%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN052^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:41:38 AM UTC 2026
% Result : Theorem 2.14s 0.61s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 214 ( 104 unt; 0 typ; 3 def)
% Number of atoms : 2266 ( 192 equ; 0 cnn)
% Maximal formula atoms : 35 ( 10 avg)
% Number of connectives : 5012 ( 762 ~; 685 |; 25 &;2938 @)
% ( 3 <=>; 109 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 134 ( 134 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 62 usr; 14 con; 0-4 aty)
% ( 486 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 787 ( 0 sgn 77 !; 2 ?; 787 :)
% 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,
p: $i > $o ).
thf(func_def_37,type,
big_f: mu > $i > $o ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
vNOT: $o > $o ).
thf(func_def_53,type,
sK0: $i > mu ).
thf(func_def_61,type,
sK8: mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f14,axiom,
! [X0: $i] :
? [X1: mu] : ( exists_in_world @ X1 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',nonempty_ax) ).
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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,axiom,
! [X1: $i,X2: $i,X0: mu] :
( ( ( rel_s4 @ X1 @ X2 )
& ( exists_in_world @ X0 @ X1 ) )
=> ( exists_in_world @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^1.ax',cumulative_ax) ).
thf(f37,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X0 ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel22) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X0 ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f42,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f46,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f48,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f53,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X3 @ X2 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f54,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f69,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f71,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f72,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
! [X0: $i] :
? [X1: mu] : ( exists_in_world @ X1 @ X0 ),
inference(rectify,[],[f14]) ).
thf(f74,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f73]) ).
thf(f85,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f86,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f88,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X0 ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X2: mu] : ( mbox_s4 @ ( big_f @ X2 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f89,plain,
( ( ~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ Y0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ Y0 ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_f @ Y0 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_f @ Y0 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f88]) ).
thf(f91,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f92,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f91]) ).
thf(f94,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f95,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f99,plain,
! [X0: $i,X1: $i,X2: mu] :
( ( ( rel_s4 @ X0 @ X1 )
& ( exists_in_world @ X2 @ X0 ) )
=> ( exists_in_world @ X2 @ X1 ) ),
inference(rectify,[],[f36]) ).
thf(f100,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( exists_in_world @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f104,plain,
( ( ~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ Y0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ Y0 ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_f @ Y0 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_f @ Y0 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f89]) ).
thf(f106,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f107,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f108,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( exists_in_world @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f109,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f111,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f114,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f122,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f126,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f129,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f74]) ).
thf(f130,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f131,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f132,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f134,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f143,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,[],[f122,f126,f130,f126,f126]) ).
thf(f144,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,[],[f111,f130,f126]) ).
thf(f152,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ p )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( big_f @ Y0 ) ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( big_f @ Y0 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ p ) ) ) ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( big_f @ Y0 ) ) ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( big_f @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f104,f109,f131,f144,f131,f106,f143,f131,f144,f131,f131,f131,f144,f131,f131,f143,f131,f144,f131,f131,f106,f131,f131,f144,f131,f106,f131,f131]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f107,f132]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f114,f134]) ).
thf(f155,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f156,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( p @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( p @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y4 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y4 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f157,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y0 @ Y2 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f158,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f159,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f129]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( ?? @ mu
@ ^ [Y0: mu] : ( exists_in_world @ Y0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( ^ [Y0: mu] : ( exists_in_world @ Y0 @ X1 )
@ ( sK0 @ X1 ) )
= $true ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( exists_in_world @ ( sK0 @ X1 ) @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( p @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( p @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y4 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y4 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f165,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( p @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( p @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y4 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( big_f @ Y4 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( p @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( p @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( p @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( p @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( big_f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f170,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f171,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( exists_in_world @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f172,plain,
! [X1: mu] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( exists_in_world @ X1 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f176,plain,
! [X2: $i,X1: mu] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( exists_in_world @ X1 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ X1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f177,plain,
! [X2: $i,X1: mu] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( exists_in_world @ X1 @ Y0 )
& ( rel_s4 @ Y0 @ X2 ) )
=> ( exists_in_world @ X1 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ^ [Y0: $i] :
( ( ( exists_in_world @ X1 @ Y0 )
& ( rel_s4 @ Y0 @ X2 ) )
=> ( exists_in_world @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: mu] :
( $true
= ( ( ( exists_in_world @ X1 @ X3 )
& ( rel_s4 @ X3 @ X2 ) )
=> ( exists_in_world @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f186,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f191,plain,
! [X0: $i,X1: $i] :
( ( ( $true
& ( rel_s4 @ X0 @ X1 ) )
=> ( exists_in_world @ ( sK0 @ X0 ) @ X1 ) )
= $true ),
inference(superposition,[],[f184,f163]) ).
thf(f196,plain,
! [X0: $i,X1: $i] :
( ( ( rel_s4 @ X0 @ X1 )
=> ( exists_in_world @ ( sK0 @ X0 ) @ X1 ) )
= $true ),
inference(boolean_simplification,[],[f191]) ).
thf(f202,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y0 @ Y2 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f203,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ X1 @ Y1 ) )
=> ( rel_s4 @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ X1 @ Y1 ) )
=> ( rel_s4 @ X1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X1 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f219,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f211]) ).
thf(f220,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X1 @ X3 ) )
=> ( rel_s4 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f260,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f261,plain,
! [X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f263,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) ) ) ) )
| ~ $true )
= $true ),
inference(superposition,[],[f261,f159]) ).
thf(f264,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[],[f263]) ).
thf(f265,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f264]) ).
thf(f266,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f273,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK2 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f274,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ X1 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ X1 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f277,definition,
( spl3_1
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f279,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f281,definition,
( spl3_2
<=> ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f283,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f284,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f275,f281,f277]) ).
thf(f285,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ~ spl3_2 ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f286,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK4 ) )
| ~ spl3_2 ),
inference(sigma_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ sK4 ) ) )
| ~ spl3_2 ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f288,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK4 ) ) )
| ~ spl3_2 ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f289,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
| ~ spl3_2 ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f290,plain,
( ( ( rel_s4 @ sK2 @ sK4 )
= $true )
| ~ spl3_2 ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f300,plain,
( ( $true
= ( $true
=> ( exists_in_world @ ( sK0 @ sK2 ) @ sK4 ) ) )
| ~ spl3_2 ),
inference(superposition,[],[f196,f290]) ).
thf(f306,plain,
( ( ( exists_in_world @ ( sK0 @ sK2 ) @ sK4 )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f300]) ).
thf(f317,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) )
| ~ spl3_2 ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f318,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
| ~ spl3_2 ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f335,plain,
( ( $true
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
= $true ),
inference(superposition,[],[f274,f163]) ).
thf(f336,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f335]) ).
thf(f385,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
= $true )
| ~ spl3_2 ),
inference(not_proxy_clausification,[],[f318]) ).
thf(f388,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) )
@ X1 )
= $true )
| ~ spl3_2 ),
inference(pi_proxy_clausification,[],[f385]) ).
thf(f389,plain,
( ! [X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ X1 ) )
= $true )
| ~ spl3_2 ),
inference(beta-eta_normalization,[],[f388]) ).
thf(f394,plain,
( ( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) )
| ~ $true )
= $true )
| ~ spl3_2 ),
inference(superposition,[],[f389,f159]) ).
thf(f397,plain,
( ( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) )
| $false ) )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f394]) ).
thf(f398,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f397]) ).
thf(f419,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f336]) ).
thf(f439,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f419]) ).
thf(f534,plain,
( ! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl3_2 ),
inference(pi_proxy_clausification,[],[f398]) ).
thf(f535,plain,
( ! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
| ~ spl3_2 ),
inference(beta-eta_normalization,[],[f534]) ).
thf(f552,plain,
( ( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) )
= $true )
| ~ spl3_2 ),
inference(superposition,[],[f535,f306]) ).
thf(f555,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f552]) ).
thf(f573,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f439]) ).
thf(f587,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f573]) ).
thf(f588,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f587]) ).
thf(f604,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ~ $true )
= $true )
| ~ spl3_2 ),
inference(superposition,[],[f588,f290]) ).
thf(f612,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| $false )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f604]) ).
thf(f613,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ ( sK0 @ sK2 ) @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f612]) ).
thf(f617,plain,
( ( $true
= ( ~ $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f613,f555]) ).
thf(f618,plain,
( ( ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f617]) ).
thf(f619,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
= $true )
| ~ spl3_2 ),
inference(boolean_simplification,[],[f618]) ).
thf(f623,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f619,f317]) ).
thf(f624,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f623]) ).
thf(f625,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f624]) ).
thf(f636,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f639,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( big_f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK6 ) )
| ~ spl3_1 ),
inference(sigma_proxy_clausification,[],[f636]) ).
thf(f640,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ sK6 ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f639]) ).
thf(f645,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK6 ) ) )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f640]) ).
thf(f646,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) ) )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f640]) ).
thf(f650,plain,
( ( ( rel_s4 @ sK2 @ sK6 )
= $true )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f645]) ).
thf(f681,plain,
( ! [X0: $i] :
( ( ( ( rel_s4 @ sK6 @ X0 )
& $true )
=> ( rel_s4 @ sK2 @ X0 ) )
= $true )
| ~ spl3_1 ),
inference(superposition,[],[f220,f650]) ).
thf(f686,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK6 @ X0 )
=> ( rel_s4 @ sK2 @ X0 ) )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f681]) ).
thf(f702,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
= $false )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f646]) ).
thf(f703,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) ) )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f646]) ).
thf(f768,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
= $true )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f703]) ).
thf(f778,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) )
@ X1 )
= $true )
| ~ spl3_1 ),
inference(pi_proxy_clausification,[],[f768]) ).
thf(f779,plain,
( ! [X1: $i] :
( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK6 @ X1 ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f778]) ).
thf(f780,plain,
( ! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK6 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f779]) ).
thf(f788,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) )
@ sK7 ) )
| ~ spl3_1 ),
inference(sigma_proxy_clausification,[],[f702]) ).
thf(f789,plain,
( ( $false
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK6 @ sK7 ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f788]) ).
thf(f799,plain,
( ( $false
= ( ~ ( rel_s4 @ sK6 @ sK7 ) ) )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f789]) ).
thf(f800,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) ) )
= $false )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f789]) ).
thf(f801,plain,
( ( $true
= ( rel_s4 @ sK6 @ sK7 ) )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f799]) ).
thf(f817,plain,
( ( ( $true
=> ( rel_s4 @ sK2 @ sK7 ) )
= $true )
| ~ spl3_1 ),
inference(superposition,[],[f686,f801]) ).
thf(f820,plain,
( ! [X0: $i] :
( ( ( ( rel_s4 @ sK7 @ X0 )
& $true )
=> ( rel_s4 @ sK6 @ X0 ) )
= $true )
| ~ spl3_1 ),
inference(superposition,[],[f220,f801]) ).
thf(f824,plain,
( ( ( rel_s4 @ sK2 @ sK7 )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f817]) ).
thf(f825,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s4 @ sK7 @ X0 )
=> ( rel_s4 @ sK6 @ X0 ) ) )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f820]) ).
thf(f844,plain,
( ( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) ) ) )
| ~ $true ) )
| ~ spl3_1 ),
inference(superposition,[],[f261,f824]) ).
thf(f861,plain,
( ( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) ) ) )
| $false )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f844]) ).
thf(f862,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f861]) ).
thf(f893,plain,
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) )
@ sK8 )
= $false )
| ~ spl3_1 ),
inference(sigma_proxy_clausification,[],[f800]) ).
thf(f894,plain,
( ( $false
= ( ( exists_in_world @ sK8 @ sK7 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f893]) ).
thf(f901,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f894]) ).
thf(f902,plain,
( ( ( exists_in_world @ sK8 @ sK7 )
= $true )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f894]) ).
thf(f1578,definition,
( spl3_5
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f1579,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
!= $true )
| spl3_5 ),
inference(avatar_component_clause,[],[f1578]) ).
thf(f1580,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
= $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f1578]) ).
thf(f1917,plain,
( ! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( big_f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK7 @ Y1 ) ) ) ) )
@ X1 )
= $true )
| ~ spl3_1 ),
inference(pi_proxy_clausification,[],[f862]) ).
thf(f1918,plain,
( ! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK7 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ X1 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ X1 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f1917]) ).
thf(f1926,plain,
( ( ( $true
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) )
= $true )
| ~ spl3_1 ),
inference(superposition,[],[f1918,f902]) ).
thf(f1930,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f1926]) ).
thf(f1966,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f1930]) ).
thf(f1976,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) )
| ~ spl3_1 ),
inference(or_proxy_clausification,[],[f1966]) ).
thf(f2182,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
= $true )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f1976]) ).
thf(f2183,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( big_f @ sK8 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) )
@ X1 )
= $true )
| ~ spl3_1 ),
inference(pi_proxy_clausification,[],[f2182]) ).
thf(f2184,plain,
( ! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK7 @ X1 ) )
= $true )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f2183]) ).
thf(f2186,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ $true )
= $true )
| ~ spl3_1 ),
inference(superposition,[],[f2184,f159]) ).
thf(f2192,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| $false )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f2186]) ).
thf(f2193,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
= $true )
| ~ spl3_1 ),
inference(boolean_simplification,[],[f2192]) ).
thf(f2200,plain,
( ( $true
= ( ~ $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) ) )
| ~ spl3_1
| ~ spl3_5 ),
inference(forward_demodulation,[],[f2193,f1580]) ).
thf(f2201,plain,
( ( ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
= $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(boolean_simplification,[],[f2200]) ).
thf(f2202,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( big_f @ sK8 @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
= $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(boolean_simplification,[],[f2201]) ).
thf(f2203,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_5 ),
inference(forward_demodulation,[],[f2202,f901]) ).
thf(f2204,plain,
( $false
| ~ spl3_1
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f2203]) ).
thf(f2205,plain,
( ~ spl3_1
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f2204]) ).
thf(f2235,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) )
@ sK11 ) )
| spl3_5 ),
inference(sigma_proxy_clausification,[],[f1579]) ).
thf(f2236,plain,
( ( $false
= ( ( p @ sK11 )
| ~ ( rel_s4 @ sK7 @ sK11 ) ) )
| spl3_5 ),
inference(beta-eta_normalization,[],[f2235]) ).
thf(f2237,plain,
( ( $false
= ( ~ ( rel_s4 @ sK7 @ sK11 ) ) )
| spl3_5 ),
inference(or_proxy_clausification,[],[f2236]) ).
thf(f2238,plain,
( ( $false
= ( p @ sK11 ) )
| spl3_5 ),
inference(or_proxy_clausification,[],[f2236]) ).
thf(f2250,plain,
( ( ( rel_s4 @ sK7 @ sK11 )
= $true )
| spl3_5 ),
inference(not_proxy_clausification,[],[f2237]) ).
thf(f2260,plain,
( ( ( $true
=> ( rel_s4 @ sK6 @ sK11 ) )
= $true )
| ~ spl3_1
| spl3_5 ),
inference(superposition,[],[f825,f2250]) ).
thf(f2285,plain,
( ( ( rel_s4 @ sK6 @ sK11 )
= $true )
| ~ spl3_1
| spl3_5 ),
inference(boolean_simplification,[],[f2260]) ).
thf(f2316,plain,
( ( ( p @ sK11 )
= $true )
| ( ( ~ $true ) = $true )
| ~ spl3_1
| spl3_5 ),
inference(superposition,[],[f780,f2285]) ).
thf(f2366,plain,
( ( ( p @ sK11 )
= $true )
| ( $false = $true )
| ~ spl3_1
| spl3_5 ),
inference(boolean_simplification,[],[f2316]) ).
thf(f2367,plain,
( ( ( p @ sK11 )
= $true )
| ~ spl3_1
| spl3_5 ),
inference(trivial_inequality_removal,[],[f2366]) ).
thf(f2371,plain,
( ( $false = $true )
| ~ spl3_1
| spl3_5 ),
inference(forward_demodulation,[],[f2367,f2238]) ).
thf(f2372,plain,
( $false
| ~ spl3_1
| spl3_5 ),
inference(trivial_inequality_removal,[],[f2371]) ).
thf(f2373,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f2372]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f284]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f625]) ).
cnf(s9,plain,
( ~ spl3_1
| ~ spl3_5 ),
inference(sat_conversion,[],[f2205]) ).
cnf(s16,plain,
( ~ spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f2373]) ).
cnf(s17,plain,
spl3_1,
inference(rat,[],[s1,s3]) ).
cnf(s18,plain,
spl3_5,
inference(rat,[],[s16,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s9,s18,s17]) ).
thf(f2374,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN052^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n017.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:09:37 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.39 % (523001)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.39 % (523009)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=1914910428: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)
% 0.23/0.39 % (523012)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.39 % (523012)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
% 0.23/0.39 % (523006)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1765882669:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.39 % (523007)lrs+10_16_si=on:nwc=1.5:random_seed=2756958587:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.39 % (523008)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2056406734:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.39 % (523010)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1995973937:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.39 % (523011)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3590513155:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.39 % (523012)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=3115086977:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.39 % (523008)Instruction limit reached!
% 0.23/0.39 % (523008)------------------------------
% 0.23/0.39 % (523008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.39 % (523008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.39 % (523008)CaDiCaL version: 2.1.3
% 0.23/0.39 % (523008)Termination reason: Instruction limit
% 0.23/0.39 % (523008)Termination phase: Property scanning
% 0.23/0.39 % (523008)Time elapsed: 0.002 s
% 0.23/0.39 % (523008)Peak memory usage: 10 MB
% 0.23/0.39 % (523008)Instructions burned: 5 (million)
% 0.23/0.39 % (523007)Instruction limit reached!
% 0.23/0.39 % (523007)------------------------------
% 0.23/0.39 % (523007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.39 % (523007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.39 % (523007)CaDiCaL version: 2.1.3
% 0.23/0.39 % (523007)Termination reason: Instruction limit
% 0.23/0.39 % (523007)Termination phase: Saturation
% 0.23/0.39 % (523007)Time elapsed: 0.009 s
% 0.23/0.39 % (523007)Peak memory usage: 11 MB
% 0.23/0.39 % (523007)Instructions burned: 20 (million)
% 0.23/0.39 % (523010)Instruction limit reached!
% 0.23/0.39 % (523010)------------------------------
% 0.23/0.39 % (523010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.39 % (523010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.39 % (523010)CaDiCaL version: 2.1.3
% 0.23/0.39 % (523010)Termination reason: Instruction limit
% 0.23/0.39 % (523010)Termination phase: Saturation
% 0.23/0.39 % (523010)Time elapsed: 0.014 s
% 0.23/0.39 % (523010)Peak memory usage: 12 MB
% 0.23/0.39 % (523010)Instructions burned: 26 (million)
% 0.23/0.39 % (523020)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=82686999:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.39 % (523020)Instruction limit reached!
% 0.23/0.39 % (523020)------------------------------
% 0.23/0.39 % (523020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.39 % (523020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.39 % (523020)CaDiCaL version: 2.1.3
% 0.23/0.39 % (523020)Termination reason: Instruction limit
% 0.23/0.39 % (523020)Termination phase: Preprocessing 1
% 0.23/0.39 % (523020)Time elapsed: 0.002 s
% 0.23/0.39 % (523020)Peak memory usage: 10 MB
% 0.23/0.39 % (523020)Instructions burned: 5 (million)
% 0.23/0.39 % (523021)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1182748226:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.39 % (523022)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.95/0.42 % (523021)Instruction limit reached!
% 0.95/0.42 % (523021)------------------------------
% 0.95/0.42 % (523021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.42 % (523021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.42 % (523021)CaDiCaL version: 2.1.3
% 0.95/0.42 % (523021)Termination reason: Instruction limit
% 0.95/0.42 % (523021)Termination phase: Property scanning
% 0.95/0.42 % (523021)Time elapsed: 0.003 s
% 0.95/0.42 % (523021)Peak memory usage: 10 MB
% 0.95/0.42 % (523021)Instructions burned: 6 (million)
% 0.95/0.42 % (523022)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3003144409:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.95/0.42 % (523011)Instruction limit reached!
% 0.95/0.42 % (523011)------------------------------
% 0.95/0.42 % (523011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.42 % (523011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.42 % (523011)CaDiCaL version: 2.1.3
% 0.95/0.42 % (523011)Termination reason: Instruction limit
% 0.95/0.42 % (523011)Termination phase: Saturation
% 0.95/0.42 % (523011)Time elapsed: 0.036 s
% 0.95/0.42 % (523011)Peak memory usage: 12 MB
% 0.95/0.42 % (523011)Instructions burned: 75 (million)
% 0.95/0.42 % (523022)Instruction limit reached!
% 0.95/0.42 % (523022)------------------------------
% 0.95/0.42 % (523022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.42 % (523022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.42 % (523022)CaDiCaL version: 2.1.3
% 0.95/0.42 % (523022)Termination reason: Instruction limit
% 0.95/0.42 % (523022)Termination phase: Property scanning
% 0.95/0.42 % (523022)Time elapsed: 0.004 s
% 0.95/0.42 % (523022)Peak memory usage: 10 MB
% 0.95/0.42 % (523022)Instructions burned: 9 (million)
% 0.95/0.42 % (523006)Instruction limit reached!
% 0.95/0.42 % (523006)------------------------------
% 0.95/0.42 % (523006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.42 % (523006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.42 % (523006)CaDiCaL version: 2.1.3
% 0.95/0.42 % (523006)Termination reason: Instruction limit
% 0.95/0.42 % (523006)Termination phase: Saturation
% 0.95/0.42 % (523006)Time elapsed: 0.044 s
% 0.95/0.42 % (523006)Peak memory usage: 12 MB
% 0.95/0.42 % (523006)Instructions burned: 88 (million)
% 0.95/0.42 % (523024)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1843024281:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.95/0.42 % (523024)Instruction limit reached!
% 0.95/0.42 % (523024)------------------------------
% 0.95/0.42 % (523024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.42 % (523024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.42 % (523024)CaDiCaL version: 2.1.3
% 0.95/0.42 % (523024)Termination reason: Instruction limit
% 0.95/0.42 % (523024)Termination phase: Saturation
% 0.95/0.42 % (523024)Time elapsed: 0.006 s
% 0.95/0.42 % (523024)Peak memory usage: 11 MB
% 0.95/0.42 % (523024)Instructions burned: 14 (million)
% 0.95/0.42 % (523026)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
% 0.95/0.42 % (523026)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.95/0.42 % (523028)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=2369922693:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.95/0.42 % (523029)lrs+10_1_si=on:cs=on:random_seed=4236728350:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.95/0.42 % (523030)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.95/0.42 % (523026)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3676613357:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.95/0.45 % (523030)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=3475949928:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.95/0.45 % (523029)Instruction limit reached!
% 0.95/0.45 % (523029)------------------------------
% 0.95/0.45 % (523029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.45 % (523029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.45 % (523029)CaDiCaL version: 2.1.3
% 0.95/0.45 % (523029)Termination reason: Instruction limit
% 0.95/0.45 % (523029)Termination phase: Saturation
% 0.95/0.45 % (523029)Time elapsed: 0.005 s
% 0.95/0.45 % (523029)Peak memory usage: 11 MB
% 0.95/0.45 % (523029)Instructions burned: 10 (million)
% 0.95/0.45 % (523030)Instruction limit reached!
% 0.95/0.45 % (523030)------------------------------
% 0.95/0.45 % (523030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.45 % (523030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.45 % (523030)CaDiCaL version: 2.1.3
% 0.95/0.45 % (523030)Termination reason: Instruction limit
% 0.95/0.45 % (523030)Termination phase: Property scanning
% 0.95/0.45 % (523030)Time elapsed: 0.003 s
% 0.95/0.45 % (523030)Peak memory usage: 10 MB
% 0.95/0.45 % (523030)Instructions burned: 5 (million)
% 0.95/0.45 % (523032)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3035702589:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.95/0.45 % (523012)Instruction limit reached!
% 0.95/0.45 % (523012)------------------------------
% 0.95/0.45 % (523012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.45 % (523012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.45 % (523012)CaDiCaL version: 2.1.3
% 0.95/0.45 % (523012)Termination reason: Instruction limit
% 0.95/0.45 % (523012)Termination phase: Saturation
% 0.95/0.45 % (523012)Time elapsed: 0.078 s
% 0.95/0.45 % (523012)Peak memory usage: 13 MB
% 0.95/0.45 % (523012)Instructions burned: 157 (million)
% 0.95/0.45 % (523037)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=916829384:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.95/0.45 % (523038)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2832137026:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.95/0.45 % (523026)Instruction limit reached!
% 0.95/0.45 % (523026)------------------------------
% 0.95/0.45 % (523026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.45 % (523026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.45 % (523026)CaDiCaL version: 2.1.3
% 0.95/0.45 % (523026)Termination reason: Instruction limit
% 0.95/0.45 % (523026)Termination phase: Saturation
% 0.95/0.45 % (523026)Time elapsed: 0.028 s
% 0.95/0.45 % (523026)Peak memory usage: 11 MB
% 0.95/0.45 % (523026)Instructions burned: 29 (million)
% 0.95/0.45 % (523037)Refutation not found, incomplete strategy
% 0.95/0.45 % (523037)------------------------------
% 0.95/0.45 % (523037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.45 % (523037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.45 % (523037)CaDiCaL version: 2.1.3
% 0.95/0.45 % (523037)Termination reason: Refutation not found, incomplete strategy
% 0.95/0.45 % (523037)Time elapsed: 0.007 s
% 0.95/0.45 % (523037)Peak memory usage: 12 MB
% 0.95/0.45 % (523037)Instructions burned: 14 (million)
% 0.95/0.45 % (523032)Refutation not found, incomplete strategy
% 0.95/0.45 % (523032)------------------------------
% 0.95/0.45 % (523032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.45 % (523032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.45 % (523032)CaDiCaL version: 2.1.3
% 0.95/0.45 % (523032)Termination reason: Refutation not found, incomplete strategy
% 0.95/0.45 % (523032)Time elapsed: 0.019 s
% 0.95/0.45 % (523032)Peak memory usage: 12 MB
% 0.95/0.45 % (523032)Instructions burned: 36 (million)
% 0.95/0.45 % (523037)------------------------------
% 0.95/0.45 % (523037)------------------------------
% 0.95/0.45 % (523032)------------------------------
% 0.95/0.45 % (523032)------------------------------
% 0.95/0.45 % (523038)Instruction limit reached!
% 0.95/0.45 % (523038)------------------------------
% 0.95/0.49 % (523038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.49 % (523038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.49 % (523038)CaDiCaL version: 2.1.3
% 0.95/0.49 % (523038)Termination reason: Instruction limit
% 0.95/0.49 % (523038)Termination phase: Saturation
% 0.95/0.49 % (523038)Time elapsed: 0.015 s
% 0.95/0.49 % (523038)Peak memory usage: 12 MB
% 0.95/0.49 % (523038)Instructions burned: 26 (million)
% 0.95/0.49 % (523028)Instruction limit reached!
% 0.95/0.49 % (523028)------------------------------
% 0.95/0.49 % (523028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.49 % (523028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.49 % (523028)CaDiCaL version: 2.1.3
% 0.95/0.49 % (523028)Termination reason: Instruction limit
% 0.95/0.49 % (523028)Termination phase: Saturation
% 0.95/0.49 % (523028)Time elapsed: 0.043 s
% 0.95/0.49 % (523028)Peak memory usage: 13 MB
% 0.95/0.49 % (523028)Instructions burned: 86 (million)
% 0.95/0.49 % (523040)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1263873215:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.95/0.49 % (523043)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3002672308:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.95/0.49 % (523044)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2652600777:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.95/0.49 % (523040)Instruction limit reached!
% 0.95/0.49 % (523040)------------------------------
% 0.95/0.49 % (523040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.49 % (523040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.49 % (523040)CaDiCaL version: 2.1.3
% 0.95/0.49 % (523040)Termination reason: Instruction limit
% 0.95/0.49 % (523040)Termination phase: Saturation
% 0.95/0.49 % (523040)Time elapsed: 0.009 s
% 0.95/0.49 % (523040)Peak memory usage: 11 MB
% 0.95/0.49 % (523040)Instructions burned: 14 (million)
% 0.95/0.49 % (523044)Instruction limit reached!
% 0.95/0.49 % (523044)------------------------------
% 0.95/0.49 % (523044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.49 % (523044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.49 % (523044)CaDiCaL version: 2.1.3
% 0.95/0.49 % (523044)Termination reason: Instruction limit
% 0.95/0.49 % (523044)Termination phase: Saturation
% 0.95/0.49 % (523044)Time elapsed: 0.006 s
% 0.95/0.49 % (523044)Peak memory usage: 11 MB
% 0.95/0.49 % (523044)Instructions burned: 14 (million)
% 0.95/0.49 % (523046)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2757866531:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.95/0.49 % (523045)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2351632170:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.95/0.49 % (523047)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2652434171:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.95/0.49 % (523045)Instruction limit reached!
% 0.95/0.49 % (523045)------------------------------
% 0.95/0.49 % (523045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.49 % (523045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.49 % (523045)CaDiCaL version: 2.1.3
% 0.95/0.49 % (523045)Termination reason: Instruction limit
% 0.95/0.49 % (523045)Termination phase: SInE selection
% 0.95/0.49 % (523045)Time elapsed: 0.002 s
% 0.95/0.49 % (523045)Peak memory usage: 10 MB
% 0.95/0.49 % (523045)Instructions burned: 5 (million)
% 0.95/0.49 % (523047)Instruction limit reached!
% 0.95/0.49 % (523047)------------------------------
% 0.95/0.49 % (523047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.49 % (523047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.49 % (523047)CaDiCaL version: 2.1.3
% 0.95/0.49 % (523047)Termination reason: Instruction limit
% 0.95/0.49 % (523047)Termination phase: Saturation
% 0.95/0.49 % (523047)Time elapsed: 0.011 s
% 0.95/0.49 % (523047)Peak memory usage: 11 MB
% 0.95/0.49 % (523047)Instructions burned: 24 (million)
% 0.95/0.49 % (523052)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.69/0.53 % (523046)Instruction limit reached!
% 1.69/0.53 % (523046)------------------------------
% 1.69/0.53 % (523046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.53 % (523052)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.69/0.53 % (523046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.53 % (523046)CaDiCaL version: 2.1.3
% 1.69/0.53 % (523046)Termination reason: Instruction limit
% 1.69/0.53 % (523046)Termination phase: Saturation
% 1.69/0.53 % (523046)Time elapsed: 0.013 s
% 1.69/0.53 % (523046)Peak memory usage: 12 MB
% 1.69/0.53 % (523046)Instructions burned: 27 (million)
% 1.69/0.53 % (523052)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1953842074:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.69/0.53 % (523056)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.69/0.53 % (523056)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1842298633:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.69/0.53 % (523052)Instruction limit reached!
% 1.69/0.53 % (523052)------------------------------
% 1.69/0.53 % (523052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.53 % (523052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.53 % (523052)CaDiCaL version: 2.1.3
% 1.69/0.53 % (523052)Termination reason: Instruction limit
% 1.69/0.53 % (523052)Termination phase: Saturation
% 1.69/0.53 % (523052)Time elapsed: 0.006 s
% 1.69/0.53 % (523052)Peak memory usage: 11 MB
% 1.69/0.53 % (523052)Instructions burned: 14 (million)
% 1.69/0.53 % (523056)Instruction limit reached!
% 1.69/0.53 % (523056)------------------------------
% 1.69/0.53 % (523056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.53 % (523056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.53 % (523056)CaDiCaL version: 2.1.3
% 1.69/0.53 % (523056)Termination reason: Instruction limit
% 1.69/0.53 % (523056)Termination phase: Property scanning
% 1.69/0.53 % (523056)Time elapsed: 0.005 s
% 1.69/0.53 % (523056)Peak memory usage: 11 MB
% 1.69/0.53 % (523056)Instructions burned: 10 (million)
% 1.69/0.53 % (523051)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2981655280:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.69/0.53 % (523058)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3661517354:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.69/0.53 % (523057)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=26913591:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.69/0.53 % (523058)Instruction limit reached!
% 1.69/0.53 % (523058)------------------------------
% 1.69/0.53 % (523058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.53 % (523058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.53 % (523058)CaDiCaL version: 2.1.3
% 1.69/0.53 % (523058)Termination reason: Instruction limit
% 1.69/0.53 % (523058)Termination phase: Function definition elimination
% 1.69/0.53 % (523058)Time elapsed: 0.003 s
% 1.69/0.53 % (523058)Peak memory usage: 10 MB
% 1.69/0.53 % (523058)Instructions burned: 7 (million)
% 1.69/0.53 % (523061)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3234251301:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.69/0.53 % (523062)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2918428164:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.69/0.53 % (523009)Instruction limit reached!
% 1.69/0.53 % (523009)------------------------------
% 1.69/0.53 % (523009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.53 % (523009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523009)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523009)Termination reason: Instruction limit
% 2.14/0.61 % (523009)Termination phase: Saturation
% 2.14/0.61 % (523009)Time elapsed: 0.172 s
% 2.14/0.61 % (523009)Peak memory usage: 15 MB
% 2.14/0.61 % (523009)Instructions burned: 638 (million)
% 2.14/0.61 % (523057)Instruction limit reached!
% 2.14/0.61 % (523057)------------------------------
% 2.14/0.61 % (523057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523057)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523057)Termination reason: Instruction limit
% 2.14/0.61 % (523057)Termination phase: Saturation
% 2.14/0.61 % (523057)Time elapsed: 0.016 s
% 2.14/0.61 % (523057)Peak memory usage: 12 MB
% 2.14/0.61 % (523057)Instructions burned: 31 (million)
% 2.14/0.61 % (523061)Instruction limit reached!
% 2.14/0.61 % (523061)------------------------------
% 2.14/0.61 % (523061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523066)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4243224592:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.14/0.61 % (523061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523061)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523061)Termination reason: Instruction limit
% 2.14/0.61 % (523061)Termination phase: Saturation
% 2.14/0.61 % (523061)Time elapsed: 0.011 s
% 2.14/0.61 % (523061)Peak memory usage: 11 MB
% 2.14/0.61 % (523061)Instructions burned: 25 (million)
% 2.14/0.61 % (523069)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4165969405:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.14/0.61 % (523062)Instruction limit reached!
% 2.14/0.61 % (523062)------------------------------
% 2.14/0.61 % (523062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523062)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523062)Termination reason: Instruction limit
% 2.14/0.61 % (523062)Termination phase: Saturation
% 2.14/0.61 % (523062)Time elapsed: 0.012 s
% 2.14/0.61 % (523062)Peak memory usage: 12 MB
% 2.14/0.61 % (523062)Instructions burned: 21 (million)
% 2.14/0.61 % (523051)Instruction limit reached!
% 2.14/0.61 % (523051)------------------------------
% 2.14/0.61 % (523051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523051)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523051)Termination reason: Instruction limit
% 2.14/0.61 % (523051)Termination phase: Saturation
% 2.14/0.61 % (523051)Time elapsed: 0.036 s
% 2.14/0.61 % (523051)Peak memory usage: 12 MB
% 2.14/0.61 % (523051)Instructions burned: 60 (million)
% 2.14/0.61 % (523070)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=738206632:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.14/0.61 % (523072)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2454829830:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.14/0.61 % (523074)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.14/0.61 % (523070)Refutation not found, incomplete strategy
% 2.14/0.61 % (523070)------------------------------
% 2.14/0.61 % (523070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523070)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523070)Termination reason: Refutation not found, incomplete strategy
% 2.14/0.61 % (523070)Time elapsed: 0.009 s
% 2.14/0.61 % (523070)Peak memory usage: 12 MB
% 2.14/0.61 % (523070)Instructions burned: 17 (million)
% 2.14/0.61 % (523070)------------------------------
% 2.14/0.61 % (523070)------------------------------
% 2.14/0.61 % (523074)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2092053629:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.14/0.61 % (523074)Instruction limit reached!
% 2.14/0.61 % (523074)------------------------------
% 2.14/0.61 % (523074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523074)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523074)Termination reason: Instruction limit
% 2.14/0.61 % (523074)Termination phase: Function definition elimination
% 2.14/0.61 % (523074)Time elapsed: 0.003 s
% 2.14/0.61 % (523074)Peak memory usage: 10 MB
% 2.14/0.61 % (523074)Instructions burned: 7 (million)
% 2.14/0.61 % (523072)Instruction limit reached!
% 2.14/0.61 % (523072)------------------------------
% 2.14/0.61 % (523072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523069)Instruction limit reached!
% 2.14/0.61 % (523069)------------------------------
% 2.14/0.61 % (523069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523072)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523072)Termination reason: Instruction limit
% 2.14/0.61 % (523072)Termination phase: Saturation
% 2.14/0.61 % (523072)Time elapsed: 0.020 s
% 2.14/0.61 % (523072)Peak memory usage: 12 MB
% 2.14/0.61 % (523072)Instructions burned: 43 (million)
% 2.14/0.61 % (523069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523069)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523069)Termination reason: Instruction limit
% 2.14/0.61 % (523069)Termination phase: Saturation
% 2.14/0.61 % (523069)Time elapsed: 0.037 s
% 2.14/0.61 % (523069)Peak memory usage: 13 MB
% 2.14/0.61 % (523069)Instructions burned: 144 (million)
% 2.14/0.61 % (523078)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2166895145:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.14/0.61 % (523076)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3116195109:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.14/0.61 % (523080)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.14/0.61 % (523082)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1411486362:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.14/0.61 % (523080)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1628953006:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.14/0.61 % (523082)Instruction limit reached!
% 2.14/0.61 % (523082)------------------------------
% 2.14/0.61 % (523082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523082)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523082)Termination reason: Instruction limit
% 2.14/0.61 % (523082)Termination phase: Saturation
% 2.14/0.61 % (523082)Time elapsed: 0.005 s
% 2.14/0.61 % (523082)Peak memory usage: 12 MB
% 2.14/0.61 % (523082)Instructions burned: 20 (million)
% 2.14/0.61 % (523080)Instruction limit reached!
% 2.14/0.61 % (523080)------------------------------
% 2.14/0.61 % (523080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523080)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523080)Termination reason: Instruction limit
% 2.14/0.61 % (523080)Termination phase: SInE selection
% 2.14/0.61 % (523080)Time elapsed: 0.003 s
% 2.14/0.61 % (523080)Peak memory usage: 10 MB
% 2.14/0.61 % (523080)Instructions burned: 6 (million)
% 2.14/0.61 % (523081)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=4105375875:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.14/0.61 % (523087)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=961591984:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.14/0.61 % (523081)Instruction limit reached!
% 2.14/0.61 % (523081)------------------------------
% 2.14/0.61 % (523081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523081)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523081)Termination reason: Instruction limit
% 2.14/0.61 % (523081)Termination phase: Saturation
% 2.14/0.61 % (523081)Time elapsed: 0.011 s
% 2.14/0.61 % (523081)Peak memory usage: 12 MB
% 2.14/0.61 % (523081)Instructions burned: 22 (million)
% 2.14/0.61 % (523088)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1082255150:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.14/0.61 % (523091)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3097715736:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.14/0.61 % (523043)Instruction limit reached!
% 2.14/0.61 % (523043)------------------------------
% 2.14/0.61 % (523043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523043)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523043)Termination reason: Instruction limit
% 2.14/0.61 % (523043)Termination phase: Saturation
% 2.14/0.61 % (523043)Time elapsed: 0.167 s
% 2.14/0.61 % (523043)Peak memory usage: 13 MB
% 2.14/0.61 % (523043)Instructions burned: 328 (million)
% 2.14/0.61 % (523091)Instruction limit reached!
% 2.14/0.61 % (523091)------------------------------
% 2.14/0.61 % (523091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523091)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523091)Termination reason: Instruction limit
% 2.14/0.61 % (523091)Termination phase: Saturation
% 2.14/0.61 % (523091)Time elapsed: 0.026 s
% 2.14/0.61 % (523091)Peak memory usage: 12 MB
% 2.14/0.61 % (523091)Instructions burned: 46 (million)
% 2.14/0.61 % (523094)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=898114604:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.14/0.61 % (523078)Instruction limit reached!
% 2.14/0.61 % (523078)------------------------------
% 2.14/0.61 % (523078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523078)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523078)Termination reason: Instruction limit
% 2.14/0.61 % (523078)Termination phase: Saturation
% 2.14/0.61 % (523078)Time elapsed: 0.085 s
% 2.14/0.61 % (523078)Peak memory usage: 13 MB
% 2.14/0.61 % (523078)Instructions burned: 169 (million)
% 2.14/0.61 % (523094)Refutation not found, incomplete strategy
% 2.14/0.61 % (523094)------------------------------
% 2.14/0.61 % (523094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523094)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523094)Termination reason: Refutation not found, incomplete strategy
% 2.14/0.61 % (523094)Time elapsed: 0.005 s
% 2.14/0.61 % (523094)Peak memory usage: 12 MB
% 2.14/0.61 % (523094)Instructions burned: 10 (million)
% 2.14/0.61 % (523094)------------------------------
% 2.14/0.61 % (523094)------------------------------
% 2.14/0.61 % (523095)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=4147931626:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.14/0.61 % (523097)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.14/0.61 % (523087) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-523001-523087"...
% 2.14/0.61 % (523095)Instruction limit reached!
% 2.14/0.61 % (523095)------------------------------
% 2.14/0.61 % (523095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.61 % (523095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.61 % (523095)CaDiCaL version: 2.1.3
% 2.14/0.61 % (523095)Termination reason: Instruction limit
% 2.14/0.61 % (523095)Termination phase: Saturation
% 2.14/0.61 % (523095)Time elapsed: 0.010 s
% 2.14/0.61 % (523095)Peak memory usage: 12 MB
% 2.14/0.61 % (523095)Instructions burned: 22 (million)
% 2.14/0.61 % (523097)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1844889877:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.14/0.61 % (523098)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=436408824:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.14/0.61 % (523087)...printing done.
% 2.14/0.61 % (523087)Refutation found. Thanks to Tanya!
% 2.14/0.61 % SZS status Theorem for theBenchmark
% 2.14/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 2.14/0.62 % (523087)------------------------------
% 2.14/0.62 % (523087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.62 % (523087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.62 % (523087)CaDiCaL version: 2.1.3
% 2.14/0.62 % (523087)Termination reason: Refutation
% 2.14/0.62 % (523087)Time elapsed: 0.083 s
% 2.14/0.62 % (523087)Peak memory usage: 15 MB
% 2.14/0.62 % (523087)Instructions burned: 284 (million)
% 2.14/0.62 % (523001)Success in time 0.361 s
% 2.14/0.62 % Vampire exiting
%------------------------------------------------------------------------------