%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET926^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:30 AM UTC 2026
% Result : Theorem 0.54s 0.44s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 132 ( 59 unt; 0 typ; 6 def)
% Number of atoms : 925 ( 175 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 2007 ( 208 ~; 211 |; 0 &;1476 @)
% ( 5 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 13 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 365 ( 0 sgn 71 !; 0 ?; 365 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
in: mu > mu > $i > $o ).
thf(func_def_37,type,
empty: mu > $i > $o ).
thf(func_def_38,type,
empty_set: mu ).
thf(func_def_39,type,
singleton: mu > mu ).
thf(func_def_40,type,
set_difference: mu > mu > mu ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
sK0: $i > mu ).
thf(func_def_57,type,
sF1: $o ).
thf(func_def_59,type,
sK3: mu ).
thf(func_def_60,type,
sK4: mu ).
thf(func_def_61,type,
sK5: $i > mu ).
thf(func_def_62,type,
sK6: $i > mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f11,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mequiv) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f51,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(f52,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(f55,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(f56,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
thf(f63,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f72,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f83,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f84,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f121,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f52]) ).
thf(f122,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f123,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f124,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f134,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f51]) ).
thf(f135,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f150,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f151,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f150]) ).
thf(f152,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f153,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f152]) ).
thf(f154,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f155,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f156,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f151]) ).
thf(f167,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f174,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f156]) ).
thf(f177,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f183,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f190,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f155]) ).
thf(f195,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f153]) ).
thf(f205,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f207,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f210,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f212,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f219,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f210,f183,f167,f183,f183]) ).
thf(f220,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f207,f167,f183]) ).
thf(f222,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f212,f219,f220,f220]) ).
thf(f231,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f174,f195,f190,f190,f167]) ).
thf(f232,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f177,f195,f190,f190,f222]) ).
thf(f244,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f205,f195,f190,f190,f222,f183]) ).
thf(f246,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f247,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f246]) ).
thf(f248,plain,
$true != sF1,
inference(definition_folding,[],[f231,f247]) ).
thf(f264,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f247]) ).
thf(f265,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f265]) ).
thf(f267,plain,
( ( $true = sF1 )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ sK2 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ sK2 ) ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( ( ( exists_in_world @ sK3 @ sK2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ sK2 ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f270,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ sK2 ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f271,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f272,plain,
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ sK2 ) ) )
@ sK4 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f270]) ).
thf(f273,plain,
( ( $true = sF1 )
| ( ( ( exists_in_world @ sK4 @ sK2 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ sK2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
( ( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ sK2 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ sK2 ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f275,plain,
( ( $true
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f276,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ sK2 )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f277,plain,
( ( $true = sF1 )
| ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f411,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
| ~ ~ ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ( in @ Y1 @ Y2 @ Y0 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f412,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
| ~ ~ ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ( in @ Y1 @ Y2 @ Y0 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f411]) ).
thf(f413,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 )
| ~ ~ ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ( in @ Y0 @ Y1 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f414,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 )
| ~ ~ ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ( in @ Y0 @ Y1 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f413]) ).
thf(f415,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f414]) ).
thf(f416,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f415]) ).
thf(f417,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 ) ) ) )
@ X3 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f417]) ).
thf(f419,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f418]) ).
thf(f420,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f419]) ).
thf(f422,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ X3 @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f420]) ).
thf(f423,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ~ ( in @ X2 @ X3 @ X1 ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f422]) ).
thf(f424,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ~ ( in @ X2 @ X3 @ X1 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( in @ X2 @ X3 @ X1 ) )
= $false )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f424]) ).
thf(f426,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) )
| ( $true
= ( in @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f425]) ).
thf(f464,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
| ~ ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ( in @ Y1 @ Y2 @ Y0 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f465,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
| ~ ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ( in @ Y1 @ Y2 @ Y0 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f464]) ).
thf(f466,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ( in @ Y0 @ Y1 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f465]) ).
thf(f467,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ( in @ Y0 @ Y1 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f466]) ).
thf(f468,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ( in @ X2 @ Y0 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f467]) ).
thf(f469,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ( in @ X2 @ Y0 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 ) ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ( in @ X2 @ Y0 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 ) ) ) )
@ X3 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ( in @ X2 @ X3 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f470]) ).
thf(f472,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ( in @ X2 @ X3 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f471]) ).
thf(f473,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ( in @ X2 @ X3 @ X1 )
| ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f472]) ).
thf(f475,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f473]) ).
thf(f476,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f475]) ).
thf(f477,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ( in @ X2 @ X3 @ X1 ) ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( in @ X2 @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f477]) ).
thf(f483,definition,
( spl7_1
<=> ( $true
= ( exists_in_world @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f485,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f483]) ).
thf(f487,definition,
( spl7_2
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f490,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f271,f487,f483]) ).
thf(f492,definition,
( spl7_3
<=> ( $true
= ( exists_in_world @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f494,plain,
( ( $true
= ( exists_in_world @ sK4 @ sK2 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f492]) ).
thf(f495,plain,
( spl7_2
| spl7_3 ),
inference(avatar_split_clause,[],[f275,f492,f487]) ).
thf(f497,definition,
( spl7_4
<=> ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f499,plain,
( ( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ sK2 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f497]) ).
thf(f500,plain,
( spl7_2
| spl7_4 ),
inference(avatar_split_clause,[],[f277,f497,f487]) ).
thf(f502,definition,
( spl7_5
<=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f504,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ sK2 )
= $false )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f502]) ).
thf(f505,plain,
( spl7_2
| spl7_5 ),
inference(avatar_split_clause,[],[f276,f502,f487]) ).
thf(f514,plain,
~ spl7_2,
inference(avatar_split_clause,[],[f248,f487]) ).
thf(f737,plain,
( ( ( exists_in_world @ sK4 @ sK2 )
= $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ( ( in @ sK3 @ sK4 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl7_5 ),
inference(constrained_superposition,[],[f478,f504]) ).
thf(f748,plain,
( ( ( exists_in_world @ sK4 @ sK2 )
= $false )
| ( ( in @ sK3 @ sK4 @ sK2 )
= $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f737]) ).
thf(f763,plain,
( ( $true = $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ( ( in @ sK3 @ sK4 @ sK2 )
= $false )
| ~ spl7_3
| ~ spl7_5 ),
inference(forward_demodulation,[],[f748,f494]) ).
thf(f764,plain,
( ( ( in @ sK3 @ sK4 @ sK2 )
= $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ~ spl7_3
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f763]) ).
thf(f779,plain,
( ( $true = $false )
| ( ( in @ sK3 @ sK4 @ sK2 )
= $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_5 ),
inference(forward_demodulation,[],[f764,f485]) ).
thf(f780,plain,
( ( ( in @ sK3 @ sK4 @ sK2 )
= $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f779]) ).
thf(f874,plain,
( ( $true = $false )
| ( $true
= ( in @ sK3 @ sK4 @ sK2 ) )
| ( ( exists_in_world @ sK4 @ sK2 )
= $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ~ spl7_4 ),
inference(constrained_superposition,[],[f499,f426]) ).
thf(f883,plain,
( ( ( exists_in_world @ sK4 @ sK2 )
= $false )
| ( $true
= ( in @ sK3 @ sK4 @ sK2 ) )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f874]) ).
thf(f901,plain,
( ( $true
= ( in @ sK3 @ sK4 @ sK2 ) )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f883,f494]) ).
thf(f902,plain,
( ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ( $true
= ( in @ sK3 @ sK4 @ sK2 ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f901]) ).
thf(f921,plain,
( ( $true
= ( in @ sK3 @ sK4 @ sK2 ) )
| ( $true = $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f902,f485]) ).
thf(f922,plain,
( ( $true
= ( in @ sK3 @ sK4 @ sK2 ) )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f921]) ).
thf(f928,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(forward_demodulation,[],[f922,f780]) ).
thf(f929,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f928]) ).
thf(f930,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f929]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f490]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f495]) ).
cnf(s3,plain,
( spl7_2
| spl7_4 ),
inference(sat_conversion,[],[f500]) ).
cnf(s4,plain,
( spl7_2
| spl7_5 ),
inference(sat_conversion,[],[f505]) ).
cnf(s6,plain,
~ spl7_2,
inference(sat_conversion,[],[f514]) ).
cnf(s9,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(sat_conversion,[],[f930]) ).
cnf(s11,plain,
spl7_5,
inference(rat,[],[s4,s6]) ).
cnf(s12,plain,
spl7_4,
inference(rat,[],[s3,s6]) ).
cnf(s13,plain,
spl7_3,
inference(rat,[],[s2,s6]) ).
cnf(s14,plain,
~ spl7_1,
inference(rat,[],[s9,s11,s12,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s6,s14]) ).
thf(f931,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n009.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 13:41:16 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.31 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
% 0.54/0.44 % (4006960)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.44 % (4006966)lrs+10_16_si=on:nwc=1.5:random_seed=2616694233:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.44 % (4006966)Instruction limit reached!
% 0.54/0.44 % (4006966)------------------------------
% 0.54/0.44 % (4006966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006966)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006966)Termination reason: Instruction limit
% 0.54/0.44 % (4006966)Termination phase: Saturation
% 0.54/0.44 % (4006966)Time elapsed: 0.008 s
% 0.54/0.44 % (4006966)Peak memory usage: 11 MB
% 0.54/0.44 % (4006966)Instructions burned: 18 (million)
% 0.54/0.44 % (4006971)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.44 % (4006971)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
% 0.54/0.44 % (4006965)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1813060799:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.44 % (4006969)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=813042428:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.44 % (4006970)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2758425117:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.44 % (4006968)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=3511849968: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)
% 0.54/0.44 % (4006971)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=3682549796:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.44 % (4006967)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=943505554:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.44 % (4006967)Instruction limit reached!
% 0.54/0.44 % (4006967)------------------------------
% 0.54/0.44 % (4006967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006967)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006967)Termination reason: Instruction limit
% 0.54/0.44 % (4006967)Termination phase: shuffling
% 0.54/0.44 % (4006967)Time elapsed: 0.003 s
% 0.54/0.44 % (4006967)Peak memory usage: 9 MB
% 0.54/0.44 % (4006967)Instructions burned: 3 (million)
% 0.54/0.44 % (4006973)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=75115252:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.44 % (4006973)Instruction limit reached!
% 0.54/0.44 % (4006973)------------------------------
% 0.54/0.44 % (4006973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006973)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006973)Termination reason: Instruction limit
% 0.54/0.44 % (4006973)Termination phase: shuffling
% 0.54/0.44 % (4006973)Time elapsed: 0.001 s
% 0.54/0.44 % (4006973)Peak memory usage: 10 MB
% 0.54/0.44 % (4006973)Instructions burned: 3 (million)
% 0.54/0.44 % (4006969)Instruction limit reached!
% 0.54/0.44 % (4006969)------------------------------
% 0.54/0.44 % (4006969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006969)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006969)Termination reason: Instruction limit
% 0.54/0.44 % (4006969)Termination phase: Saturation
% 0.54/0.44 % (4006969)Time elapsed: 0.022 s
% 0.54/0.44 % (4006969)Peak memory usage: 12 MB
% 0.54/0.44 % (4006969)Instructions burned: 24 (million)
% 0.54/0.44 % (4006982)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (4006982)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=252230503:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.44 % (4006982)Instruction limit reached!
% 0.54/0.44 % (4006982)------------------------------
% 0.54/0.44 % (4006982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006982)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006982)Termination reason: Instruction limit
% 0.54/0.44 % (4006982)Termination phase: Preprocessing 1
% 0.54/0.44 % (4006982)Time elapsed: 0.003 s
% 0.54/0.44 % (4006982)Peak memory usage: 10 MB
% 0.54/0.44 % (4006982)Instructions burned: 7 (million)
% 0.54/0.44 % (4006980)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4044652427:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.44 % (4006980)Instruction limit reached!
% 0.54/0.44 % (4006980)------------------------------
% 0.54/0.44 % (4006980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006980)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006980)Termination reason: Instruction limit
% 0.54/0.44 % (4006980)Termination phase: Property scanning
% 0.54/0.44 % (4006980)Time elapsed: 0.005 s
% 0.54/0.44 % (4006980)Peak memory usage: 10 MB
% 0.54/0.44 % (4006980)Instructions burned: 6 (million)
% 0.54/0.44 % (4006985)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
% 0.54/0.44 % (4006985)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (4006985)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4031307549:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.44 % (4006983)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3569523482:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.44 % (4006970)Instruction limit reached!
% 0.54/0.44 % (4006970)------------------------------
% 0.54/0.44 % (4006970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006970)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006970)Termination reason: Instruction limit
% 0.54/0.44 % (4006970)Termination phase: Saturation
% 0.54/0.44 % (4006970)Time elapsed: 0.063 s
% 0.54/0.44 % (4006970)Peak memory usage: 12 MB
% 0.54/0.44 % (4006970)Instructions burned: 75 (million)
% 0.54/0.44 % (4006985)Instruction limit reached!
% 0.54/0.44 % (4006985)------------------------------
% 0.54/0.44 % (4006985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006985)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006985)Termination reason: Instruction limit
% 0.54/0.44 % (4006985)Termination phase: Saturation
% 0.54/0.44 % (4006985)Time elapsed: 0.012 s
% 0.54/0.44 % (4006985)Peak memory usage: 11 MB
% 0.54/0.44 % (4006985)Instructions burned: 28 (million)
% 0.54/0.44 % (4006983)Instruction limit reached!
% 0.54/0.44 % (4006983)------------------------------
% 0.54/0.44 % (4006983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006983)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006983)Termination reason: Instruction limit
% 0.54/0.44 % (4006983)Termination phase: Function definition elimination
% 0.54/0.44 % (4006983)Time elapsed: 0.011 s
% 0.54/0.44 % (4006983)Peak memory usage: 10 MB
% 0.54/0.44 % (4006983)Instructions burned: 14 (million)
% 0.54/0.44 % (4006971) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4006960-4006971"...
% 0.54/0.44 % (4006965)Instruction limit reached!
% 0.54/0.44 % (4006965)------------------------------
% 0.54/0.44 % (4006965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (4006965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (4006965)CaDiCaL version: 2.1.3
% 0.54/0.44 % (4006965)Termination reason: Instruction limit
% 0.54/0.44 % (4006965)Termination phase: Saturation
% 0.54/0.44 % (4006965)Time elapsed: 0.072 s
% 0.54/0.44 % (4006965)Peak memory usage: 12 MB
% 0.54/0.44 % (4006965)Instructions burned: 87 (million)
% 0.54/0.44 % (4006987)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=1903084531:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.44 % (4006971)...printing done.
% 0.54/0.44 % (4006971)Refutation found. Thanks to Tanya!
% 0.54/0.44 % SZS status Theorem for theBenchmark
% 0.54/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.45 % (4006971)------------------------------
% 0.54/0.45 % (4006971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.45 % (4006971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.45 % (4006971)CaDiCaL version: 2.1.3
% 0.54/0.45 % (4006971)Termination reason: Refutation
% 0.54/0.45 % (4006971)Time elapsed: 0.078 s
% 0.54/0.45 % (4006971)Peak memory usage: 13 MB
% 0.54/0.45 % (4006971)Instructions burned: 91 (million)
% 0.54/0.45 % (4006960)Success in time 0.12 s
% 0.54/0.45 % Vampire exiting
%------------------------------------------------------------------------------