%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:23:34 AM UTC 2026
% Result : Theorem 17.16s 2.87s
% Output : Refutation 17.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 11
% Syntax : Number of formulae : 96 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 696 ( 149 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1352 ( 114 ~; 135 |; 0 &; 991 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 6 con; 0-4 aty)
% ( 54 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 319 ( 233 ^; 86 !; 0 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
equal_set: mu > mu > $i > $o ).
thf(func_def_37,type,
member: mu > mu > $i > $o ).
thf(func_def_38,type,
subset: mu > mu > $i > $o ).
thf(func_def_39,type,
power_set: mu > mu ).
thf(func_def_40,type,
intersection: mu > mu > mu ).
thf(func_def_41,type,
union: mu > mu > mu ).
thf(func_def_42,type,
difference: mu > mu > mu ).
thf(func_def_43,type,
singleton: mu > mu ).
thf(func_def_44,type,
unordered_pair: mu > mu > mu ).
thf(func_def_45,type,
sum: mu > mu ).
thf(func_def_46,type,
product: mu > mu ).
thf(func_def_47,type,
empty_set: mu ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
vOR: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
vAND: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
sK0: $i > mu ).
thf(func_def_65,type,
sK2: mu ).
thf(func_def_66,type,
sK3: mu > $i > mu > mu ).
thf(func_def_67,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_68,type,
sK4: mu > $i > mu > mu ).
thf(func_def_69,type,
sK5: mu > $i > mu > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( 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(f45,axiom,
! [X0: $i] : ( exists_in_world @ empty_set @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(f67,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(f72,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mnot @ ( member @ X0 @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(f78,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ empty_set @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI15) ).
thf(f79,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ empty_set @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f78]) ).
thf(f81,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f82,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f84,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f90,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f91,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f93,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f98,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f99,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f124,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f125,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f157,plain,
! [X0: $i] : ( exists_in_world @ empty_set @ X0 ),
inference(rectify,[],[f45]) ).
thf(f158,plain,
! [X0: $i] :
( ( exists_in_world @ empty_set @ X0 )
= $true ),
inference(fool_elimination,[],[f157]) ).
thf(f201,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f202,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f201]) ).
thf(f211,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mnot @ ( member @ X0 @ empty_set ) ) ) ),
inference(rectify,[],[f72]) ).
thf(f212,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mnot @ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(fool_elimination,[],[f211]) ).
thf(f223,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( subset @ empty_set @ X0 ) ) ),
inference(rectify,[],[f79]) ).
thf(f224,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(fool_elimination,[],[f223]) ).
thf(f225,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(flattening,[],[f224]) ).
thf(f230,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f231,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f236,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f237,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f239,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f243,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f256,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f273,plain,
! [X0: $i] :
( ( exists_in_world @ empty_set @ X0 )
= $true ),
inference(cnf_transformation,[],[f158]) ).
thf(f295,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f202]) ).
thf(f300,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mnot @ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(cnf_transformation,[],[f212]) ).
thf(f306,plain,
( $true
!= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f310,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,[],[f236,f230,f231,f230,f230]) ).
thf(f311,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,[],[f237,f231,f230]) ).
thf(f313,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,[],[f239,f310,f311,f311]) ).
thf(f342,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( subset @ Y0 @ Y1 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f295,f256,f243,f243,f313,f243,f311]) ).
thf(f347,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(definition_unfolding,[],[f300,f256,f243,f230]) ).
thf(f353,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( subset @ empty_set @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f306,f256,f243]) ).
thf(f354,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ empty_set @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( subset @ empty_set @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f354]) ).
thf(f356,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( subset @ empty_set @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f355]) ).
thf(f357,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( subset @ empty_set @ Y0 @ sK1 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f356]) ).
thf(f358,plain,
( $false
= ( ( exists_in_world @ sK2 @ sK1 )
=> ( subset @ empty_set @ sK2 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f357]) ).
thf(f359,plain,
( $false
= ( subset @ empty_set @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f358]) ).
thf(f360,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f358]) ).
thf(f504,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( member @ Y1 @ empty_set @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f505,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( member @ Y1 @ empty_set @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f504]) ).
thf(f506,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( member @ Y0 @ empty_set @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f505]) ).
thf(f507,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( member @ Y0 @ empty_set @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f506]) ).
thf(f508,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ~ ( member @ X2 @ empty_set @ X1 ) ) ),
inference(beta-eta_normalization,[],[f507]) ).
thf(f509,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( member @ X2 @ empty_set @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f508]) ).
thf(f510,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( member @ X2 @ empty_set @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f509]) ).
thf(f612,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f342]) ).
thf(f613,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( subset @ Y1 @ Y2 @ Y0 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f612]) ).
thf(f614,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ~ ( member @ Y2 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ~ ( member @ Y2 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) )
| ( subset @ Y0 @ Y1 @ X1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f613]) ).
thf(f615,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( subset @ Y0 @ Y1 @ X1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ~ ( member @ Y2 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ( ~ ( member @ Y2 @ Y0 @ X1 )
| ( member @ Y2 @ Y1 @ X1 ) ) ) )
| ( subset @ Y0 @ Y1 @ X1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f614]) ).
thf(f616,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( subset @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f615]) ).
thf(f617,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( subset @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f616]) ).
thf(f618,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( subset @ X2 @ Y0 @ X1 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( member @ Y1 @ X2 @ X1 )
| ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( subset @ X2 @ Y0 @ X1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f617]) ).
thf(f619,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f618]) ).
thf(f620,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f619]) ).
thf(f621,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( subset @ X2 @ X3 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f620]) ).
thf(f622,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f621]) ).
thf(f632,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( subset @ X2 @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f622]) ).
thf(f633,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f633]) ).
thf(f635,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( member @ Y0 @ X2 @ X1 )
| ( member @ Y0 @ X3 @ X1 ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f634]) ).
thf(f636,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( ( exists_in_world @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ~ ( member @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ( member @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f635]) ).
thf(f637,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( member @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ( member @ ( sK5 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f636]) ).
thf(f638,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f636]) ).
thf(f640,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( member @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f637]) ).
thf(f641,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( member @ ( sK5 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( subset @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f640]) ).
thf(f2392,plain,
! [X0: mu,X1: $i] :
( ( $true = $false )
| ( $false
= ( exists_in_world @ ( sK5 @ X0 @ X1 @ empty_set ) @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) ) ),
inference(constrained_superposition,[],[f510,f641]) ).
thf(f2393,plain,
! [X0: mu,X1: $i] :
( ( $false
= ( exists_in_world @ ( sK5 @ X0 @ X1 @ empty_set ) @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f2392]) ).
thf(f2407,plain,
! [X0: mu,X1: $i] :
( ( $true = $false )
| ( $false
= ( exists_in_world @ ( sK5 @ X0 @ X1 @ empty_set ) @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f2393,f273]) ).
thf(f2408,plain,
! [X0: mu,X1: $i] :
( ( $false
= ( exists_in_world @ ( sK5 @ X0 @ X1 @ empty_set ) @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f2407]) ).
thf(f3180,plain,
! [X0: mu,X1: $i] :
( ( $true = $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f638,f2408]) ).
thf(f3181,plain,
! [X0: mu,X1: $i] :
( ( $true = $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f3180]) ).
thf(f3182,plain,
! [X0: mu,X1: $i] :
( ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( $false
= ( exists_in_world @ empty_set @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f3181]) ).
thf(f3190,plain,
! [X0: mu,X1: $i] :
( ( $true = $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ empty_set @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f3182,f273]) ).
thf(f3191,plain,
! [X0: mu,X1: $i] :
( ( $true
= ( subset @ empty_set @ X0 @ X1 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f3190]) ).
thf(f3228,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f359,f3191]) ).
thf(f3229,plain,
( $false
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f3228]) ).
thf(f3243,plain,
$true = $false,
inference(constrained_superposition,[],[f360,f3229]) ).
thf(f3246,plain,
$false,
inference(trivial_inequality_removal,[],[f3243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:36:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 4.24/0.93 % (96938)Will run a generic schedule for satisfiability detection.
% 4.24/0.93 % (96950)dis+10_1_sil=32000:sp=arity:random_seed=339466961:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.24/0.93 % (96948)% WARNING: option uhcvi not known.
% 4.24/0.93 % (96947)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=805520876_2999 on theBenchmark for (2999ds/0Mi)
% 4.24/0.93 % (96951)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2940865191:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.24/0.93 % (96948)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4239900349:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.24/0.93 % (96949)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3795860997:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.24/0.93 % (96952)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1260590469:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.24/0.93 % (96953)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=313397747:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.24/0.93 % (96951)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.24/0.93 % (96948)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.24/0.93 % Exception at run slice level
% 4.24/0.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.24/0.93 % (96948)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.24/0.93 % (96950)Instruction limit reached!
% 4.24/0.93 % (96950)------------------------------
% 4.24/0.93 % (96950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.24/0.93 % (96950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/0.93 % (96950)CaDiCaL version: 2.1.3
% 4.24/0.93 % (96950)Termination reason: Instruction limit
% 4.24/0.93 % (96950)Termination phase: Saturation
% 4.24/0.93 % (96950)Time elapsed: 0.025 s
% 4.24/0.93 % (96950)Peak memory usage: 13 MB
% 4.24/0.93 % (96950)Instructions burned: 106 (million)
% 4.24/0.93 % (96962)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=268268979:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.24/0.93 % (96961)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2190059498:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.24/0.93 % Exception at run slice level
% 4.24/0.93 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.24/0.93 % (96951)Instruction limit reached!
% 4.24/0.93 % (96951)------------------------------
% 4.24/0.93 % (96951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.24/0.93 % (96951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/0.93 % (96951)CaDiCaL version: 2.1.3
% 4.24/0.93 % (96951)Termination reason: Instruction limit
% 4.24/0.93 % (96951)Termination phase: Saturation
% 4.24/0.93 % (96951)Time elapsed: 0.051 s
% 4.24/0.93 % (96951)Peak memory usage: 13 MB
% 4.24/0.93 % (96951)Instructions burned: 117 (million)
% 4.24/0.93 % (96952)Instruction limit reached!
% 4.24/0.93 % (96952)------------------------------
% 4.24/0.93 % (96952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.24/0.93 % (96952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/0.93 % (96952)CaDiCaL version: 2.1.3
% 4.24/0.93 % (96952)Termination reason: Instruction limit
% 4.24/0.93 % (96952)Termination phase: Saturation
% 4.24/0.93 % (96952)Time elapsed: 0.058 s
% 4.24/0.93 % (96952)Peak memory usage: 13 MB
% 4.24/0.93 % (96952)Instructions burned: 131 (million)
% 4.24/0.93 % (96962)Instruction limit reached!
% 4.24/0.93 % (96962)------------------------------
% 4.24/0.93 % (96962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.24/0.93 % (96962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/0.93 % (96962)CaDiCaL version: 2.1.3
% 4.24/0.93 % (96962)Termination reason: Instruction limit
% 4.24/0.93 % (96962)Termination phase: Saturation
% 4.24/0.93 % (96962)Time elapsed: 0.031 s
% 4.24/0.93 % (96962)Peak memory usage: 13 MB
% 4.24/0.93 % (96962)Instructions burned: 136 (million)
% 4.24/0.93 % (96965)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=652413752:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 16.16/2.68 % (96967)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4061504141:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 16.16/2.68 % (96966)ott-21_1_sil=16000:fs=off:random_seed=882251315:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 16.16/2.68 % (96953)Instruction limit reached!
% 16.16/2.68 % (96953)------------------------------
% 16.16/2.68 % (96953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.16/2.68 % (96953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.16/2.68 % (96953)CaDiCaL version: 2.1.3
% 16.16/2.68 % (96953)Termination reason: Instruction limit
% 16.16/2.68 % (96953)Termination phase: Saturation
% 16.16/2.68 % (96953)Time elapsed: 0.069 s
% 16.16/2.68 % (96953)Peak memory usage: 13 MB
% 16.16/2.68 % (96953)Instructions burned: 160 (million)
% 16.16/2.68 % (96965)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.16/2.68 % (96968)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2849066778:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.16/2.68 % (96965)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.16/2.68 % (96972)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1398533074:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.16/2.68 % Exception at run slice level
% 16.16/2.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.16/2.68 % (96975)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=45345230:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 16.16/2.68 % Exception at run slice level
% 16.16/2.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.16/2.68 % (96977)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2838224844:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 16.16/2.68 % (96966)Instruction limit reached!
% 16.16/2.68 % (96966)------------------------------
% 16.16/2.68 % (96966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.16/2.68 % (96966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.16/2.68 % (96966)CaDiCaL version: 2.1.3
% 16.16/2.68 % (96966)Termination reason: Instruction limit
% 16.16/2.68 % (96966)Termination phase: Saturation
% 16.16/2.68 % (96966)Time elapsed: 0.078 s
% 16.16/2.68 % (96966)Peak memory usage: 13 MB
% 16.16/2.68 % (96966)Instructions burned: 180 (million)
% 16.16/2.68 % (96977)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.16/2.68 % (96979)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3131010168:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 16.16/2.68 % (96979)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.16/2.68 % (96967)Instruction limit reached!
% 16.16/2.68 % (96967)------------------------------
% 16.16/2.68 % (96967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.16/2.68 % (96967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.16/2.68 % (96967)CaDiCaL version: 2.1.3
% 16.16/2.68 % (96967)Termination reason: Instruction limit
% 16.16/2.68 % (96967)Termination phase: Saturation
% 16.16/2.68 % (96967)Time elapsed: 0.129 s
% 16.16/2.68 % (96967)Peak memory usage: 14 MB
% 16.16/2.68 % (96967)Instructions burned: 481 (million)
% 16.16/2.68 % (96981)fmb+10_1_sil=64000:random_seed=4143464576:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 16.16/2.68 % (96981)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 16.16/2.68 % Exception at run slice level
% 16.16/2.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.16/2.68 % (96983)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4045977691:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 16.16/2.68 % Exception at run slice level
% 16.16/2.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.16/2.68 % (96985)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3631810076:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 16.16/2.68 % Exception at run slice level
% 16.16/2.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (96987)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=152311004:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 17.16/2.87 % (96987)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.16/2.87 % (96965)Instruction limit reached!
% 17.16/2.87 % (96965)------------------------------
% 17.16/2.87 % (96965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96965)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96965)Termination reason: Instruction limit
% 17.16/2.87 % (96965)Termination phase: Saturation
% 17.16/2.87 % (96965)Time elapsed: 0.299 s
% 17.16/2.87 % (96965)Peak memory usage: 14 MB
% 17.16/2.87 % (96965)Instructions burned: 684 (million)
% 17.16/2.87 % (96989)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2824679956:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 17.16/2.87 % (96989)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.16/2.87 % (96989)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.16/2.87 % (96977)Instruction limit reached!
% 17.16/2.87 % (96977)------------------------------
% 17.16/2.87 % (96977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96977)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96977)Termination reason: Instruction limit
% 17.16/2.87 % (96977)Termination phase: Saturation
% 17.16/2.87 % (96977)Time elapsed: 0.266 s
% 17.16/2.87 % (96977)Peak memory usage: 14 MB
% 17.16/2.87 % (96977)Instructions burned: 693 (million)
% 17.16/2.87 % (96991)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1620575318:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (96993)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1646772484:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (96995)ott-2_1_sil=16000:newcnf=on:random_seed=4147542202:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 17.16/2.87 % (96995)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.16/2.87 % (96972)Instruction limit reached!
% 17.16/2.87 % (96972)------------------------------
% 17.16/2.87 % (96972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96972)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96972)Termination reason: Instruction limit
% 17.16/2.87 % (96972)Termination phase: Saturation
% 17.16/2.87 % (96972)Time elapsed: 0.495 s
% 17.16/2.87 % (96972)Peak memory usage: 15 MB
% 17.16/2.87 % (96972)Instructions burned: 1180 (million)
% 17.16/2.87 % (96979)Instruction limit reached!
% 17.16/2.87 % (96979)------------------------------
% 17.16/2.87 % (96979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96979)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96979)Termination reason: Instruction limit
% 17.16/2.87 % (96979)Termination phase: Saturation
% 17.16/2.87 % (96979)Time elapsed: 0.425 s
% 17.16/2.87 % (96979)Peak memory usage: 15 MB
% 17.16/2.87 % (96979)Instructions burned: 880 (million)
% 17.16/2.87 % (96997)ott+10_1_sil=32000:tgt=ground:random_seed=364248309:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 17.16/2.87 % (96998)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2450851409:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (97001)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3760820997:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 17.16/2.87 % (97001)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.16/2.87 % (96995)Instruction limit reached!
% 17.16/2.87 % (96995)------------------------------
% 17.16/2.87 % (96995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96995)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96995)Termination reason: Instruction limit
% 17.16/2.87 % (96995)Termination phase: Saturation
% 17.16/2.87 % (96995)Time elapsed: 0.367 s
% 17.16/2.87 % (96995)Peak memory usage: 15 MB
% 17.16/2.87 % (96995)Instructions burned: 869 (million)
% 17.16/2.87 % (97003)dis+21_1_sil=32000:sas=cadical:random_seed=1217481631:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 17.16/2.87 % (96989)Instruction limit reached!
% 17.16/2.87 % (96989)------------------------------
% 17.16/2.87 % (96989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96989)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96989)Termination reason: Instruction limit
% 17.16/2.87 % (96989)Termination phase: Saturation
% 17.16/2.87 % (96989)Time elapsed: 0.751 s
% 17.16/2.87 % (96989)Peak memory usage: 18 MB
% 17.16/2.87 % (96989)Instructions burned: 1473 (million)
% 17.16/2.87 % (97005)ott+11_1_sil=16000:gs=on:random_seed=2792915230:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 17.16/2.87 % (97005)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.16/2.87 % (96987)Instruction limit reached!
% 17.16/2.87 % (96987)------------------------------
% 17.16/2.87 % (96987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (96987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (96987)CaDiCaL version: 2.1.3
% 17.16/2.87 % (96987)Termination reason: Instruction limit
% 17.16/2.87 % (96987)Termination phase: Saturation
% 17.16/2.87 % (96987)Time elapsed: 1.098 s
% 17.16/2.87 % (96987)Peak memory usage: 22 MB
% 17.16/2.87 % (96987)Instructions burned: 5136 (million)
% 17.16/2.87 % (97007)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=4035286594:fmbsr=1.6:i=67534_2985 on theBenchmark for (2985ds/67534Mi)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (97009)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=2209500328:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2985 on theBenchmark for (2985ds/4591Mi)
% 17.16/2.87 % (97005)Instruction limit reached!
% 17.16/2.87 % (97005)------------------------------
% 17.16/2.87 % (97005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (97005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (97005)CaDiCaL version: 2.1.3
% 17.16/2.87 % (97005)Termination reason: Instruction limit
% 17.16/2.87 % (97005)Termination phase: Saturation
% 17.16/2.87 % (97005)Time elapsed: 0.864 s
% 17.16/2.87 % (97005)Peak memory usage: 15 MB
% 17.16/2.87 % (97005)Instructions burned: 2253 (million)
% 17.16/2.87 % (97001)Instruction limit reached!
% 17.16/2.87 % (97001)------------------------------
% 17.16/2.87 % (97001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (97011)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=2788974927:i=29340_2979 on theBenchmark for (2979ds/29340Mi)
% 17.16/2.87 % (97001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (97001)CaDiCaL version: 2.1.3
% 17.16/2.87 % (97001)Termination reason: Instruction limit
% 17.16/2.87 % (97001)Termination phase: Saturation
% 17.16/2.87 % (97001)Time elapsed: 1.397 s
% 17.16/2.87 % (97001)Peak memory usage: 19 MB
% 17.16/2.87 % (97001)Instructions burned: 3514 (million)
% 17.16/2.87 % (97013)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1833827905:i=5211_2979 on theBenchmark for (2979ds/5211Mi)
% 17.16/2.87 % (97003)Instruction limit reached!
% 17.16/2.87 % (97003)------------------------------
% 17.16/2.87 % (97003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (97003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (97003)CaDiCaL version: 2.1.3
% 17.16/2.87 % (97003)Termination reason: Instruction limit
% 17.16/2.87 % (97003)Termination phase: Saturation
% 17.16/2.87 % (97003)Time elapsed: 1.516 s
% 17.16/2.87 % (97003)Peak memory usage: 20 MB
% 17.16/2.87 % (97003)Instructions burned: 3774 (million)
% 17.16/2.87 % (97015)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=436925703:i=5497:nm=2_2975 on theBenchmark for (2975ds/5497Mi)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (97017)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=2171357240:fmbsr=2:i=46332_2975 on theBenchmark for (2975ds/46332Mi)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (97019)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=1872952116:i=14071_2974 on theBenchmark for (2974ds/14071Mi)
% 17.16/2.87 % (97009)Instruction limit reached!
% 17.16/2.87 % (97009)------------------------------
% 17.16/2.87 % (97009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (97009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (97009)CaDiCaL version: 2.1.3
% 17.16/2.87 % (97009)Termination reason: Instruction limit
% 17.16/2.87 % (97009)Termination phase: Saturation
% 17.16/2.87 % (97009)Time elapsed: 1.104 s
% 17.16/2.87 % (97009)Peak memory usage: 28 MB
% 17.16/2.87 % (97009)Instructions burned: 4591 (million)
% 17.16/2.87 % Exception at run slice level
% 17.16/2.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.16/2.87 % (97021)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=393892775:i=22565:add=on:rawr=on_2974 on theBenchmark for (2974ds/22565Mi)
% 17.16/2.87 % (97022)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=753414590:i=8173:av=off_2974 on theBenchmark for (2974ds/8173Mi)
% 17.16/2.87 % (97021) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-96938-97021"...
% 17.16/2.87 % (97021)...printing done.
% 17.16/2.87 % (97021)Refutation found. Thanks to Tanya!
% 17.16/2.87 % SZS status Theorem for theBenchmark
% 17.16/2.87 % SZS output start Proof for theBenchmark
% See solution above
% 17.16/2.87 % (97021)------------------------------
% 17.16/2.87 % (97021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.16/2.87 % (97021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.16/2.87 % (97021)CaDiCaL version: 2.1.3
% 17.16/2.87 % (97021)Termination reason: Refutation
% 17.16/2.87 % (97021)Time elapsed: 0.078 s
% 17.16/2.87 % (97021)Peak memory usage: 14 MB
% 17.16/2.87 % (97021)Instructions burned: 296 (million)
% 17.16/2.87 % (96938)Success in time 2.638 s
% 17.16/2.87 % Vampire exiting
%------------------------------------------------------------------------------