatar_split_clause,[],[f672,f597,f441,f689,f692]) ).
thf(f855,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ france )
= $false )
| ( $true = $false )
| ( ( c @ X0 @ paris )
= $true ) )
| ~ spl20_29
| ~ spl20_37 ),
inference(superposition,[],[f602,f694]) ).
thf(f858,plain,
( ! [X0: reg] :
( ( ( c @ X0 @ france )
= $false )
| ( ( c @ X0 @ paris )
= $true ) )
| ~ spl20_29
| ~ spl20_37 ),
inference(trivial_inequality_removal,[],[f855]) ).
thf(f971,plain,
! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( ( c @ X3 @ france )
= $false )
| ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ ( sK6 @ X1 ) @ france )
= $false )
| ( ( c @ ( sK6 @ X2 ) @ france )
= $false )
| ( ( c @ X0 @ X1 )
= $true )
| ( ( c @ X0 @ france )
= $false )
| ( $true = $false ) ),
inference(superposition,[],[f276,f271]) ).
thf(f980,plain,
! [X2: reg,X3: reg,X0: reg,X1: reg] :
( ( ( c @ X3 @ X2 )
= $true )
| ( ( c @ X3 @ france )
= $false )
| ( ( c @ ( sK6 @ X2 ) @ france )
= $false )
| ( ( c @ X0 @ X1 )
= $true )
| ( ( c @ ( sK6 @ X1 ) @ france )
= $false )
| ( ( c @ X0 @ france )
= $false ) ),
inference(trivial_inequality_removal,[],[f971]) ).
thf(f1177,plain,
( ( $true = $false )
| ( ( c @ sK10 @ france )
= $false )
| ~ spl20_10
| ~ spl20_36 ),
inference(superposition,[],[f452,f690]) ).
thf(f1180,plain,
( ( ( c @ sK10 @ france )
= $false )
| ~ spl20_10
| ~ spl20_36 ),
inference(trivial_inequality_removal,[],[f1177]) ).
thf(f1182,plain,
( ( $true = $false )
| ~ spl20_9
| ~ spl20_10
| ~ spl20_36 ),
inference(superposition,[],[f1180,f447]) ).
thf(f1188,plain,
( $false
| ~ spl20_9
| ~ spl20_10
| ~ spl20_36 ),
inference(trivial_inequality_removal,[],[f1182]) ).
thf(f1189,plain,
( ~ spl20_9
| ~ spl20_10
| ~ spl20_36 ),
inference(avatar_contradiction_clause,[],[f1188]) ).
thf(f1190,plain,
( spl20_36
| ~ spl20_29
| ~ spl20_37 ),
inference(avatar_split_clause,[],[f858,f692,f601,f689]) ).
thf(f1196,plain,
( spl20_29
| spl20_29 ),
inference(avatar_split_clause,[],[f980,f601,f601]) ).
cnf(s6,plain,
( spl20_7
| spl20_8 ),
inference(sat_conversion,[],[f443]) ).
cnf(s7,plain,
( spl20_7
| spl20_9 ),
inference(sat_conversion,[],[f448]) ).
cnf(s8,plain,
( spl20_7
| spl20_10 ),
inference(sat_conversion,[],[f453]) ).
cnf(s31,plain,
( spl20_28
| spl20_28 ),
inference(sat_conversion,[],[f613]) ).
cnf(s32,plain,
spl20_28,
inference(rat,[],[s31]) ).
cnf(s38,plain,
~ spl20_7,
inference(sat_conversion,[],[f641]) ).
cnf(s46,plain,
( ~ spl20_8
| ~ spl20_28
| spl20_36
| spl20_37 ),
inference(sat_conversion,[],[f696]) ).
cnf(s91,plain,
( ~ spl20_9
| ~ spl20_10
| ~ spl20_36 ),
inference(sat_conversion,[],[f1189]) ).
cnf(s92,plain,
( ~ spl20_29
| spl20_36
| ~ spl20_37 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s97,plain,
( spl20_29
| spl20_29 ),
inference(sat_conversion,[],[f1196]) ).
cnf(s98,plain,
spl20_29,
inference(rat,[],[s97]) ).
cnf(s99,plain,
( spl20_36
| ~ spl20_37 ),
inference(rat,[],[s92,s98]) ).
cnf(s120,plain,
spl20_10,
inference(rat,[],[s8,s38]) ).
cnf(s121,plain,
spl20_9,
inference(rat,[],[s7,s38]) ).
cnf(s122,plain,
~ spl20_36,
inference(rat,[],[s91,s120,s121]) ).
cnf(s123,plain,
~ spl20_37,
inference(rat,[],[s99,s122]) ).
cnf(s124,plain,
~ spl20_8,
inference(rat,[],[s46,s123,s32,s122]) ).
cnf(s125,plain,
$false,
inference(rat,[],[s6,s124,s38]) ).
thf(f1197,plain,
$false,
inference(avatar_sat_refutation,[],[s125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG015^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 18:34:16 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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
% 0.77/0.43 % (2041177)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.77/0.43 % (2041186)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1683065903:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.77/0.43 % (2041184)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3560052465:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.77/0.43 % (2041182)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2821385711:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.77/0.43 % (2041185)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=675513873: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)
% 0.77/0.43 % (2041184)Instruction limit reached!
% 0.77/0.43 % (2041184)------------------------------
% 0.77/0.43 % (2041184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2041184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2041184)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2041184)Termination reason: Instruction limit
% 0.77/0.43 % (2041184)Termination phase: shuffling
% 0.77/0.43 % (2041184)Time elapsed: 0.002 s
% 0.77/0.43 % (2041184)Peak memory usage: 9 MB
% 0.77/0.43 % (2041184)Instructions burned: 3 (million)
% 0.77/0.43 % (2041188)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.77/0.43 % (2041188)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
% 0.77/0.43 % (2041188)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=3954951151:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.77/0.43 % (2041183)lrs+10_16_si=on:nwc=1.5:random_seed=3194794350:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.77/0.43 % (2041186)Instruction limit reached!
% 0.77/0.43 % (2041186)------------------------------
% 0.77/0.43 % (2041186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2041186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2041186)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2041186)Termination reason: Instruction limit
% 0.77/0.43 % (2041186)Termination phase: Saturation
% 0.77/0.43 % (2041186)Time elapsed: 0.013 s
% 0.77/0.43 % (2041186)Peak memory usage: 11 MB
% 0.77/0.43 % (2041186)Instructions burned: 25 (million)
% 0.77/0.43 % (2041187)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=679362674:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.77/0.43 % (2041183)Instruction limit reached!
% 0.77/0.43 % (2041183)------------------------------
% 0.77/0.43 % (2041183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2041183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2041183)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2041183)Termination reason: Instruction limit
% 0.77/0.43 % (2041183)Termination phase: Saturation
% 0.77/0.43 % (2041183)Time elapsed: 0.015 s
% 0.77/0.43 % (2041183)Peak memory usage: 11 MB
% 0.77/0.43 % (2041183)Instructions burned: 18 (million)
% 0.77/0.43 % (2041198)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.43 % (2041182)Instruction limit reached!
% 0.77/0.43 % (2041182)------------------------------
% 0.77/0.43 % (2041182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (2041182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (2041182)CaDiCaL version: 2.1.3
% 0.77/0.43 % (2041182)Termination reason: Instruction limit
% 0.77/0.43 % (2041182)Termination phase: Saturation
% 0.77/0.43 % (2041182)Time elapsed: 0.042 s
% 0.77/0.43 % (2041182)Peak memory usage: 12 MB
% 0.77/0.43 % (2041182)Instructions burned: 88 (million)
% 0.77/0.43 % (2041198)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4184491442:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.77/0.48 % (2041196)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2501557481:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.77/0.48 % (2041198)Instruction limit reached!
% 0.77/0.48 % (2041198)------------------------------
% 0.77/0.48 % (2041198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041198)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041198)Termination reason: Instruction limit
% 0.77/0.48 % (2041198)Termination phase: Property scanning
% 0.77/0.48 % (2041198)Time elapsed: 0.004 s
% 0.77/0.48 % (2041198)Peak memory usage: 10 MB
% 0.77/0.48 % (2041198)Instructions burned: 8 (million)
% 0.77/0.48 % (2041196)Instruction limit reached!
% 0.77/0.48 % (2041196)------------------------------
% 0.77/0.48 % (2041196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041196)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041196)Termination reason: Instruction limit
% 0.77/0.48 % (2041196)Termination phase: Property scanning
% 0.77/0.48 % (2041196)Time elapsed: 0.004 s
% 0.77/0.48 % (2041196)Peak memory usage: 10 MB
% 0.77/0.48 % (2041196)Instructions burned: 5 (million)
% 0.77/0.48 % (2041193)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2837158288:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.48 % (2041193)Instruction limit reached!
% 0.77/0.48 % (2041193)------------------------------
% 0.77/0.48 % (2041193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041193)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041193)Termination reason: Instruction limit
% 0.77/0.48 % (2041193)Termination phase: shuffling
% 0.77/0.48 % (2041193)Time elapsed: 0.004 s
% 0.77/0.48 % (2041193)Peak memory usage: 9 MB
% 0.77/0.48 % (2041193)Instructions burned: 3 (million)
% 0.77/0.48 % (2041202)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
% 0.77/0.48 % (2041202)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.48 % (2041199)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2637257159:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.77/0.48 % (2041202)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3135850535:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.77/0.48 % (2041199)Instruction limit reached!
% 0.77/0.48 % (2041199)------------------------------
% 0.77/0.48 % (2041199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041199)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041199)Termination reason: Instruction limit
% 0.77/0.48 % (2041199)Termination phase: Property scanning
% 0.77/0.48 % (2041199)Time elapsed: 0.007 s
% 0.77/0.48 % (2041199)Peak memory usage: 10 MB
% 0.77/0.48 % (2041199)Instructions burned: 14 (million)
% 0.77/0.48 % (2041202)Instruction limit reached!
% 0.77/0.48 % (2041202)------------------------------
% 0.77/0.48 % (2041202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041202)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041202)Termination reason: Instruction limit
% 0.77/0.48 % (2041202)Termination phase: Saturation
% 0.77/0.48 % (2041202)Time elapsed: 0.013 s
% 0.77/0.48 % (2041202)Peak memory usage: 11 MB
% 0.77/0.48 % (2041202)Instructions burned: 30 (million)
% 0.77/0.48 % (2041187)Instruction limit reached!
% 0.77/0.48 % (2041187)------------------------------
% 0.77/0.48 % (2041187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041187)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041187)Termination reason: Instruction limit
% 0.77/0.48 % (2041187)Termination phase: Saturation
% 0.77/0.48 % (2041187)Time elapsed: 0.067 s
% 0.77/0.48 % (2041187)Peak memory usage: 13 MB
% 0.77/0.48 % (2041187)Instructions burned: 76 (million)
% 0.77/0.48 % (2041204)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=4013334322:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.77/0.48 % (2041208)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.77/0.48 % (2041205)lrs+10_1_si=on:cs=on:random_seed=777211229:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.77/0.48 % (2041205)Instruction limit reached!
% 0.77/0.48 % (2041205)------------------------------
% 0.77/0.48 % (2041205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041205)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041205)Termination reason: Instruction limit
% 0.77/0.48 % (2041205)Termination phase: Property scanning
% 0.77/0.48 % (2041205)Time elapsed: 0.007 s
% 0.77/0.48 % (2041205)Peak memory usage: 10 MB
% 0.77/0.48 % (2041205)Instructions burned: 8 (million)
% 0.77/0.48 % (2041208)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=221181370:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.77/0.48 % (2041208)Instruction limit reached!
% 0.77/0.48 % (2041208)------------------------------
% 0.77/0.48 % (2041208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041208)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041208)Termination reason: Instruction limit
% 0.77/0.48 % (2041208)Termination phase: Property scanning
% 0.77/0.48 % (2041208)Time elapsed: 0.002 s
% 0.77/0.48 % (2041208)Peak memory usage: 9 MB
% 0.77/0.48 % (2041208)Instructions burned: 4 (million)
% 0.77/0.48 % (2041188)Instruction limit reached!
% 0.77/0.48 % (2041188)------------------------------
% 0.77/0.48 % (2041188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041188)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041188)Termination reason: Instruction limit
% 0.77/0.48 % (2041188)Termination phase: Saturation
% 0.77/0.48 % (2041188)Time elapsed: 0.099 s
% 0.77/0.48 % (2041188)Peak memory usage: 13 MB
% 0.77/0.48 % (2041188)Instructions burned: 157 (million)
% 0.77/0.48 % (2041209)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3635208375:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.77/0.48 % (2041210)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1070808787:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.77/0.48 % (2041209)Refutation not found, incomplete strategy
% 0.77/0.48 % (2041209)------------------------------
% 0.77/0.48 % (2041209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041209)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041209)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.48 % (2041209)Time elapsed: 0.009 s
% 0.77/0.48 % (2041209)Peak memory usage: 12 MB
% 0.77/0.48 % (2041209)Instructions burned: 9 (million)
% 0.77/0.48 % (2041210)Refutation not found, incomplete strategy
% 0.77/0.48 % (2041210)------------------------------
% 0.77/0.48 % (2041210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041210)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041210)Termination reason: Refutation not found, incomplete strategy
% 0.77/0.48 % (2041210)Time elapsed: 0.006 s
% 0.77/0.48 % (2041210)Peak memory usage: 12 MB
% 0.77/0.48 % (2041210)Instructions burned: 11 (million)
% 0.77/0.48 % (2041209)------------------------------
% 0.77/0.48 % (2041209)------------------------------
% 0.77/0.48 % (2041210)------------------------------
% 0.77/0.48 % (2041210)------------------------------
% 0.77/0.48 % (2041216)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1078693327:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.77/0.48 % (2041214)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1389402087:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.77/0.48 % (2041215)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4197973323:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.77/0.48 % (2041219)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=480979329:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.77/0.48 % (2041220)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3709955732: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)
% 0.77/0.48 % (2041220)Instruction limit reached!
% 0.77/0.48 % (2041220)------------------------------
% 0.77/0.48 % (2041220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041220)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041220)Termination reason: Instruction limit
% 0.77/0.48 % (2041220)Termination phase: SInE selection
% 0.77/0.48 % (2041220)Time elapsed: 0.003 s
% 0.77/0.48 % (2041220)Peak memory usage: 10 MB
% 0.77/0.48 % (2041220)Instructions burned: 6 (million)
% 0.77/0.48 % (2041219)Instruction limit reached!
% 0.77/0.48 % (2041219)------------------------------
% 0.77/0.48 % (2041219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041219)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041219)Termination reason: Instruction limit
% 0.77/0.48 % (2041219)Termination phase: Saturation
% 0.77/0.48 % (2041219)Time elapsed: 0.007 s
% 0.77/0.48 % (2041219)Peak memory usage: 11 MB
% 0.77/0.48 % (2041219)Instructions burned: 14 (million)
% 0.77/0.48 % (2041215)Instruction limit reached!
% 0.77/0.48 % (2041215)------------------------------
% 0.77/0.48 % (2041215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041204)Instruction limit reached!
% 0.77/0.48 % (2041204)------------------------------
% 0.77/0.48 % (2041204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041215)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041204)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041215)Termination reason: Instruction limit
% 0.77/0.48 % (2041215)Termination phase: Saturation
% 0.77/0.48 % (2041215)Time elapsed: 0.011 s
% 0.77/0.48 % (2041215)Peak memory usage: 11 MB
% 0.77/0.48 % (2041204)Termination reason: Instruction limit
% 0.77/0.48 % (2041204)Termination phase: Saturation
% 0.77/0.48 % (2041204)Time elapsed: 0.076 s
% 0.77/0.48 % (2041204)Peak memory usage: 12 MB
% 0.77/0.48 % (2041215)Instructions burned: 14 (million)
% 0.77/0.48 % (2041204)Instructions burned: 86 (million)
% 0.77/0.48 % (2041214)Instruction limit reached!
% 0.77/0.48 % (2041214)------------------------------
% 0.77/0.48 % (2041214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.48 % (2041214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.48 % (2041214)CaDiCaL version: 2.1.3
% 0.77/0.48 % (2041214)Termination reason: Instruction limit
% 0.77/0.48 % (2041214)Termination phase: Saturation
% 0.77/0.48 % (2041214)Time elapsed: 0.029 s
% 0.77/0.48 % (2041214)Peak memory usage: 12 MB
% 0.77/0.48 % (2041214)Instructions burned: 25 (million)
% 0.77/0.48 % (2041216) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2041177-2041216"...
% 0.77/0.48 % (2041216)...printing done.
% 0.77/0.48 % (2041216)Refutation found. Thanks to Tanya!
% 0.77/0.48 % SZS status Theorem for theBenchmark
% 0.77/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.77/0.49 % (2041216)------------------------------
% 0.77/0.49 % (2041216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.49 % (2041216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.49 % (2041216)CaDiCaL version: 2.1.3
% 0.77/0.49 % (2041216)Termination reason: Refutation
% 0.77/0.49 % (2041216)Time elapsed: 0.051 s
% 0.77/0.49 % (2041216)Peak memory usage: 13 MB
% 0.77/0.49 % (2041216)Instructions burned: 97 (million)
% 0.77/0.49 % (2041177)Success in time 0.218 s
% 0.77/0.49 % Vampire exiting
%------------------------------------------------------------------------------