%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET583^7 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:17 AM UTC 2026
% Result : Theorem 0.21s 0.36s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of formulae : 149 ( 62 unt; 0 typ; 8 def)
% Number of atoms : 1148 ( 214 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2065 ( 315 ~; 293 |; 0 &;1343 @)
% ( 7 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 182 ( 182 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 64 usr; 14 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 420 ( 0 sgn 77 !; 0 ?; 420 :)
% 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_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $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 > $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,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f38,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( qmltpeq @ X0 @ X1 ) @ ( qmltpeq @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(f44,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(f47,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( qmltpeq @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_extensionality) ).
thf(f48,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( qmltpeq @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
thf(f63,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f64,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f72,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f82,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f89,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( qmltpeq @ X0 @ X1 ) @ ( qmltpeq @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f90,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( qmltpeq @ Y0 @ Y1 ) @ ( qmltpeq @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f92,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) @ ( qmltpeq @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f48]) ).
thf(f93,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( qmltpeq @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f113,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f114,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f113]) ).
thf(f120,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( qmltpeq @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f44]) ).
thf(f121,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f120]) ).
thf(f124,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f125,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f132,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( qmltpeq @ Y0 @ Y1 ) ) ) ) ) ),
inference(flattening,[],[f93]) ).
thf(f137,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) @ ( qmltpeq @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f138,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f148,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f149,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( qmltpeq @ Y0 @ Y1 ) @ ( qmltpeq @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f157,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( qmltpeq @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f121]) ).
thf(f159,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f114]) ).
thf(f163,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f167,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f180,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f183,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f187,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,[],[f180,f138,f163,f138,f138]) ).
thf(f188,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,[],[f183,f163,f138]) ).
thf(f190,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,[],[f148,f187,f188,f188]) ).
thf(f196,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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) )
@ ( qmltpeq @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f137,f159,f167,f167,f188,f187]) ).
thf(f200,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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( qmltpeq @ Y0 @ Y1 )
@ ( qmltpeq @ Y1 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f149,f159,f167,f167,f188]) ).
thf(f204,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 @ Y0 @ Y1 )
@ ( ^ [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 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f157,f159,f167,f167,f190,f187]) ).
thf(f209,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) )
@ ( qmltpeq @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f210,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) )
@ ( qmltpeq @ Y0 @ Y1 ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f209]) ).
thf(f211,plain,
$true != sF1,
inference(definition_folding,[],[f196,f210]) ).
thf(f231,plain,
( ( $false
= ( ^ [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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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 ) ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) )
@ ( qmltpeq @ Y0 @ Y1 ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f210]) ).
thf(f232,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y1 @ Y0 ) )
| ( qmltpeq @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y1 @ Y0 ) )
| ( qmltpeq @ Y1 @ Y2 @ Y0 ) ) ) ) ) )
@ sK2 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ Y0 @ Y1 @ sK2 )
| ~ ( subset @ Y1 @ Y0 @ sK2 ) )
| ( qmltpeq @ Y0 @ Y1 @ sK2 ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ Y0 @ Y1 @ sK2 )
| ~ ( subset @ Y1 @ Y0 @ sK2 ) )
| ( qmltpeq @ Y0 @ Y1 @ sK2 ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( $false
= ( ( exists_in_world @ sK3 @ sK2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ Y0 @ sK2 )
| ~ ( subset @ Y0 @ sK3 @ sK2 ) )
| ( qmltpeq @ sK3 @ Y0 @ sK2 ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ Y0 @ sK2 )
| ~ ( subset @ Y0 @ sK3 @ sK2 ) )
| ( qmltpeq @ sK3 @ Y0 @ sK2 ) ) ) ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $true = sF1 )
| ( $true
= ( exists_in_world @ sK3 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f239,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ Y0 @ sK2 )
| ~ ( subset @ Y0 @ sK3 @ sK2 ) )
| ( qmltpeq @ sK3 @ Y0 @ sK2 ) ) )
@ sK4 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f237]) ).
thf(f240,plain,
( ( $true = sF1 )
| ( $false
= ( ( exists_in_world @ sK4 @ sK2 )
=> ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK3 @ sK2 ) )
| ( qmltpeq @ sK3 @ sK4 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK3 @ sK2 ) )
| ( qmltpeq @ sK3 @ sK4 @ sK2 ) ) ) ),
inference(imp_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $true = sF1 )
| ( $true
= ( exists_in_world @ sK4 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f240]) ).
thf(f243,plain,
( ( $true = sF1 )
| ( $false
= ( qmltpeq @ sK3 @ sK4 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f244,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK3 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f245,plain,
( ( $true
= ( ~ ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK3 @ sK2 ) ) ) )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( subset @ sK3 @ sK4 @ sK2 )
| ~ ( subset @ sK4 @ sK3 @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( $false
= ( ~ ( subset @ sK4 @ sK3 @ sK2 ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( subset @ sK3 @ sK4 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f249,plain,
( ( $true = sF1 )
| ( $true
= ( subset @ sK3 @ sK4 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( $true = sF1 )
| ( ( subset @ sK4 @ sK3 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f281,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( qmltpeq @ Y1 @ Y2 @ Y0 )
| ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y1 @ Y0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y1 @ Y0 ) )
| ( qmltpeq @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f282,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( qmltpeq @ Y1 @ Y2 @ Y0 )
| ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y1 @ Y0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ~ ( subset @ Y2 @ Y1 @ Y0 ) )
| ( qmltpeq @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ Y0 @ Y1 @ X1 )
| ~ ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ~ ( subset @ Y1 @ Y0 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ~ ( subset @ Y1 @ Y0 @ X1 ) )
| ( qmltpeq @ Y0 @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ Y0 @ Y1 @ X1 )
| ~ ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ~ ( subset @ Y1 @ Y0 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ~ ( subset @ Y1 @ Y0 @ X1 ) )
| ( qmltpeq @ Y0 @ Y1 @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ X2 @ Y0 @ X1 )
| ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ~ ( subset @ Y0 @ X2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ~ ( subset @ Y0 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ X2 @ Y0 @ X1 )
| ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ~ ( subset @ Y0 @ X2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ~ ( subset @ Y0 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ X2 @ Y0 @ X1 )
| ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ~ ( subset @ Y0 @ X2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ~ ( subset @ Y0 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ Y0 @ X1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( qmltpeq @ X2 @ X3 @ X1 )
| ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( ~ ( ~ ( qmltpeq @ X2 @ X3 @ X1 )
| ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( ~ ( ~ ( qmltpeq @ X2 @ X3 @ X1 )
| ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ X3 @ X1 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( ~ ( ~ ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ X3 @ X1 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f301,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) )
| ( qmltpeq @ X2 @ X3 @ X1 ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f302,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( ~ ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( subset @ X2 @ X3 @ X1 )
| ~ ( subset @ X3 @ X2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( ~ ( subset @ X2 @ X3 @ X1 ) ) )
| ( $true
= ( ~ ( subset @ X3 @ X2 @ X1 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( subset @ X2 @ X3 @ X1 ) )
| ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( subset @ X3 @ X2 @ X1 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( $false
= ( subset @ X3 @ X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f344,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( qmltpeq @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f345,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( qmltpeq @ Y1 @ Y2 @ Y0 )
| ( qmltpeq @ Y2 @ Y1 @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( qmltpeq @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ Y1 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f347,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( qmltpeq @ Y0 @ Y1 @ X1 )
| ( qmltpeq @ Y1 @ Y0 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( qmltpeq @ X2 @ Y0 @ X1 )
| ( qmltpeq @ Y0 @ X2 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( qmltpeq @ X2 @ Y0 @ X1 )
| ( qmltpeq @ Y0 @ X2 @ X1 ) ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( qmltpeq @ X2 @ Y0 @ X1 )
| ( qmltpeq @ Y0 @ X2 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( qmltpeq @ X2 @ X3 @ X1 )
| ( qmltpeq @ X3 @ X2 @ X1 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f350]) ).
thf(f352,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $true
= ( ~ ( qmltpeq @ X2 @ X3 @ X1 )
| ( qmltpeq @ X3 @ X2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ X3 @ X2 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ X3 @ X2 @ X1 ) )
| ( $false
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f353]) ).
thf(f431,definition,
( spl6_1
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f435,definition,
( spl6_2
<=> ( $true
= ( exists_in_world @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f437,plain,
( ( $true
= ( exists_in_world @ sK3 @ sK2 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f435]) ).
thf(f438,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f238,f435,f431]) ).
thf(f440,definition,
( spl6_3
<=> ( $true
= ( exists_in_world @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f442,plain,
( ( $true
= ( exists_in_world @ sK4 @ sK2 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f440]) ).
thf(f443,plain,
( spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f242,f431,f440]) ).
thf(f445,definition,
( spl6_4
<=> ( $true
= ( subset @ sK3 @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f447,plain,
( ( $true
= ( subset @ sK3 @ sK4 @ sK2 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f445]) ).
thf(f448,plain,
( spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f249,f431,f445]) ).
thf(f450,definition,
( spl6_5
<=> ( ( subset @ sK4 @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f452,plain,
( ( ( subset @ sK4 @ sK3 @ sK2 )
= $true )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f450]) ).
thf(f453,plain,
( spl6_1
| spl6_5 ),
inference(avatar_split_clause,[],[f250,f450,f431]) ).
thf(f455,definition,
( spl6_6
<=> ( $false
= ( qmltpeq @ sK3 @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f457,plain,
( ( $false
= ( qmltpeq @ sK3 @ sK4 @ sK2 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f455]) ).
thf(f458,plain,
( spl6_6
| spl6_1 ),
inference(avatar_split_clause,[],[f243,f431,f455]) ).
thf(f464,definition,
( spl6_8
<=> ! [X2: mu,X1: $i,X3: mu] :
( ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X2 @ X1 ) )
| ( $false
= ( subset @ X2 @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f465,plain,
( ! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( qmltpeq @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( subset @ X3 @ X2 @ X1 ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( subset @ X2 @ X3 @ X1 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f464]) ).
thf(f467,plain,
spl6_8,
inference(avatar_split_clause,[],[f307,f464]) ).
thf(f468,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f211,f431]) ).
thf(f487,plain,
( ( $false
= ( qmltpeq @ sK4 @ sK3 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ~ spl6_6 ),
inference(constrained_superposition,[],[f457,f354]) ).
thf(f489,plain,
( ( $false
= ( qmltpeq @ sK4 @ sK3 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f487]) ).
thf(f492,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( qmltpeq @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_3
| ~ spl6_6 ),
inference(forward_demodulation,[],[f489,f442]) ).
thf(f493,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( qmltpeq @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_3
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f492]) ).
thf(f496,plain,
( ( $false
= ( qmltpeq @ sK4 @ sK3 @ sK2 ) )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6 ),
inference(forward_demodulation,[],[f493,f437]) ).
thf(f497,plain,
( ( $false
= ( qmltpeq @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f496]) ).
thf(f518,plain,
( ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false = $true )
| ( $false
= ( subset @ sK3 @ sK4 @ sK2 ) )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(constrained_superposition,[],[f497,f465]) ).
thf(f523,plain,
( ( $false
= ( subset @ sK3 @ sK4 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f530,plain,
( ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(forward_demodulation,[],[f523,f447]) ).
thf(f531,plain,
( ( $false
= ( exists_in_world @ sK4 @ sK2 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f538,plain,
( ( $false = $true )
| ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(forward_demodulation,[],[f531,f442]) ).
thf(f539,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK2 ) )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f538]) ).
thf(f546,plain,
( ( $false = $true )
| ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(forward_demodulation,[],[f539,f437]) ).
thf(f547,plain,
( ( $false
= ( subset @ sK4 @ sK3 @ sK2 ) )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f546]) ).
thf(f557,plain,
( ( $false = $true )
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_8 ),
inference(forward_demodulation,[],[f547,f452]) ).
thf(f558,plain,
( $false
| ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f557]) ).
thf(f559,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f558]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f438]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f443]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f448]) ).
cnf(s4,plain,
( spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f453]) ).
cnf(s5,plain,
( spl6_1
| spl6_6 ),
inference(sat_conversion,[],[f458]) ).
cnf(s7,plain,
spl6_8,
inference(sat_conversion,[],[f467]) ).
cnf(s8,plain,
~ spl6_1,
inference(sat_conversion,[],[f468]) ).
cnf(s13,plain,
( ~ spl6_2
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6
| ~ spl6_8 ),
inference(sat_conversion,[],[f559]) ).
cnf(s15,plain,
spl6_6,
inference(rat,[],[s5,s8]) ).
cnf(s16,plain,
spl6_5,
inference(rat,[],[s4,s8]) ).
cnf(s17,plain,
spl6_4,
inference(rat,[],[s3,s8]) ).
cnf(s18,plain,
spl6_3,
inference(rat,[],[s2,s8]) ).
cnf(s19,plain,
~ spl6_2,
inference(rat,[],[s13,s7,s15,s16,s17,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s19,s8]) ).
thf(f560,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET583^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n009.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 13:38:00 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.23 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
% 0.21/0.36 % (3997456)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (3997464)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=826724619:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.36 % (3997463)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=776499447:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (3997462)lrs+10_16_si=on:nwc=1.5:random_seed=3502832462:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (3997465)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1123440638:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (3997463)Instruction limit reached!
% 0.21/0.36 % (3997463)------------------------------
% 0.21/0.36 % (3997463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997463)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997463)Termination reason: Instruction limit
% 0.21/0.36 % (3997463)Termination phase: Property scanning
% 0.21/0.36 % (3997463)Time elapsed: 0.002 s
% 0.21/0.36 % (3997463)Peak memory usage: 10 MB
% 0.21/0.36 % (3997463)Instructions burned: 4 (million)
% 0.21/0.36 % (3997461)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2435390210:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (3997466)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=228072406:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (3997462)Instruction limit reached!
% 0.21/0.36 % (3997462)------------------------------
% 0.21/0.36 % (3997462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997462)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997462)Termination reason: Instruction limit
% 0.21/0.36 % (3997462)Termination phase: Saturation
% 0.21/0.36 % (3997462)Time elapsed: 0.008 s
% 0.21/0.36 % (3997462)Peak memory usage: 11 MB
% 0.21/0.36 % (3997462)Instructions burned: 19 (million)
% 0.21/0.36 % (3997467)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (3997467)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (3997465)Instruction limit reached!
% 0.21/0.36 % (3997465)------------------------------
% 0.21/0.36 % (3997465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997465)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997465)Termination reason: Instruction limit
% 0.21/0.36 % (3997465)Termination phase: Saturation
% 0.21/0.36 % (3997465)Time elapsed: 0.014 s
% 0.21/0.36 % (3997465)Peak memory usage: 12 MB
% 0.21/0.36 % (3997465)Instructions burned: 25 (million)
% 0.21/0.36 % (3997467)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=819612913:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (3997472)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2143677414:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (3997472)Instruction limit reached!
% 0.21/0.36 % (3997472)------------------------------
% 0.21/0.36 % (3997472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997472)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997472)Termination reason: Instruction limit
% 0.21/0.36 % (3997472)Termination phase: Property scanning
% 0.21/0.36 % (3997472)Time elapsed: 0.002 s
% 0.21/0.36 % (3997472)Peak memory usage: 10 MB
% 0.21/0.36 % (3997472)Instructions burned: 4 (million)
% 0.21/0.36 % (3997475)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=161891318:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (3997476)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (3997475)Instruction limit reached!
% 0.21/0.36 % (3997475)------------------------------
% 0.21/0.36 % (3997475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997475)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997475)Termination reason: Instruction limit
% 0.21/0.36 % (3997475)Termination phase: Property scanning
% 0.21/0.36 % (3997475)Time elapsed: 0.002 s
% 0.21/0.36 % (3997475)Peak memory usage: 10 MB
% 0.21/0.36 % (3997475)Instructions burned: 5 (million)
% 0.21/0.36 % (3997476)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1727346022:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.36 % (3997476)Instruction limit reached!
% 0.21/0.36 % (3997476)------------------------------
% 0.21/0.36 % (3997476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997476)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997476)Termination reason: Instruction limit
% 0.21/0.36 % (3997476)Termination phase: Function definition elimination
% 0.21/0.36 % (3997476)Time elapsed: 0.004 s
% 0.21/0.36 % (3997476)Peak memory usage: 10 MB
% 0.21/0.36 % (3997476)Instructions burned: 9 (million)
% 0.21/0.36 % (3997466)Instruction limit reached!
% 0.21/0.36 % (3997466)------------------------------
% 0.21/0.36 % (3997466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997466)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997466)Termination reason: Instruction limit
% 0.21/0.36 % (3997466)Termination phase: Saturation
% 0.21/0.36 % (3997466)Time elapsed: 0.035 s
% 0.21/0.36 % (3997466)Peak memory usage: 13 MB
% 0.21/0.36 % (3997466)Instructions burned: 75 (million)
% 0.21/0.36 % (3997479)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4264760175:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.36 % (3997481)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (3997481)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (3997479)Instruction limit reached!
% 0.21/0.36 % (3997479)------------------------------
% 0.21/0.36 % (3997479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997479)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997479)Termination reason: Instruction limit
% 0.21/0.36 % (3997479)Termination phase: Property scanning
% 0.21/0.36 % (3997479)Time elapsed: 0.006 s
% 0.21/0.36 % (3997479)Peak memory usage: 11 MB
% 0.21/0.36 % (3997479)Instructions burned: 13 (million)
% 0.21/0.36 % (3997481)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3555281878:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.36 % (3997483)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3612912622:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.36 % (3997467) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3997456-3997467"...
% 0.21/0.36 % (3997461)Instruction limit reached!
% 0.21/0.36 % (3997461)------------------------------
% 0.21/0.36 % (3997461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997461)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997461)Termination reason: Instruction limit
% 0.21/0.36 % (3997461)Termination phase: Saturation
% 0.21/0.36 % (3997461)Time elapsed: 0.058 s
% 0.21/0.36 % (3997461)Peak memory usage: 12 MB
% 0.21/0.36 % (3997461)Instructions burned: 88 (million)
% 0.21/0.36 % (3997486)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.36 % (3997481)Instruction limit reached!
% 0.21/0.36 % (3997481)------------------------------
% 0.21/0.36 % (3997481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997481)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997481)Termination reason: Instruction limit
% 0.21/0.36 % (3997481)Termination phase: Saturation
% 0.21/0.36 % (3997481)Time elapsed: 0.016 s
% 0.21/0.36 % (3997481)Peak memory usage: 12 MB
% 0.21/0.36 % (3997481)Instructions burned: 37 (million)
% 0.21/0.36 % (3997486)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=957967708:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (3997467)...printing done.
% 0.21/0.36 % (3997486)Instruction limit reached!
% 0.21/0.36 % (3997486)------------------------------
% 0.21/0.36 % (3997486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (3997486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (3997486)CaDiCaL version: 2.1.3
% 0.21/0.36 % (3997486)Termination reason: Instruction limit
% 0.21/0.36 % (3997486)Termination phase: shuffling
% 0.21/0.36 % (3997486)Time elapsed: 0.001 s
% 0.21/0.36 % (3997486)Peak memory usage: 9 MB
% 0.21/0.36 % (3997486)Instructions burned: 2 (million)
% 0.21/0.36 % (3997467)Refutation found. Thanks to Tanya!
% 0.21/0.36 % SZS status Theorem for theBenchmark
% 0.21/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.36 % (3997467)------------------------------
% 0.83/0.36 % (3997467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.36 % (3997467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.36 % (3997467)CaDiCaL version: 2.1.3
% 0.83/0.36 % (3997467)Termination reason: Refutation
% 0.83/0.36 % (3997467)Time elapsed: 0.050 s
% 0.83/0.36 % (3997467)Peak memory usage: 13 MB
% 0.83/0.36 % (3997467)Instructions burned: 57 (million)
% 0.83/0.36 % (3997456)Success in time 0.116 s
% 0.83/0.36 % Vampire exiting
%------------------------------------------------------------------------------