%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET027^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:11 AM UTC 2026
% Result : Theorem 0.24s 0.32s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 18
% Syntax : Number of formulae : 162 ( 55 unt; 0 typ; 9 def)
% Number of atoms : 1633 ( 350 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 2713 ( 272 ~; 421 |; 0 &;1843 @)
% ( 8 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 180 ( 180 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 16 con; 0-4 aty)
% ( 81 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 525 ( 0 sgn 154 !; 0 ?; 525 :)
% 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,
member: mu > mu > $i > $o ).
thf(func_def_37,type,
subset: mu > mu > $i > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK0: $i > mu ).
thf(func_def_54,type,
sF1: $o ).
thf(func_def_56,type,
sK3: mu ).
thf(func_def_57,type,
sK4: mu ).
thf(func_def_58,type,
sK5: mu ).
thf(func_def_59,type,
sK6: mu > $i > mu > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f37,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/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(f39,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(f40,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
thf(f41,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f44,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,[],[f37]) ).
thf(f45,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,[],[f44]) ).
thf(f46,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f58,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f59,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f70,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f71,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f81,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X2 ) ) @ ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f84,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f93,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f108,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(flattening,[],[f84]) ).
thf(f116,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y2 ) ) @ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f117,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f118,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f128,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,[],[f45]) ).
thf(f131,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f137,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f146,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f149,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f151,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f155,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f151,f118,f131,f118,f118]) ).
thf(f156,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f146,f131,f118]) ).
thf(f158,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f117,f155,f156,f156]) ).
thf(f164,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: 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y2 ) )
@ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f116,f137,f149,f149,f149,f156,f155]) ).
thf(f165,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] :
( ( Y6 @ Y8 )
| ( Y7 @ 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] :
( ( Y6 @ Y8 )
| ( Y7 @ 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] :
( ( Y6 @ Y8 )
| ( Y7 @ 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f128,f137,f149,f149,f158,f149,f156]) ).
thf(f169,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: 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y2 ) )
@ ( subset @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f170,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: 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y2 ) )
@ ( subset @ Y0 @ Y2 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f169]) ).
thf(f171,plain,
$true != sF1,
inference(definition_folding,[],[f164,f170]) ).
thf(f179,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: 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y2 ) )
@ ( subset @ Y0 @ Y2 ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f170]) ).
thf(f180,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y3 @ Y0 ) )
| ( subset @ Y1 @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
( ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y3 @ Y0 ) )
| ( subset @ Y1 @ Y3 @ Y0 ) ) ) ) ) ) ) )
@ sK2 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ Y0 @ Y1 @ sK2 )
| ~ ( subset @ Y1 @ Y2 @ sK2 ) )
| ( subset @ Y0 @ Y2 @ sK2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ Y0 @ Y1 @ sK2 )
| ~ ( subset @ Y1 @ Y2 @ sK2 ) )
| ( subset @ Y0 @ Y2 @ sK2 ) ) ) ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $true = sF1 )
| ( $false
= ( ( exists_in_world @ sK3 @ sK2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ Y0 @ sK2 )
| ~ ( subset @ Y0 @ Y1 @ sK2 ) )
| ( subset @ sK3 @ Y1 @ sK2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( ( $true = sF1 )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ Y0 @ sK2 )
| ~ ( subset @ Y0 @ Y1 @ sK2 ) )
| ( subset @ sK3 @ Y1 @ sK2 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ Y0 @ sK2 )
| ~ ( subset @ Y0 @ Y1 @ sK2 ) )
| ( subset @ sK3 @ Y1 @ sK2 ) ) ) ) )
@ sK4 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( ( ( exists_in_world @ sK4 @ sK2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ Y0 @ sK2 ) )
| ( subset @ sK3 @ Y0 @ sK2 ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ Y0 @ sK2 ) )
| ( subset @ sK3 @ Y0 @ sK2 ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ Y0 @ sK2 ) )
| ( subset @ sK3 @ Y0 @ sK2 ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( $false
= ( ( exists_in_world @ sK5 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK5 @ sK2 ) )
| ( subset @ sK3 @ sK5 @ sK2 ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
( ( $true = sF1 )
| ( ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK5 @ sK2 ) )
| ( subset @ sK3 @ sK5 @ sK2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( $true = sF1 )
| ( $true
= ( exists_in_world @ sK5 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( $true = sF1 )
| ( $false
= ( subset @ sK3 @ sK5 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK5 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f197,plain,
( ( ( ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK5 @ sK2 ) ) )
= $true )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $true = sF1 )
| ( ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK5 @ sK2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( ( ~ ( subset @ sK4 @ sK5 @ sK2 ) )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( ( ~ ( subset @ sK3 @ sK4 @ sK2 ) )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f201,plain,
( ( $true = sF1 )
| ( $true
= ( subset @ sK3 @ sK4 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $true = sF1 )
| ( ( subset @ sK4 @ sK5 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f224,plain,
( ( !! @ $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 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f225,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 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f226,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 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ~ ( member @ Y2 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) )
| ( subset @ Y0 @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,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 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ~ ( member @ Y2 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) )
| ( subset @ Y0 @ Y1 @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,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 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( subset @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,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 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( subset @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f230,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 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( subset @ X2 @ Y0 @ X1 ) ) ) )
@ X3 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,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 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,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 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $false
= ( ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f236,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( subset @ X2 @ X3 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
= $true )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ( subset @ X2 @ X3 @ X1 ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) )
@ X4 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X4 @ X1 )
=> ( ~ ( member @ X4 @ X2 @ X1 )
| ( member @ X4 @ X3 @ X1 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( ~ ( member @ X4 @ X2 @ X1 )
| ( member @ X4 @ X3 @ X1 ) ) )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( member @ X4 @ X3 @ X1 ) )
| ( $true
= ( ~ ( member @ X4 @ X2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( $true
= ( member @ X4 @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( member @ X4 @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f245,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) )
@ ( sK6 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ( exists_in_world @ ( sK6 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ~ ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ ( sK6 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f251,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $false
= ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f252,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f253,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( member @ ( sK6 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f252]) ).
thf(f264,definition,
( spl7_1
<=> ( $true
= ( exists_in_world @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f266,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f268,definition,
( spl7_2
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f271,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f186,f268,f264]) ).
thf(f273,definition,
( spl7_3
<=> ( $true
= ( exists_in_world @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f275,plain,
( ( $true
= ( exists_in_world @ sK4 @ sK2 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f276,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f190,f268,f273]) ).
thf(f278,definition,
( spl7_4
<=> ( $true
= ( exists_in_world @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f280,plain,
( ( $true
= ( exists_in_world @ sK5 @ sK2 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f281,plain,
( spl7_4
| spl7_2 ),
inference(avatar_split_clause,[],[f194,f268,f278]) ).
thf(f283,definition,
( spl7_5
<=> ( $true
= ( subset @ sK3 @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f285,plain,
( ( $true
= ( subset @ sK3 @ sK4 @ sK2 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f286,plain,
( spl7_2
| spl7_5 ),
inference(avatar_split_clause,[],[f201,f283,f268]) ).
thf(f288,definition,
( spl7_6
<=> ( ( subset @ sK4 @ sK5 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f290,plain,
( ( ( subset @ sK4 @ sK5 @ sK2 )
= $true )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f291,plain,
( spl7_6
| spl7_2 ),
inference(avatar_split_clause,[],[f202,f268,f288]) ).
thf(f293,definition,
( spl7_7
<=> ( $false
= ( subset @ sK3 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f295,plain,
( ( $false
= ( subset @ sK3 @ sK5 @ sK2 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f293]) ).
thf(f296,plain,
( spl7_7
| spl7_2 ),
inference(avatar_split_clause,[],[f195,f268,f293]) ).
thf(f298,definition,
( spl7_8
<=> ! [X4: mu,X3: mu,X2: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( subset @ X3 @ X4 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X4 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f299,plain,
( ! [X2: mu,X3: mu,X1: $i,X4: mu] :
( ( $true
= ( subset @ X2 @ X4 @ X1 ) )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( subset @ X3 @ X4 @ X1 )
= $false ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f305,plain,
~ spl7_2,
inference(avatar_split_clause,[],[f171,f268]) ).
thf(f328,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true = $false )
| ( ( member @ ( sK6 @ X0 @ X1 @ X2 ) @ X3 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f243,f251]) ).
thf(f331,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( $true = $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( member @ ( sK6 @ X0 @ X1 @ X2 ) @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f328]) ).
thf(f332,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( ( member @ ( sK6 @ X0 @ X1 @ X2 ) @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f331]) ).
thf(f340,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( $false
= ( subset @ X4 @ X3 @ X1 ) )
| ( $false
= ( member @ ( sK6 @ X0 @ X1 @ X2 ) @ X4 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f243,f332]) ).
thf(f341,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X4: mu] :
( ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( member @ ( sK6 @ X0 @ X1 @ X2 ) @ X4 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $false
= ( subset @ X4 @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f340]) ).
thf(f342,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X4: mu] :
( ( $false
= ( member @ ( sK6 @ X0 @ X1 @ X2 ) @ X4 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X4 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( $false
= ( subset @ X4 @ X3 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f350,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true = $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f342,f253]) ).
thf(f358,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f350]) ).
thf(f359,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( ( exists_in_world @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f364,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f359,f250]) ).
thf(f370,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( $true = $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) )
| ( $true
= ( subset @ X2 @ X0 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f364]) ).
thf(f371,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i] :
( ( $true
= ( subset @ X2 @ X0 @ X1 ) )
| ( ( subset @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f378,plain,
spl7_8,
inference(avatar_split_clause,[],[f371,f298]) ).
thf(f379,plain,
( ! [X0: mu] :
( ( ( subset @ X0 @ sK5 @ sK2 )
= $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ( ( subset @ sK3 @ X0 @ sK2 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK2 ) )
| ( $true = $false )
| ( ( exists_in_world @ sK5 @ sK2 )
= $false ) )
| ~ spl7_7
| ~ spl7_8 ),
inference(constrained_superposition,[],[f299,f295]) ).
thf(f385,plain,
( ! [X0: mu] :
( ( $false
= ( exists_in_world @ X0 @ sK2 ) )
| ( ( subset @ X0 @ sK5 @ sK2 )
= $false )
| ( ( exists_in_world @ sK3 @ sK2 )
= $false )
| ( ( exists_in_world @ sK5 @ sK2 )
= $false )
| ( ( subset @ sK3 @ X0 @ sK2 )
= $false ) )
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f387,plain,
( ! [X0: mu] :
( ( ( subset @ X0 @ sK5 @ sK2 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK2 ) )
| ( $true = $false )
| ( ( subset @ sK3 @ X0 @ sK2 )
= $false )
| ( ( exists_in_world @ sK5 @ sK2 )
= $false ) )
| ~ spl7_1
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f385,f266]) ).
thf(f388,plain,
( ! [X0: mu] :
( ( $false
= ( exists_in_world @ X0 @ sK2 ) )
| ( ( exists_in_world @ sK5 @ sK2 )
= $false )
| ( ( subset @ X0 @ sK5 @ sK2 )
= $false )
| ( ( subset @ sK3 @ X0 @ sK2 )
= $false ) )
| ~ spl7_1
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f387]) ).
thf(f391,plain,
( ! [X0: mu] :
( ( ( subset @ X0 @ sK5 @ sK2 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK2 ) )
| ( $true = $false )
| ( ( subset @ sK3 @ X0 @ sK2 )
= $false ) )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f388,f280]) ).
thf(f392,plain,
( ! [X0: mu] :
( ( ( subset @ sK3 @ X0 @ sK2 )
= $false )
| ( ( subset @ X0 @ sK5 @ sK2 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK2 ) ) )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f397,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( ( subset @ sK4 @ sK5 @ sK2 )
= $false )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(constrained_superposition,[],[f392,f285]) ).
thf(f411,plain,
( ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( ( subset @ sK4 @ sK5 @ sK2 )
= $false )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f419,plain,
( ( ( subset @ sK4 @ sK5 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f411,f275]) ).
thf(f420,plain,
( ( ( subset @ sK4 @ sK5 @ sK2 )
= $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f424,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f420,f290]) ).
thf(f425,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f426,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f425]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f271]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f276]) ).
cnf(s3,plain,
( spl7_2
| spl7_4 ),
inference(sat_conversion,[],[f281]) ).
cnf(s4,plain,
( spl7_2
| spl7_5 ),
inference(sat_conversion,[],[f286]) ).
cnf(s5,plain,
( spl7_2
| spl7_6 ),
inference(sat_conversion,[],[f291]) ).
cnf(s6,plain,
( spl7_2
| spl7_7 ),
inference(sat_conversion,[],[f296]) ).
cnf(s8,plain,
~ spl7_2,
inference(sat_conversion,[],[f305]) ).
cnf(s9,plain,
spl7_8,
inference(sat_conversion,[],[f378]) ).
cnf(s12,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6
| ~ spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f426]) ).
cnf(s13,plain,
spl7_7,
inference(rat,[],[s6,s8]) ).
cnf(s14,plain,
spl7_6,
inference(rat,[],[s5,s8]) ).
cnf(s15,plain,
spl7_5,
inference(rat,[],[s4,s8]) ).
cnf(s16,plain,
spl7_4,
inference(rat,[],[s3,s8]) ).
cnf(s17,plain,
spl7_3,
inference(rat,[],[s2,s8]) ).
cnf(s18,plain,
~ spl7_1,
inference(rat,[],[s12,s9,s13,s14,s15,s16,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s8,s18]) ).
thf(f427,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:33:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.32 % (3359819)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.32 % (3359826)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=226613647:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.32 % (3359826)Instruction limit reached!
% 0.24/0.32 % (3359826)------------------------------
% 0.24/0.32 % (3359826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3359826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3359826)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3359826)Termination reason: Instruction limit
% 0.24/0.32 % (3359826)Termination phase: Function definition elimination
% 0.24/0.32 % (3359826)Time elapsed: 0.002 s
% 0.24/0.32 % (3359826)Peak memory usage: 10 MB
% 0.24/0.32 % (3359826)Instructions burned: 6 (million)
% 0.24/0.32 % (3359830)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.32 % (3359830)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
% 0.24/0.32 % (3359828)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3672755255:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.32 % (3359825)lrs+10_16_si=on:nwc=1.5:random_seed=103746526:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.32 % (3359824)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=16864961:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.32 % (3359829)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3625000939:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.32 % (3359827)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=1585628220: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)
% 0.24/0.32 % (3359830)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=3963733834:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.32 % (3359832)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4090097069:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.32 % (3359832)Instruction limit reached!
% 0.24/0.32 % (3359832)------------------------------
% 0.24/0.32 % (3359832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3359832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3359832)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3359832)Termination reason: Instruction limit
% 0.24/0.32 % (3359832)Termination phase: Property scanning
% 0.24/0.32 % (3359832)Time elapsed: 0.002 s
% 0.24/0.32 % (3359832)Peak memory usage: 10 MB
% 0.24/0.32 % (3359832)Instructions burned: 9 (million)
% 0.24/0.32 % (3359825)Instruction limit reached!
% 0.24/0.32 % (3359825)------------------------------
% 0.24/0.32 % (3359825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3359825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3359825)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3359825)Termination reason: Instruction limit
% 0.24/0.32 % (3359825)Termination phase: Saturation
% 0.24/0.32 % (3359825)Time elapsed: 0.009 s
% 0.24/0.32 % (3359825)Peak memory usage: 12 MB
% 0.24/0.32 % (3359825)Instructions burned: 19 (million)
% 0.24/0.32 % (3359828)Instruction limit reached!
% 0.24/0.32 % (3359828)------------------------------
% 0.24/0.32 % (3359828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3359828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3359828)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3359828)Termination reason: Instruction limit
% 0.24/0.32 % (3359828)Termination phase: Saturation
% 0.24/0.32 % (3359828)Time elapsed: 0.014 s
% 0.24/0.32 % (3359828)Peak memory usage: 12 MB
% 0.24/0.32 % (3359828)Instructions burned: 24 (million)
% 0.24/0.32 % (3359830) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3359819-3359830"...
% 0.24/0.32 % (3359840)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3423606714:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.24/0.32 % (3359840)Instruction limit reached!
% 0.24/0.32 % (3359840)------------------------------
% 0.24/0.32 % (3359840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3359840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3359840)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3359840)Termination reason: Instruction limit
% 0.24/0.32 % (3359840)Termination phase: Property scanning
% 0.24/0.32 % (3359840)Time elapsed: 0.001 s
% 0.24/0.32 % (3359840)Peak memory usage: 10 MB
% 0.24/0.32 % (3359840)Instructions burned: 6 (million)
% 0.24/0.32 % (3359841)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.24/0.32 % (3359830)...printing done.
% 0.24/0.32 % (3359830)Refutation found. Thanks to Tanya!
% 0.24/0.32 % SZS status Theorem for theBenchmark
% 0.24/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.33 % (3359830)------------------------------
% 0.24/0.33 % (3359830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (3359830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (3359830)CaDiCaL version: 2.1.3
% 0.24/0.33 % (3359830)Termination reason: Refutation
% 0.24/0.33 % (3359830)Time elapsed: 0.024 s
% 0.24/0.33 % (3359830)Peak memory usage: 13 MB
% 0.24/0.33 % (3359830)Instructions burned: 48 (million)
% 0.24/0.33 % (3359819)Success in time 0.061 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------