%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET062^7 : 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 : n014.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 08:23:13 AM UTC 2026
% Result : Theorem 0.78s 0.36s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 16
% Syntax : Number of formulae : 122 ( 63 unt; 0 typ; 5 def)
% Number of atoms : 813 ( 170 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 1480 ( 138 ~; 167 |; 0 &;1050 @)
% ( 4 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 11 con; 0-4 aty)
% ( 60 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 341 ( 0 sgn 90 !; 0 ?; 341 :)
% 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,
equal_set: mu > mu > $i > $o ).
thf(func_def_37,type,
member: mu > mu > $i > $o ).
thf(func_def_38,type,
subset: mu > mu > $i > $o ).
thf(func_def_39,type,
power_set: mu > mu ).
thf(func_def_40,type,
intersection: mu > mu > mu ).
thf(func_def_41,type,
union: mu > mu > mu ).
thf(func_def_42,type,
difference: mu > mu > mu ).
thf(func_def_43,type,
singleton: mu > mu ).
thf(func_def_44,type,
unordered_pair: mu > mu > mu ).
thf(func_def_45,type,
sum: mu > mu ).
thf(func_def_46,type,
product: mu > mu ).
thf(func_def_47,type,
empty_set: mu ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_54,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vAND: $o > $o > $o ).
thf(func_def_58,type,
vIMP: $o > $o > $o ).
thf(func_def_59,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_61,type,
vOR: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
sK0: $i > mu ).
thf(func_def_64,type,
sF1: $o ).
thf(func_def_66,type,
sK3: mu ).
thf(func_def_67,type,
sK4: mu > $i > mu > mu ).
thf(func_def_68,type,
sK5: mu > $i > mu > mu ).
thf(func_def_69,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_70,type,
sK6: mu > $i > mu > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
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,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f45,axiom,
! [X0: $i] : ( exists_in_world @ empty_set @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(f67,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(f72,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mnot @ ( member @ X0 @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(f78,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ empty_set @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI15) ).
thf(f79,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ empty_set @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f78]) ).
thf(f92,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f93,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f122,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f130,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f139,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f140,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f139]) ).
thf(f147,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f148,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f147]) ).
thf(f155,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mnot @ ( member @ X0 @ empty_set ) ) ) ),
inference(rectify,[],[f72]) ).
thf(f156,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mnot @ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(fool_elimination,[],[f155]) ).
thf(f172,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f173,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f172]) ).
thf(f174,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f175,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f174]) ).
thf(f190,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f199,plain,
! [X0: $i] : ( exists_in_world @ empty_set @ X0 ),
inference(rectify,[],[f45]) ).
thf(f200,plain,
! [X0: $i] :
( ( exists_in_world @ empty_set @ X0 )
= $true ),
inference(fool_elimination,[],[f199]) ).
thf(f203,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ empty_set @ X0 ) ) ),
inference(rectify,[],[f79]) ).
thf(f204,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f225,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(flattening,[],[f204]) ).
thf(f235,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f239,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f242,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f266,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f140]) ).
thf(f267,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f130]) ).
thf(f269,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f273,plain,
! [X0: $i] :
( ( exists_in_world @ empty_set @ X0 )
= $true ),
inference(cnf_transformation,[],[f200]) ).
thf(f278,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f173]) ).
thf(f288,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f300,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mnot @ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(cnf_transformation,[],[f156]) ).
thf(f302,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f148]) ).
thf(f316,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,[],[f267,f266,f242,f266,f266]) ).
thf(f317,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,[],[f288,f242,f266]) ).
thf(f319,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,[],[f239,f316,f317,f317]) ).
thf(f325,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] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f235,f269,f278]) ).
thf(f353,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: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(definition_unfolding,[],[f300,f269,f278,f266]) ).
thf(f355,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 > $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 ) )
@ ( subset @ Y0 @ Y1 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f302,f269,f278,f278,f319,f278,f317]) ).
thf(f360,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] : ( subset @ empty_set @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f361,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] : ( subset @ empty_set @ Y0 ) ) )
= sF1 ),
inference(reorient_equations,[],[f360]) ).
thf(f362,plain,
$true != sF1,
inference(definition_folding,[],[f325,f361]) ).
thf(f456,plain,
( ( $true = 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] : ( subset @ empty_set @ Y0 ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f361]) ).
thf(f457,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ empty_set @ Y1 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f456]) ).
thf(f458,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ empty_set @ Y1 @ Y0 ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f457]) ).
thf(f459,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( subset @ empty_set @ Y0 @ sK2 ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f458]) ).
thf(f460,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( subset @ empty_set @ Y0 @ sK2 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f459]) ).
thf(f461,plain,
( ( $true = sF1 )
| ( ( ( exists_in_world @ sK3 @ sK2 )
=> ( subset @ empty_set @ sK3 @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f460]) ).
thf(f462,plain,
( ( $true = sF1 )
| ( $false
= ( subset @ empty_set @ sK3 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f461]) ).
thf(f463,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f461]) ).
thf(f593,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( member @ Y3 @ Y2 @ Y0 )
| ~ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( member @ Y3 @ Y2 @ Y0 )
| ~ ( member @ Y3 @ Y1 @ Y0 ) ) ) )
| ~ ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f355]) ).
thf(f594,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( member @ Y3 @ Y2 @ Y0 )
| ~ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( member @ Y3 @ Y2 @ Y0 )
| ~ ( member @ Y3 @ Y1 @ Y0 ) ) ) )
| ~ ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f593]) ).
thf(f595,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ( subset @ Y0 @ Y1 @ X1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ( member @ Y2 @ Y1 @ X1 )
| ~ ( member @ Y2 @ Y0 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ( member @ Y2 @ Y1 @ X1 )
| ~ ( member @ Y2 @ Y0 @ X1 ) ) ) )
| ~ ( subset @ Y0 @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f594]) ).
thf(f596,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ( subset @ Y0 @ Y1 @ X1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ( member @ Y2 @ Y1 @ X1 )
| ~ ( member @ Y2 @ Y0 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ( member @ Y2 @ Y1 @ X1 )
| ~ ( member @ Y2 @ Y0 @ X1 ) ) ) )
| ~ ( subset @ Y0 @ Y1 @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f595]) ).
thf(f597,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( subset @ X2 @ Y0 @ X1 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ( member @ Y1 @ Y0 @ X1 )
| ~ ( member @ Y1 @ X2 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ( member @ Y1 @ Y0 @ X1 )
| ~ ( member @ Y1 @ X2 @ X1 ) ) ) )
| ~ ( subset @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f596]) ).
thf(f598,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( subset @ X2 @ Y0 @ X1 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ( member @ Y1 @ Y0 @ X1 )
| ~ ( member @ Y1 @ X2 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ( member @ Y1 @ Y0 @ X1 )
| ~ ( member @ Y1 @ X2 @ X1 ) ) ) )
| ~ ( subset @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ( subset @ X2 @ Y0 @ X1 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ( member @ Y1 @ Y0 @ X1 )
| ~ ( member @ Y1 @ X2 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ( member @ Y1 @ Y0 @ X1 )
| ~ ( member @ Y1 @ X2 @ X1 ) ) ) )
| ~ ( subset @ X2 @ Y0 @ X1 ) ) ) )
@ X3 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f598]) ).
thf(f600,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ( subset @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) )
| ~ ( subset @ X2 @ X3 @ X1 ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f599]) ).
thf(f601,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( ~ ( ( subset @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) )
| ~ ( subset @ X2 @ X3 @ X1 ) ) ) ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f600]) ).
thf(f602,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( ~ ( ( subset @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) ) )
| ~ ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) )
| ~ ( subset @ X2 @ X3 @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f601]) ).
thf(f604,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( ( subset @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f602]) ).
thf(f605,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ( subset @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f604]) ).
thf(f606,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f605]) ).
thf(f607,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f606]) ).
thf(f608,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( member @ Y0 @ X3 @ X1 )
| ~ ( member @ Y0 @ X2 @ X1 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f607]) ).
thf(f609,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( ( exists_in_world @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 )
| ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f608]) ).
thf(f610,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $false
= ( ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 )
| ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f609]) ).
thf(f611,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f609]) ).
thf(f612,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f610]) ).
thf(f614,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f612]) ).
thf(f693,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( member @ Y1 @ empty_set @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f694,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( member @ Y1 @ empty_set @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f693]) ).
thf(f695,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( member @ Y0 @ empty_set @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f694]) ).
thf(f696,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( member @ Y0 @ empty_set @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f695]) ).
thf(f697,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
=> ~ ( member @ X2 @ empty_set @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f696]) ).
thf(f698,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ~ ( member @ X2 @ empty_set @ X1 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f697]) ).
thf(f699,plain,
! [X2: mu,X1: $i] :
( ( ( member @ X2 @ empty_set @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f698]) ).
thf(f969,definition,
( spl7_1
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f973,definition,
( spl7_2
<=> ( $true
= ( exists_in_world @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f975,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f973]) ).
thf(f976,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f463,f973,f969]) ).
thf(f978,definition,
( spl7_3
<=> ( $false
= ( subset @ empty_set @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f980,plain,
( ( $false
= ( subset @ empty_set @ sK3 @ sK2 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f978]) ).
thf(f981,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f462,f978,f969]) ).
thf(f983,definition,
( spl7_4
<=> ! [X2: mu,X1: $i] :
( ( $true
= ( subset @ empty_set @ X2 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f984,plain,
( ! [X2: mu,X1: $i] :
( ( $true
= ( subset @ empty_set @ X2 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f983]) ).
thf(f990,plain,
~ spl7_1,
inference(avatar_split_clause,[],[f362,f969]) ).
thf(f1008,plain,
( ( $true = $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ~ spl7_3
| ~ spl7_4 ),
inference(constrained_superposition,[],[f984,f980]) ).
thf(f1011,plain,
( ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f1008]) ).
thf(f1015,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f1011,f975]) ).
thf(f1016,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f1015]) ).
thf(f1017,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f1016]) ).
thf(f1085,plain,
! [X0: mu,X1: $i] :
( ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ empty_set ) @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f614,f699]) ).
thf(f1092,plain,
! [X0: mu,X1: $i] :
( ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ empty_set ) @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f1085]) ).
thf(f1102,plain,
! [X0: mu,X1: $i] :
( ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $true = $false )
| ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ empty_set ) @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(forward_demodulation,[],[f1092,f273]) ).
thf(f1103,plain,
! [X0: mu,X1: $i] :
( ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ empty_set ) @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1102]) ).
thf(f1114,plain,
! [X0: mu,X1: $i] :
( ( $false
= ( exists_in_world @ empty_set @ X1 ) )
| ( $true = $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f1103,f611]) ).
thf(f1121,plain,
! [X0: mu,X1: $i] :
( ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f1114]) ).
thf(f1122,plain,
! [X0: mu,X1: $i] :
( ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f1121]) ).
thf(f1126,plain,
! [X0: mu,X1: $i] :
( ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true = $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f1122,f273]) ).
thf(f1127,plain,
! [X0: mu,X1: $i] :
( ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f1126]) ).
thf(f1130,plain,
spl7_4,
inference(avatar_split_clause,[],[f1127,f983]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f976]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f981]) ).
cnf(s4,plain,
~ spl7_1,
inference(sat_conversion,[],[f990]) ).
cnf(s7,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s8,plain,
spl7_4,
inference(sat_conversion,[],[f1130]) ).
cnf(s10,plain,
( ~ spl7_2
| ~ spl7_3 ),
inference(rat,[],[s7,s8]) ).
cnf(s13,plain,
spl7_3,
inference(rat,[],[s2,s4]) ).
cnf(s14,plain,
~ spl7_2,
inference(rat,[],[s10,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s4]) ).
thf(f1131,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:36:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.36 % (2659133)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (2659142)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1314595674:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (2659144)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (2659144)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
% 0.21/0.36 % (2659138)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=945365910:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (2659139)lrs+10_16_si=on:nwc=1.5:random_seed=2885646932:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (2659140)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2789692721:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (2659142)Instruction limit reached!
% 0.21/0.36 % (2659142)------------------------------
% 0.21/0.36 % (2659142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659142)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659142)Termination reason: Instruction limit
% 0.21/0.36 % (2659142)Termination phase: Saturation
% 0.21/0.36 % (2659142)Time elapsed: 0.007 s
% 0.21/0.36 % (2659142)Peak memory usage: 12 MB
% 0.21/0.36 % (2659142)Instructions burned: 27 (million)
% 0.21/0.36 % (2659141)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=1262277382: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)
% 0.21/0.36 % (2659143)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3543842787:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (2659144)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=3350908304:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (2659140)Instruction limit reached!
% 0.21/0.36 % (2659140)------------------------------
% 0.21/0.36 % (2659140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659140)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659140)Termination reason: Instruction limit
% 0.21/0.36 % (2659140)Termination phase: shuffling
% 0.21/0.36 % (2659140)Time elapsed: 0.002 s
% 0.21/0.36 % (2659140)Peak memory usage: 10 MB
% 0.21/0.36 % (2659140)Instructions burned: 4 (million)
% 0.21/0.36 % (2659139)Instruction limit reached!
% 0.21/0.36 % (2659139)------------------------------
% 0.21/0.36 % (2659139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659139)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659139)Termination reason: Instruction limit
% 0.21/0.36 % (2659139)Termination phase: Function definition elimination
% 0.21/0.36 % (2659139)Time elapsed: 0.008 s
% 0.21/0.36 % (2659139)Peak memory usage: 10 MB
% 0.21/0.36 % (2659139)Instructions burned: 19 (million)
% 0.21/0.36 % (2659152)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1665565425:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (2659152)Instruction limit reached!
% 0.21/0.36 % (2659152)------------------------------
% 0.21/0.36 % (2659152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659152)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659152)Termination reason: Instruction limit
% 0.21/0.36 % (2659152)Termination phase: shuffling
% 0.21/0.36 % (2659152)Time elapsed: 0.001 s
% 0.21/0.36 % (2659152)Peak memory usage: 10 MB
% 0.21/0.36 % (2659152)Instructions burned: 4 (million)
% 0.21/0.36 % (2659153)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3864613720:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (2659156)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3880095287:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.36 % (2659154)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (2659153)Instruction limit reached!
% 0.21/0.36 % (2659153)------------------------------
% 0.21/0.36 % (2659153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659153)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659153)Termination reason: Instruction limit
% 0.21/0.36 % (2659153)Termination phase: shuffling
% 0.21/0.36 % (2659153)Time elapsed: 0.003 s
% 0.21/0.36 % (2659153)Peak memory usage: 10 MB
% 0.21/0.36 % (2659153)Instructions burned: 7 (million)
% 0.21/0.36 % (2659156)Instruction limit reached!
% 0.21/0.36 % (2659156)------------------------------
% 0.21/0.36 % (2659156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659156)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659156)Termination reason: Instruction limit
% 0.21/0.36 % (2659156)Termination phase: SInE selection
% 0.21/0.36 % (2659156)Time elapsed: 0.003 s
% 0.21/0.36 % (2659156)Peak memory usage: 10 MB
% 0.21/0.36 % (2659156)Instructions burned: 14 (million)
% 0.21/0.36 % (2659154)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2540649770:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.36 % (2659154)Instruction limit reached!
% 0.21/0.36 % (2659154)------------------------------
% 0.21/0.36 % (2659154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659154)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659154)Termination reason: Instruction limit
% 0.21/0.36 % (2659154)Termination phase: Property scanning
% 0.21/0.36 % (2659154)Time elapsed: 0.004 s
% 0.21/0.36 % (2659154)Peak memory usage: 10 MB
% 0.21/0.36 % (2659154)Instructions burned: 9 (million)
% 0.21/0.36 % (2659143)Instruction limit reached!
% 0.21/0.36 % (2659143)------------------------------
% 0.21/0.36 % (2659143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659143)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659143)Termination reason: Instruction limit
% 0.21/0.36 % (2659143)Termination phase: Saturation
% 0.21/0.36 % (2659143)Time elapsed: 0.033 s
% 0.21/0.36 % (2659143)Peak memory usage: 12 MB
% 0.21/0.36 % (2659143)Instructions burned: 77 (million)
% 0.21/0.36 % (2659138)Instruction limit reached!
% 0.21/0.36 % (2659138)------------------------------
% 0.21/0.36 % (2659138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659138)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659138)Termination reason: Instruction limit
% 0.21/0.36 % (2659138)Termination phase: Saturation
% 0.21/0.36 % (2659138)Time elapsed: 0.037 s
% 0.21/0.36 % (2659138)Peak memory usage: 12 MB
% 0.21/0.36 % (2659138)Instructions burned: 88 (million)
% 0.21/0.36 % (2659160)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=2093273810:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.36 % (2659159)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
% 0.21/0.36 % (2659159)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (2659159)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2992696257:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.36 % (2659163)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.36 % (2659162)lrs+10_1_si=on:cs=on:random_seed=848168808:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.36 % (2659163)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=3389308815:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (2659144) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2659133-2659144"...
% 0.21/0.36 % (2659163)Instruction limit reached!
% 0.21/0.36 % (2659163)------------------------------
% 0.21/0.36 % (2659163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659162)Instruction limit reached!
% 0.21/0.36 % (2659162)------------------------------
% 0.21/0.36 % (2659162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659163)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659163)Termination reason: Instruction limit
% 0.21/0.36 % (2659163)Termination phase: shuffling
% 0.21/0.36 % (2659163)Time elapsed: 0.002 s
% 0.21/0.36 % (2659163)Peak memory usage: 10 MB
% 0.21/0.36 % (2659162)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659162)Termination reason: Instruction limit
% 0.21/0.36 % (2659162)Termination phase: Property scanning
% 0.21/0.36 % (2659163)Instructions burned: 5 (million)
% 0.21/0.36 % (2659162)Time elapsed: 0.004 s
% 0.21/0.36 % (2659162)Peak memory usage: 10 MB
% 0.21/0.36 % (2659162)Instructions burned: 10 (million)
% 0.21/0.36 % (2659160)Instruction limit reached!
% 0.21/0.36 % (2659160)------------------------------
% 0.21/0.36 % (2659160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2659160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2659160)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2659160)Termination reason: Instruction limit
% 0.21/0.36 % (2659160)Termination phase: Saturation
% 0.21/0.36 % (2659160)Time elapsed: 0.019 s
% 0.21/0.36 % (2659160)Peak memory usage: 12 MB
% 0.21/0.36 % (2659160)Instructions burned: 86 (million)
% 0.21/0.36 % (2659159)Instruction limit reached!
% 0.78/0.36 % (2659159)------------------------------
% 0.78/0.36 % (2659159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.36 % (2659159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.36 % (2659159)CaDiCaL version: 2.1.3
% 0.78/0.36 % (2659159)Termination reason: Instruction limit
% 0.78/0.36 % (2659159)Termination phase: Property scanning
% 0.78/0.36 % (2659159)Time elapsed: 0.013 s
% 0.78/0.36 % (2659159)Peak memory usage: 10 MB
% 0.78/0.36 % (2659159)Instructions burned: 30 (million)
% 0.78/0.36 % (2659165)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1040686032:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.78/0.36 % (2659144)...printing done.
% 0.78/0.36 % (2659144)Refutation found. Thanks to Tanya!
% 0.78/0.36 % SZS status Theorem for theBenchmark
% 0.78/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.78/0.36 % (2659144)------------------------------
% 0.78/0.36 % (2659144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.36 % (2659144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.36 % (2659144)CaDiCaL version: 2.1.3
% 0.78/0.36 % (2659144)Termination reason: Refutation
% 0.78/0.36 % (2659144)Time elapsed: 0.059 s
% 0.78/0.36 % (2659144)Peak memory usage: 14 MB
% 0.78/0.36 % (2659144)Instructions burned: 129 (million)
% 0.78/0.36 % (2659133)Success in time 0.109 s
% 0.78/0.36 % Vampire exiting
%------------------------------------------------------------------------------