%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN397^7 : 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 : n026.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 08:41:43 AM UTC 2026
% Result : Theorem 1.79s 0.59s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 221 ( 80 unt; 0 typ; 5 def)
% Number of atoms : 2218 ( 301 equ; 0 cnn)
% Maximal formula atoms : 28 ( 10 avg)
% Number of connectives : 4251 ( 597 ~; 559 |; 24 &;2587 @)
% ( 5 <=>; 115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 13 con; 0-4 aty)
% ( 364 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 730 ( 0 sgn 144 !; 0 ?; 730 :)
% 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,
f: mu > $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_56,type,
sK4: mu ).
thf(func_def_57,type,
sK5: $i > mu > $i ).
thf(func_def_58,type,
sK6: $i > mu ).
thf(func_def_60,type,
sK8: $i > $i ).
thf(func_def_61,type,
sK9: $i > mu ).
thf(func_def_62,type,
sK10: $i > $i ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f16,axiom,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mexists_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] :
! [X3: $i,X2: $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,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
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,
! [X0: mu,X1: $i,X2: $i] :
( ( ( 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
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( f @ X0 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X1 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( f @ X0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish204) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( f @ X0 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X1 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( f @ X0 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f40,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f42,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f43,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f45,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f51,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f52,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f58,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f59,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f75,plain,
~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( f @ X0 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X1 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X2: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ X2 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X3: mu] : ( mbox_s4 @ ( f @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f76,plain,
( $true
= ( ~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( f @ Y0 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y0 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y0 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( f @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f83,plain,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
inference(rectify,[],[f16]) ).
thf(f84,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f86,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f90,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f91,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f97,plain,
! [X0: mu,X1: $i,X2: $i] :
( ( ( rel_s4 @ X1 @ X2 )
& ( exists_in_world @ X0 @ X1 ) )
=> ( exists_in_world @ X0 @ X2 ) ),
inference(rectify,[],[f36]) ).
thf(f98,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( ( exists_in_world @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f100,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f101,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f104,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f107,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f109,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f110,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f112,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f114,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f115,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f116,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f118,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f125,plain,
( $true
= ( ~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( f @ Y0 ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y0 ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y0 ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( f @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f128,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f130,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f132,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( ( exists_in_world @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f139,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f99]) ).
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,[],[f128,f109,f118,f109,f109]) ).
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,[],[f139,f118,f109]) ).
thf(f149,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f104,f109,f110,f109]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f115,f107]) ).
thf(f153,plain,
( $true
= ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( 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 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f125,f112,f143,f116,f144,f116,f109,f149,f116,f116,f110,f116,f109,f116,f116,f144,f116,f110,f116,f109,f116,f116,f109,f149,f116]) ).
thf(f154,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f130,f114]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f156,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( 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] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f157,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( 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] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f156]) ).
thf(f158,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f159,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( 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] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( 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] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( f @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y3 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f167,definition,
( spl1_1
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f169,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f171,definition,
( spl1_2
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f173,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f174,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f165,f171,f167]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f178,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f182,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f184,plain,
( ( $false
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK3 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ sK3 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK3 @ Y1 ) ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK3 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f201,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f202,plain,
( ! [X1: $i] :
( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( ! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ! [X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f206,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK3 @ Y1 ) ) ) )
@ sK4 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f210,plain,
( ( $false
= ( ( exists_in_world @ sK4 @ sK3 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ sK4 @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f211,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ sK4 @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $true
= ( exists_in_world @ sK4 @ sK3 ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ sK4 @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( ! [X2: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) )
@ X2 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f215,plain,
( ! [X2: mu,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ X2 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ! [X2: mu,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ X2 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ X2 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X3 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X3 @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X3 @ Y0 ) ) ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X3 @ Y0 ) ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X3 @ Y0 ) ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f224,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( f @ sK4 @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f225,plain,
( ! [X1: $i] :
( $true
= ( ( f @ sK4 @ X1 )
| ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
( ! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( f @ sK4 @ X1 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ! [X1: $i] :
( ( $true
= ( f @ sK4 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X3 @ Y0 ) )
@ ( sK5 @ X3 @ X2 ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f231,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( ( f @ X2 @ ( sK5 @ X3 @ X2 ) )
| ~ ( rel_s4 @ X3 @ ( sK5 @ X3 @ X2 ) ) ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f232,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( ~ ( rel_s4 @ X3 @ ( sK5 @ X3 @ X2 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( ( f @ X2 @ ( sK5 @ X3 @ X2 ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f234,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f239,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK3 @ ( sK5 @ X0 @ sK4 ) ) )
| ( $true = $false )
| ( $false
= ( exists_in_world @ sK4 @ X1 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X0 ) ) )
| ~ spl1_2 ),
inference(superposition,[],[f227,f233]) ).
thf(f241,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK3 @ ( sK5 @ X0 @ sK4 ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ sK4 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ X0 ) ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f244,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ X0 ) )
| ( $false
= ( exists_in_world @ sK4 @ X0 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ sK3 ) )
| ( $false
= ( exists_in_world @ sK4 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK3 ) ) )
| ~ spl1_2 ),
inference(superposition,[],[f241,f234]) ).
thf(f248,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ sK4 @ X0 ) )
| ( $false
= ( rel_s4 @ X1 @ sK3 ) )
| ( $false
= ( rel_s4 @ sK2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( exists_in_world @ sK4 @ X1 ) ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f251,definition,
( spl1_3
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ sK4 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f252,plain,
( ! [X1: $i] :
( ( $false
= ( exists_in_world @ sK4 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ sK3 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f253,plain,
( spl1_3
| spl1_3
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f248,f171,f251,f251]) ).
thf(f255,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( ( exists_in_world @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f256,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( ( exists_in_world @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( exists_in_world @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( ( exists_in_world @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( exists_in_world @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( ( exists_in_world @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( exists_in_world @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK3 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK3 @ sK3 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[],[f252,f212]) ).
thf(f263,plain,
( ( $false
= ( rel_s4 @ sK2 @ sK3 ) )
| ( $false
= ( rel_s4 @ sK3 @ sK3 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f267,plain,
( ( $false
= ( rel_s4 @ sK3 @ sK3 ) )
| ( $true = $false )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f263,f187]) ).
thf(f268,plain,
( ( $false
= ( rel_s4 @ sK3 @ sK3 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f269,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f268,f206]) ).
thf(f270,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f271,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f270]) ).
thf(f272,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( f @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK7 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f275,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ sK7 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f277,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f279,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f277]) ).
thf(f280,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f277]) ).
thf(f281,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f296,plain,
! [X2: $i,X3: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( ( exists_in_world @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( exists_in_world @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f258]) ).
thf(f297,plain,
! [X2: $i,X3: mu,X1: $i] :
( $true
= ( ( ( exists_in_world @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( exists_in_world @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $false
= ( ( exists_in_world @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) ) )
| ( $true
= ( exists_in_world @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f301,plain,
( ! [X1: $i] :
( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f300]) ).
thf(f302,plain,
( ! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK7 @ X1 ) ) )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ! [X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) )
@ X2 ) ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f303]) ).
thf(f305,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f304]) ).
thf(f306,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f305]) ).
thf(f307,plain,
( ! [X2: mu,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $false )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f321,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f322,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f321]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f322]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ X1 @ X2 ) )
=> ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f344,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ X1 @ X2 ) )
=> ( rel_s4 @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f337]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X1 @ X2 ) )
=> ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f346]) ).
thf(f373,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK5 @ X1 @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f307]) ).
thf(f376,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( ( f @ X2 @ ( sK5 @ X1 @ X2 ) )
| ~ ( rel_s4 @ X1 @ ( sK5 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f373]) ).
thf(f377,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ X1 @ ( sK5 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( ! [X2: mu,X1: $i] :
( ( $false
= ( f @ X2 @ ( sK5 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f379,plain,
( ! [X2: mu,X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK5 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f406,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ Y0 ) )
@ ( sK8 @ sK7 ) ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f279]) ).
thf(f408,plain,
( ( $false
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( sK8 @ sK7 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK7 @ ( sK8 @ sK7 ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f406]) ).
thf(f410,plain,
( ( $false
= ( ~ ( rel_s4 @ sK7 @ ( sK8 @ sK7 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f408]) ).
thf(f411,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( sK8 @ sK7 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ Y1 ) ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f408]) ).
thf(f412,plain,
( ( $true
= ( rel_s4 @ sK7 @ ( sK8 @ sK7 ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f410]) ).
thf(f448,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( sK8 @ sK7 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ Y1 ) ) ) )
@ ( sK9 @ sK7 ) ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f411]) ).
thf(f450,plain,
( ( ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK8 @ sK7 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f448]) ).
thf(f452,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f450]) ).
thf(f453,plain,
( ( $true
= ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK8 @ sK7 ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f450]) ).
thf(f510,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ Y0 ) )
@ ( sK10 @ sK7 ) ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f452]) ).
thf(f513,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y0 )
| ~ ( rel_s4 @ ( sK10 @ sK7 ) @ Y0 ) ) )
| ~ ( rel_s4 @ ( sK8 @ sK7 ) @ ( sK10 @ sK7 ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f510]) ).
thf(f514,plain,
( ( $false
= ( ~ ( rel_s4 @ ( sK8 @ sK7 ) @ ( sK10 @ sK7 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f513]) ).
thf(f515,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y0 )
| ~ ( rel_s4 @ ( sK10 @ sK7 ) @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f513]) ).
thf(f516,plain,
( ( $true
= ( rel_s4 @ ( sK8 @ sK7 ) @ ( sK10 @ sK7 ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f514]) ).
thf(f517,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y0 )
| ~ ( rel_s4 @ ( sK10 @ sK7 ) @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f515]) ).
thf(f518,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( f @ ( sK9 @ sK7 ) @ Y0 )
| ~ ( rel_s4 @ ( sK10 @ sK7 ) @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f517]) ).
thf(f519,plain,
( ! [X1: $i] :
( $true
= ( ( f @ ( sK9 @ sK7 ) @ X1 )
| ~ ( rel_s4 @ ( sK10 @ sK7 ) @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f518]) ).
thf(f520,plain,
( ! [X1: $i] :
( ( $true
= ( f @ ( sK9 @ sK7 ) @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ ( sK10 @ sK7 ) @ X1 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f519]) ).
thf(f521,plain,
( ! [X1: $i] :
( ( $true
= ( f @ ( sK9 @ sK7 ) @ X1 ) )
| ( $false
= ( rel_s4 @ ( sK10 @ sK7 ) @ X1 ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f520]) ).
thf(f530,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X0 ) )
| ( $false
= ( exists_in_world @ ( sK9 @ sK7 ) @ X0 ) )
| ( $false
= ( rel_s4 @ ( sK10 @ sK7 ) @ ( sK5 @ X0 @ ( sK9 @ sK7 ) ) ) )
| ( $true = $false ) )
| ~ spl1_1 ),
inference(superposition,[],[f378,f521]) ).
thf(f532,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ ( sK10 @ sK7 ) @ ( sK5 @ X0 @ ( sK9 @ sK7 ) ) ) )
| ( $false
= ( exists_in_world @ ( sK9 @ sK7 ) @ X0 ) )
| ( $false
= ( rel_s4 @ sK7 @ X0 ) ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f545,plain,
( ( ( rel_s4 @ sK7 @ ( sK10 @ sK7 ) )
= $false )
| ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK10 @ sK7 ) )
= $false )
| ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK10 @ sK7 ) )
= $false )
| ( $true = $false )
| ( ( rel_s4 @ sK7 @ ( sK10 @ sK7 ) )
= $false )
| ~ spl1_1 ),
inference(superposition,[],[f532,f379]) ).
thf(f572,plain,
( ( ( rel_s4 @ sK7 @ ( sK10 @ sK7 ) )
= $false )
| ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK10 @ sK7 ) )
= $false )
| ( $true = $false )
| ~ spl1_1 ),
inference(duplicate_literal_removal,[],[f545]) ).
thf(f573,plain,
( ( ( rel_s4 @ sK7 @ ( sK10 @ sK7 ) )
= $false )
| ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK10 @ sK7 ) )
= $false )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f572]) ).
thf(f579,definition,
( spl1_6
<=> ( ( rel_s4 @ sK7 @ ( sK10 @ sK7 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f581,plain,
( ( ( rel_s4 @ sK7 @ ( sK10 @ sK7 ) )
= $false )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f579]) ).
thf(f586,definition,
( spl1_8
<=> ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK10 @ sK7 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
thf(f588,plain,
( ( ( exists_in_world @ ( sK9 @ sK7 ) @ ( sK10 @ sK7 ) )
= $false )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f586]) ).
thf(f605,plain,
( spl1_8
| spl1_6
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f573,f167,f579,f586]) ).
thf(f656,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ ( sK10 @ sK7 ) ) )
| ( $true = $false ) )
| ~ spl1_6 ),
inference(superposition,[],[f347,f581]) ).
thf(f658,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ ( sK10 @ sK7 ) ) )
| ( $false
= ( rel_s4 @ sK7 @ X0 ) ) )
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f656]) ).
thf(f660,plain,
( ! [X0: $i] :
( ( $false
= ( exists_in_world @ ( sK9 @ sK7 ) @ X0 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK10 @ sK7 ) ) ) )
| ~ spl1_8 ),
inference(superposition,[],[f588,f299]) ).
thf(f663,plain,
( ! [X0: $i] :
( ( $false
= ( exists_in_world @ ( sK9 @ sK7 ) @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ ( sK10 @ sK7 ) ) ) )
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f660]) ).
thf(f742,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK7 @ ( sK8 @ sK7 ) ) )
| ~ spl1_1
| ~ spl1_6 ),
inference(superposition,[],[f516,f658]) ).
thf(f750,plain,
( ( $false
= ( rel_s4 @ sK7 @ ( sK8 @ sK7 ) ) )
| ~ spl1_1
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f742]) ).
thf(f755,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_6 ),
inference(superposition,[],[f412,f750]) ).
thf(f761,plain,
( $false
| ~ spl1_1
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f755]) ).
thf(f762,plain,
( ~ spl1_1
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f761]) ).
thf(f848,plain,
( ( $false
= ( rel_s4 @ ( sK8 @ sK7 ) @ ( sK10 @ sK7 ) ) )
| ( $true = $false )
| ~ spl1_1
| ~ spl1_8 ),
inference(superposition,[],[f453,f663]) ).
thf(f851,plain,
( ( $false
= ( rel_s4 @ ( sK8 @ sK7 ) @ ( sK10 @ sK7 ) ) )
| ~ spl1_1
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f848]) ).
thf(f857,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_8 ),
inference(superposition,[],[f516,f851]) ).
thf(f864,plain,
( $false
| ~ spl1_1
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f857]) ).
thf(f865,plain,
( ~ spl1_1
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[],[f864]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s2,plain,
( spl1_3
| ~ spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f253]) ).
cnf(s3,plain,
( ~ spl1_2
| spl1_3 ),
inference(rat,[],[s2]) ).
cnf(s6,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f271]) ).
cnf(s16,plain,
( ~ spl1_1
| spl1_6
| spl1_8 ),
inference(sat_conversion,[],[f605]) ).
cnf(s32,plain,
( ~ spl1_1
| ~ spl1_6 ),
inference(sat_conversion,[],[f762]) ).
cnf(s34,plain,
( ~ spl1_1
| ~ spl1_8 ),
inference(sat_conversion,[],[f865]) ).
cnf(s35,plain,
~ spl1_2,
inference(rat,[],[s3,s6]) ).
cnf(s36,plain,
spl1_1,
inference(rat,[],[s1,s35]) ).
cnf(s37,plain,
~ spl1_8,
inference(rat,[],[s34,s36]) ).
cnf(s38,plain,
~ spl1_6,
inference(rat,[],[s32,s36]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s16,s37,s38,s36]) ).
thf(f866,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN397^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n026.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:19:13 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.19/0.27 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
% 0.57/0.44 % (802734)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.57/0.44 % (802740)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3004625095:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.57/0.44 % (802741)lrs+10_16_si=on:nwc=1.5:random_seed=3694395502:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.57/0.44 % (802741)Instruction limit reached!
% 0.57/0.44 % (802741)------------------------------
% 0.57/0.44 % (802741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (802741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (802741)CaDiCaL version: 2.1.3
% 0.57/0.44 % (802741)Termination reason: Instruction limit
% 0.57/0.44 % (802741)Termination phase: Saturation
% 0.57/0.44 % (802741)Time elapsed: 0.009 s
% 0.57/0.44 % (802741)Peak memory usage: 11 MB
% 0.57/0.44 % (802741)Instructions burned: 20 (million)
% 0.57/0.44 % (802743)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=2612574291: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)
% 0.57/0.44 % (802750)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=373430084:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.57/0.44 % (802750)Instruction limit reached!
% 0.57/0.44 % (802750)------------------------------
% 0.57/0.44 % (802750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (802750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (802750)CaDiCaL version: 2.1.3
% 0.57/0.44 % (802750)Termination reason: Instruction limit
% 0.57/0.44 % (802750)Termination phase: Property scanning
% 0.57/0.44 % (802750)Time elapsed: 0.003 s
% 0.57/0.44 % (802750)Peak memory usage: 10 MB
% 0.57/0.44 % (802750)Instructions burned: 6 (million)
% 0.57/0.44 % (802746)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.57/0.44 % (802746)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
% 0.57/0.44 % (802753)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3764177545:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.57/0.44 % (802744)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1984487371:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.57/0.44 % (802742)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=976894073:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.57/0.44 % (802753)Instruction limit reached!
% 0.57/0.44 % (802753)------------------------------
% 0.57/0.44 % (802753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (802753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (802753)CaDiCaL version: 2.1.3
% 0.57/0.44 % (802753)Termination reason: Instruction limit
% 0.57/0.44 % (802753)Termination phase: Property scanning
% 0.57/0.44 % (802753)Time elapsed: 0.003 s
% 0.57/0.44 % (802753)Peak memory usage: 10 MB
% 0.57/0.44 % (802753)Instructions burned: 6 (million)
% 0.57/0.44 % (802742)Instruction limit reached!
% 0.57/0.44 % (802742)------------------------------
% 0.57/0.44 % (802742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (802742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (802742)CaDiCaL version: 2.1.3
% 0.57/0.44 % (802742)Termination reason: Instruction limit
% 0.57/0.44 % (802742)Termination phase: Property scanning
% 0.57/0.44 % (802742)Time elapsed: 0.003 s
% 0.57/0.44 % (802742)Peak memory usage: 10 MB
% 0.57/0.44 % (802742)Instructions burned: 3 (million)
% 0.57/0.44 % (802746)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=4191152372:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.57/0.44 % (802745)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3947902252:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.57/0.44 % (802744)Instruction limit reached!
% 0.57/0.48 % (802744)------------------------------
% 0.57/0.48 % (802744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (802744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (802744)CaDiCaL version: 2.1.3
% 0.57/0.48 % (802744)Termination reason: Instruction limit
% 0.57/0.48 % (802744)Termination phase: Saturation
% 0.57/0.48 % (802744)Time elapsed: 0.014 s
% 0.57/0.48 % (802744)Peak memory usage: 12 MB
% 0.57/0.48 % (802744)Instructions burned: 25 (million)
% 0.57/0.48 % (802740)Instruction limit reached!
% 0.57/0.48 % (802740)------------------------------
% 0.57/0.48 % (802740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (802740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (802740)CaDiCaL version: 2.1.3
% 0.57/0.48 % (802740)Termination reason: Instruction limit
% 0.57/0.48 % (802740)Termination phase: Saturation
% 0.57/0.48 % (802740)Time elapsed: 0.069 s
% 0.57/0.48 % (802740)Peak memory usage: 12 MB
% 0.57/0.48 % (802740)Instructions burned: 88 (million)
% 0.57/0.48 % (802759)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=226883115:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.57/0.48 % (802757)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.48 % (802759)Instruction limit reached!
% 0.57/0.48 % (802759)------------------------------
% 0.57/0.48 % (802759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (802759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (802759)CaDiCaL version: 2.1.3
% 0.57/0.48 % (802759)Termination reason: Instruction limit
% 0.57/0.48 % (802759)Termination phase: Saturation
% 0.57/0.48 % (802759)Time elapsed: 0.003 s
% 0.57/0.48 % (802759)Peak memory usage: 12 MB
% 0.57/0.48 % (802759)Instructions burned: 12 (million)
% 0.57/0.48 % (802757)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1219809319:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.57/0.48 % (802757)Instruction limit reached!
% 0.57/0.48 % (802757)------------------------------
% 0.57/0.48 % (802757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (802757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (802757)CaDiCaL version: 2.1.3
% 0.57/0.48 % (802757)Termination reason: Instruction limit
% 0.57/0.48 % (802757)Termination phase: Function definition elimination
% 0.57/0.48 % (802757)Time elapsed: 0.003 s
% 0.57/0.48 % (802757)Peak memory usage: 10 MB
% 0.57/0.48 % (802757)Instructions burned: 7 (million)
% 0.57/0.48 % (802764)lrs+10_1_si=on:cs=on:random_seed=3321927431:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.57/0.48 % (802764)Instruction limit reached!
% 0.57/0.48 % (802764)------------------------------
% 0.57/0.48 % (802764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (802764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (802764)CaDiCaL version: 2.1.3
% 0.57/0.48 % (802764)Termination reason: Instruction limit
% 0.57/0.48 % (802764)Termination phase: Property scanning
% 0.57/0.48 % (802764)Time elapsed: 0.002 s
% 0.57/0.48 % (802764)Peak memory usage: 10 MB
% 0.57/0.48 % (802764)Instructions burned: 8 (million)
% 0.57/0.48 % (802761)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
% 0.57/0.48 % (802761)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.48 % (802762)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=695413550:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.57/0.48 % (802761)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=359390973:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 0.57/0.48 % (802766)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.26/0.51 % (802768)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4126709388:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.26/0.51 % (802766)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=973335997:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.26/0.51 % (802766)Instruction limit reached!
% 1.26/0.51 % (802766)------------------------------
% 1.26/0.51 % (802766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.51 % (802766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.51 % (802766)CaDiCaL version: 2.1.3
% 1.26/0.51 % (802766)Termination reason: Instruction limit
% 1.26/0.51 % (802766)Termination phase: Property scanning
% 1.26/0.51 % (802766)Time elapsed: 0.003 s
% 1.26/0.51 % (802766)Peak memory usage: 10 MB
% 1.26/0.51 % (802766)Instructions burned: 6 (million)
% 1.26/0.51 % (802745)Instruction limit reached!
% 1.26/0.51 % (802745)------------------------------
% 1.26/0.51 % (802745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.51 % (802745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.51 % (802745)CaDiCaL version: 2.1.3
% 1.26/0.51 % (802745)Termination reason: Instruction limit
% 1.26/0.51 % (802745)Termination phase: Saturation
% 1.26/0.51 % (802745)Time elapsed: 0.041 s
% 1.26/0.51 % (802745)Peak memory usage: 13 MB
% 1.26/0.51 % (802745)Instructions burned: 76 (million)
% 1.26/0.51 % (802768)Refutation not found, incomplete strategy
% 1.26/0.51 % (802768)------------------------------
% 1.26/0.51 % (802768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.51 % (802768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.51 % (802768)CaDiCaL version: 2.1.3
% 1.26/0.51 % (802768)Termination reason: Refutation not found, incomplete strategy
% 1.26/0.51 % (802768)Time elapsed: 0.008 s
% 1.26/0.51 % (802768)Peak memory usage: 12 MB
% 1.26/0.51 % (802768)Instructions burned: 31 (million)
% 1.26/0.51 % (802768)------------------------------
% 1.26/0.51 % (802768)------------------------------
% 1.26/0.51 % (802761)Instruction limit reached!
% 1.26/0.51 % (802761)------------------------------
% 1.26/0.51 % (802761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.51 % (802761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.51 % (802761)CaDiCaL version: 2.1.3
% 1.26/0.51 % (802761)Termination reason: Instruction limit
% 1.26/0.51 % (802761)Termination phase: Saturation
% 1.26/0.51 % (802761)Time elapsed: 0.017 s
% 1.26/0.51 % (802761)Peak memory usage: 12 MB
% 1.26/0.51 % (802761)Instructions burned: 29 (million)
% 1.26/0.51 % (802775)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=964368377:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.26/0.51 % (802773)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1030484341:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.26/0.51 % (802775)Instruction limit reached!
% 1.26/0.51 % (802775)------------------------------
% 1.26/0.51 % (802775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.51 % (802775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.51 % (802775)CaDiCaL version: 2.1.3
% 1.26/0.51 % (802775)Termination reason: Instruction limit
% 1.26/0.51 % (802775)Termination phase: Saturation
% 1.26/0.51 % (802775)Time elapsed: 0.004 s
% 1.26/0.51 % (802775)Peak memory usage: 11 MB
% 1.26/0.51 % (802775)Instructions burned: 16 (million)
% 1.26/0.51 % (802774)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=543880472:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.26/0.51 % (802773)Refutation not found, incomplete strategy
% 1.26/0.51 % (802773)------------------------------
% 1.26/0.51 % (802773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.51 % (802773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.51 % (802773)CaDiCaL version: 2.1.3
% 1.26/0.51 % (802773)Termination reason: Refutation not found, incomplete strategy
% 1.26/0.51 % (802773)Time elapsed: 0.006 s
% 1.26/0.51 % (802773)Peak memory usage: 12 MB
% 1.26/0.56 % (802773)Instructions burned: 12 (million)
% 1.26/0.56 % (802773)------------------------------
% 1.26/0.56 % (802773)------------------------------
% 1.26/0.56 % (802776)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4137029294:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.26/0.56 % (802779)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1048237174:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.26/0.56 % (802779)Instruction limit reached!
% 1.26/0.56 % (802779)------------------------------
% 1.26/0.56 % (802779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.56 % (802779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.56 % (802779)CaDiCaL version: 2.1.3
% 1.26/0.56 % (802779)Termination reason: Instruction limit
% 1.26/0.56 % (802779)Termination phase: Saturation
% 1.26/0.56 % (802779)Time elapsed: 0.003 s
% 1.26/0.56 % (802779)Peak memory usage: 11 MB
% 1.26/0.56 % (802779)Instructions burned: 14 (million)
% 1.26/0.56 % (802762)Instruction limit reached!
% 1.26/0.56 % (802762)------------------------------
% 1.26/0.56 % (802762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.56 % (802762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.56 % (802762)CaDiCaL version: 2.1.3
% 1.26/0.56 % (802762)Termination reason: Instruction limit
% 1.26/0.56 % (802762)Termination phase: Saturation
% 1.26/0.56 % (802762)Time elapsed: 0.048 s
% 1.26/0.56 % (802762)Peak memory usage: 13 MB
% 1.26/0.56 % (802762)Instructions burned: 87 (million)
% 1.26/0.56 % (802774)Instruction limit reached!
% 1.26/0.56 % (802774)------------------------------
% 1.26/0.56 % (802774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.56 % (802774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.56 % (802774)CaDiCaL version: 2.1.3
% 1.26/0.56 % (802774)Termination reason: Instruction limit
% 1.26/0.56 % (802774)Termination phase: Saturation
% 1.26/0.56 % (802774)Time elapsed: 0.015 s
% 1.26/0.56 % (802774)Peak memory usage: 12 MB
% 1.26/0.56 % (802774)Instructions burned: 26 (million)
% 1.26/0.56 % (802746)Instruction limit reached!
% 1.26/0.56 % (802746)------------------------------
% 1.26/0.56 % (802746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.56 % (802746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.56 % (802746)CaDiCaL version: 2.1.3
% 1.26/0.56 % (802746)Termination reason: Instruction limit
% 1.26/0.56 % (802746)Termination phase: Saturation
% 1.26/0.56 % (802746)Time elapsed: 0.094 s
% 1.26/0.56 % (802746)Peak memory usage: 13 MB
% 1.26/0.56 % (802746)Instructions burned: 157 (million)
% 1.26/0.56 % (802782)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3849219783: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)
% 1.26/0.56 % (802786)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3352404945:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.26/0.56 % (802782)Instruction limit reached!
% 1.26/0.56 % (802782)------------------------------
% 1.26/0.56 % (802782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.26/0.56 % (802782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.26/0.56 % (802782)CaDiCaL version: 2.1.3
% 1.26/0.56 % (802782)Termination reason: Instruction limit
% 1.26/0.56 % (802782)Termination phase: shuffling
% 1.26/0.56 % (802782)Time elapsed: 0.005 s
% 1.26/0.56 % (802782)Peak memory usage: 9 MB
% 1.26/0.56 % (802782)Instructions burned: 2 (million)
% 1.26/0.56 % (802785)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1203730920:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.26/0.56 % (802784)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2925504021:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.26/0.56 % (802787)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
% 1.26/0.56 % (802787)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.79/0.59 % (802790)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.79/0.59 % (802790)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=2168480402:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.79/0.59 % (802787)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=2903828005:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.79/0.59 % (802790)Instruction limit reached!
% 1.79/0.59 % (802790)------------------------------
% 1.79/0.59 % (802790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802790)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802790)Termination reason: Instruction limit
% 1.79/0.59 % (802790)Termination phase: Property scanning
% 1.79/0.59 % (802790)Time elapsed: 0.002 s
% 1.79/0.59 % (802790)Peak memory usage: 11 MB
% 1.79/0.59 % (802790)Instructions burned: 10 (million)
% 1.79/0.59 % (802785)Instruction limit reached!
% 1.79/0.59 % (802785)------------------------------
% 1.79/0.59 % (802785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802785)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802785)Termination reason: Instruction limit
% 1.79/0.59 % (802785)Termination phase: Saturation
% 1.79/0.59 % (802785)Time elapsed: 0.014 s
% 1.79/0.59 % (802785)Peak memory usage: 12 MB
% 1.79/0.59 % (802785)Instructions burned: 24 (million)
% 1.79/0.59 % (802787)Instruction limit reached!
% 1.79/0.59 % (802787)------------------------------
% 1.79/0.59 % (802787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802787)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802787)Termination reason: Instruction limit
% 1.79/0.59 % (802787)Termination phase: Saturation
% 1.79/0.59 % (802787)Time elapsed: 0.006 s
% 1.79/0.59 % (802787)Peak memory usage: 11 MB
% 1.79/0.59 % (802787)Instructions burned: 14 (million)
% 1.79/0.59 % (802784)Instruction limit reached!
% 1.79/0.59 % (802784)------------------------------
% 1.79/0.59 % (802784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802784)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802784)Termination reason: Instruction limit
% 1.79/0.59 % (802784)Termination phase: Saturation
% 1.79/0.59 % (802784)Time elapsed: 0.013 s
% 1.79/0.59 % (802784)Peak memory usage: 12 MB
% 1.79/0.59 % (802784)Instructions burned: 27 (million)
% 1.79/0.59 % (802795)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=2426299457:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.79/0.59 % (802786)Instruction limit reached!
% 1.79/0.59 % (802786)------------------------------
% 1.79/0.59 % (802786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802786)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802786)Termination reason: Instruction limit
% 1.79/0.59 % (802786)Termination phase: Saturation
% 1.79/0.59 % (802786)Time elapsed: 0.033 s
% 1.79/0.59 % (802786)Peak memory usage: 12 MB
% 1.79/0.59 % (802786)Instructions burned: 61 (million)
% 1.79/0.59 % (802795)Instruction limit reached!
% 1.79/0.59 % (802795)------------------------------
% 1.79/0.59 % (802795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802795)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802795)Termination reason: Instruction limit
% 1.79/0.59 % (802795)Termination phase: Saturation
% 1.79/0.59 % (802795)Time elapsed: 0.009 s
% 1.79/0.59 % (802795)Peak memory usage: 12 MB
% 1.79/0.59 % (802795)Instructions burned: 33 (million)
% 1.79/0.59 % (802797)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1587081661:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.79/0.59 % (802796)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2831902972:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.79/0.59 % (802798)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2550857556:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.79/0.59 % (802796)Instruction limit reached!
% 1.79/0.59 % (802796)------------------------------
% 1.79/0.59 % (802796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802796)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802796)Termination reason: Instruction limit
% 1.79/0.59 % (802796)Termination phase: Property scanning
% 1.79/0.59 % (802796)Time elapsed: 0.004 s
% 1.79/0.59 % (802796)Peak memory usage: 10 MB
% 1.79/0.59 % (802796)Instructions burned: 8 (million)
% 1.79/0.59 % (802801)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=147100835:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.79/0.59 % (802797)Instruction limit reached!
% 1.79/0.59 % (802797)------------------------------
% 1.79/0.59 % (802797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802797)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802797)Termination reason: Instruction limit
% 1.79/0.59 % (802797)Termination phase: Saturation
% 1.79/0.59 % (802797)Time elapsed: 0.011 s
% 1.79/0.59 % (802797)Peak memory usage: 12 MB
% 1.79/0.59 % (802797)Instructions burned: 25 (million)
% 1.79/0.59 % (802800)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2549987644:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.79/0.59 % (802798)Instruction limit reached!
% 1.79/0.59 % (802798)------------------------------
% 1.79/0.59 % (802798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802798)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802798)Termination reason: Instruction limit
% 1.79/0.59 % (802798)Termination phase: Saturation
% 1.79/0.59 % (802798)Time elapsed: 0.012 s
% 1.79/0.59 % (802798)Peak memory usage: 12 MB
% 1.79/0.59 % (802798)Instructions burned: 20 (million)
% 1.79/0.59 % (802805)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=496524521:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.79/0.59 % (802807)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3093127887:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.79/0.59 % (802809)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.79/0.59 % (802805)Refutation not found, incomplete strategy
% 1.79/0.59 % (802805)------------------------------
% 1.79/0.59 % (802805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802805)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802805)Termination reason: Refutation not found, incomplete strategy
% 1.79/0.59 % (802805)Time elapsed: 0.008 s
% 1.79/0.59 % (802805)Peak memory usage: 12 MB
% 1.79/0.59 % (802805)Instructions burned: 16 (million)
% 1.79/0.59 % (802805)------------------------------
% 1.79/0.59 % (802805)------------------------------
% 1.79/0.59 % (802809)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1711977095:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.79/0.59 % (802809)Instruction limit reached!
% 1.79/0.59 % (802809)------------------------------
% 1.79/0.59 % (802809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802809)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802809)Termination reason: Instruction limit
% 1.79/0.59 % (802809)Termination phase: Property scanning
% 1.79/0.59 % (802809)Time elapsed: 0.003 s
% 1.79/0.59 % (802809)Peak memory usage: 10 MB
% 1.79/0.59 % (802809)Instructions burned: 8 (million)
% 1.79/0.59 % (802801)Instruction limit reached!
% 1.79/0.59 % (802801)------------------------------
% 1.79/0.59 % (802801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802801)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802801)Termination reason: Instruction limit
% 1.79/0.59 % (802801)Termination phase: Saturation
% 1.79/0.59 % (802801)Time elapsed: 0.043 s
% 1.79/0.59 % (802801)Peak memory usage: 13 MB
% 1.79/0.59 % (802801)Instructions burned: 144 (million)
% 1.79/0.59 % (802807)Instruction limit reached!
% 1.79/0.59 % (802807)------------------------------
% 1.79/0.59 % (802807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.59 % (802807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.59 % (802807)CaDiCaL version: 2.1.3
% 1.79/0.59 % (802807)Termination reason: Instruction limit
% 1.79/0.59 % (802807)Termination phase: Saturation
% 1.79/0.59 % (802807)Time elapsed: 0.021 s
% 1.79/0.59 % (802807)Peak memory usage: 12 MB
% 1.79/0.59 % (802807)Instructions burned: 42 (million)
% 1.79/0.59 % (802812)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3444528727:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.79/0.59 % (802814)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=3554376217: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)
% 1.79/0.59 % (802800) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-802734-802800"...
% 1.79/0.59 % (802817)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2888005352:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.79/0.59 % (802800)...printing done.
% 1.79/0.59 % (802800)Refutation found. Thanks to Tanya!
% 1.79/0.59 % SZS status Theorem for theBenchmark
% 1.79/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.79/0.60 % (802800)------------------------------
% 1.79/0.60 % (802800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.60 % (802800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.60 % (802800)CaDiCaL version: 2.1.3
% 1.79/0.60 % (802800)Termination reason: Refutation
% 1.79/0.60 % (802800)Time elapsed: 0.061 s
% 1.79/0.60 % (802800)Peak memory usage: 13 MB
% 1.79/0.60 % (802800)Instructions burned: 121 (million)
% 1.79/0.60 % (802734)Success in time 0.314 s
% 1.79/0.60 % Vampire exiting
%------------------------------------------------------------------------------