%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET926^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:23:50 AM UTC 2026
% Result : Theorem 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 101 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 745 ( 148 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 1740 ( 161 ~; 144 |; 0 &;1343 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 7 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 326 ( 255 ^; 71 !; 0 ?; 326 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
in: mu > mu > $i > $o ).
thf(func_def_37,type,
empty: mu > $i > $o ).
thf(func_def_38,type,
empty_set: mu ).
thf(func_def_39,type,
singleton: mu > mu ).
thf(func_def_40,type,
set_difference: mu > mu > mu ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vAND: $o > $o > $o ).
thf(func_def_55,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK0: $i > mu ).
thf(func_def_58,type,
sK2: mu ).
thf(func_def_59,type,
sK3: mu ).
thf(func_def_60,type,
sK4: $i > mu ).
thf(func_def_61,type,
sK5: $i > 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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f11,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mequiv) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f51,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(f52,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(f55,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(f56,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
thf(f58,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f59,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f61,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f67,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f68,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f70,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f75,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f76,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f101,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f102,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f101]) ).
thf(f146,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f51]) ).
thf(f147,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f146]) ).
thf(f148,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f52]) ).
thf(f149,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f154,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f155,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f156,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f155]) ).
thf(f161,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f162,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f167,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f168,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f170,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f174,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f187,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f210,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f147]) ).
thf(f211,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f149]) ).
thf(f214,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f156]) ).
thf(f218,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,[],[f167,f161,f162,f161,f161]) ).
thf(f219,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,[],[f168,f162,f161]) ).
thf(f221,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,[],[f170,f218,f219,f219]) ).
thf(f240,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 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f210,f187,f174,f174,f221,f161]) ).
thf(f241,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 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f211,f187,f174,f174,f221]) ).
thf(f244,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f214,f187,f174,f174,f162]) ).
thf(f245,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ sK1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f246]) ).
thf(f248,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ sK1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( $false
= ( ( exists_in_world @ sK2 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f252,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ sK1 ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f250]) ).
thf(f253,plain,
( $false
= ( ( exists_in_world @ sK3 @ sK1 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
( $false
= ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ sK1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f255,plain,
( $true
= ( exists_in_world @ sK3 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f256,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ sK1 ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f257,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ sK1 ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f277,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
| ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ( in @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f278,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
| ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ( in @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 )
| ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ( in @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f280,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 )
| ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ( in @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 )
| ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 )
| ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 )
| ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ( in @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ X1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f285,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
| ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f286]) ).
thf(f292,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f293,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) )
| ( $true
= ( ~ ( in @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
| ~ ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ~ ( in @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f296,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
| ~ ( in @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ~ ( in @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ~ ( in @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f298,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 )
| ~ ( in @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ~ ( in @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 )
| ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( in @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f300,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 )
| ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( in @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 )
| ~ ( in @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( in @ X2 @ Y0 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ X1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
| ~ ( in @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f311,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ~ ( in @ X2 @ X3 @ X1 )
| ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f312,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) )
| ( $true
= ( ~ ~ ( in @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) )
| ( $false
= ( ~ ( in @ X2 @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( in @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f1610,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f257,f294]) ).
thf(f1611,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1610]) ).
thf(f1623,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f1611,f255]) ).
thf(f1624,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1623]) ).
thf(f1631,plain,
( ( $true = $false )
| ( $false
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f1624,f251]) ).
thf(f1632,plain,
( $false
= ( in @ sK2 @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f1631]) ).
thf(f1746,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f256,f314]) ).
thf(f1747,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1746]) ).
thf(f1755,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f1747,f255]) ).
thf(f1756,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $true
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1755]) ).
thf(f1763,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f1756,f251]) ).
thf(f1764,plain,
( $true
= ( in @ sK2 @ sK3 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f1763]) ).
thf(f1771,plain,
$true = $false,
inference(forward_demodulation,[],[f1764,f1632]) ).
thf(f1772,plain,
$false,
inference(trivial_inequality_removal,[],[f1771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET926^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:46:05 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.34 % (367978)Will run a generic schedule for satisfiability detection.
% 0.20/0.34 % (368000)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3242861175:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (367996)% WARNING: option uhcvi not known.
% 0.20/0.34 % (367996)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4010942049:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.34 % (367995)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2771350491_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.34 % (367998)dis+10_1_sil=32000:sp=arity:random_seed=3594078132:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.34 % (367997)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4015670074:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.34 % (367999)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1317590406:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.34 % (368001)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1085264832:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.34 % (367996)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % (367999)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (367996)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.34 % (368016)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1763173786:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.34 % (368000)Instruction limit reached!
% 0.20/0.34 % (368000)------------------------------
% 0.20/0.34 % (368000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (368000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (368000)CaDiCaL version: 2.1.3
% 0.20/0.34 % (368000)Termination reason: Instruction limit
% 0.20/0.34 % (368000)Termination phase: Saturation
% 0.20/0.34 % (368000)Time elapsed: 0.034 s
% 0.20/0.34 % (368000)Peak memory usage: 13 MB
% 0.20/0.34 % (368000)Instructions burned: 134 (million)
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (368030)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1074915286:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (367998)Instruction limit reached!
% 0.20/0.34 % (367998)------------------------------
% 0.20/0.34 % (367998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (367998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (367998)CaDiCaL version: 2.1.3
% 0.20/0.34 % (367998)Termination reason: Instruction limit
% 0.20/0.34 % (367998)Termination phase: Saturation
% 0.20/0.34 % (367998)Time elapsed: 0.048 s
% 0.20/0.34 % (367998)Peak memory usage: 12 MB
% 0.20/0.34 % (367998)Instructions burned: 104 (million)
% 0.20/0.34 % (368035)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=660417872:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.34 % (367999)Instruction limit reached!
% 0.20/0.34 % (367999)------------------------------
% 0.20/0.34 % (367999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (367999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (367999)CaDiCaL version: 2.1.3
% 0.20/0.34 % (367999)Termination reason: Instruction limit
% 0.20/0.34 % (367999)Termination phase: Saturation
% 0.20/0.34 % (367999)Time elapsed: 0.055 s
% 0.20/0.34 % (367999)Peak memory usage: 12 MB
% 0.20/0.34 % (367999)Instructions burned: 116 (million)
% 0.20/0.34 % (368035)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % (368035)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.34 % (368046)ott-21_1_sil=16000:fs=off:random_seed=139412336:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.34 % (368001)Instruction limit reached!
% 0.20/0.34 % (368001)------------------------------
% 0.20/0.34 % (368001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (368001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (368001)CaDiCaL version: 2.1.3
% 0.20/0.34 % (368001)Termination reason: Instruction limit
% 0.20/0.34 % (368001)Termination phase: Saturation
% 0.20/0.34 % (368001)Time elapsed: 0.070 s
% 0.20/0.34 % (368001)Peak memory usage: 12 MB
% 0.20/0.34 % (368001)Instructions burned: 159 (million)
% 0.20/0.34 % (368030)Instruction limit reached!
% 0.20/0.34 % (368030)------------------------------
% 0.20/0.34 % (368030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (368030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (368030)CaDiCaL version: 2.1.3
% 0.20/0.34 % (368030)Termination reason: Instruction limit
% 0.20/0.34 % (368030)Termination phase: Saturation
% 0.20/0.34 % (368030)Time elapsed: 0.033 s
% 0.20/0.34 % (368030)Peak memory usage: 12 MB
% 0.20/0.34 % (368030)Instructions burned: 134 (million)
% 0.20/0.34 % (367997) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-367978-367997"...
% 0.20/0.34 % (368052)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3377865109:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.20/0.34 % (367997)...printing done.
% 0.20/0.34 % (367997)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (367997)------------------------------
% 0.20/0.35 % (367997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (367997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (367997)CaDiCaL version: 2.1.3
% 0.20/0.35 % (367997)Termination reason: Refutation
% 0.20/0.35 % (367997)Time elapsed: 0.077 s
% 0.20/0.35 % (367997)Peak memory usage: 13 MB
% 0.20/0.35 % (367997)Instructions burned: 148 (million)
% 0.20/0.35 % (367978)Success in time 0.12 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------