%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO497^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:48:07 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 23
% Syntax : Number of formulae : 181 ( 80 unt; 0 typ; 9 def)
% Number of atoms : 1237 ( 235 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 1914 ( 280 ~; 249 |; 13 &;1212 @)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 210 ( 210 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 16 con; 0-4 aty)
% ( 130 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 544 ( 0 sgn 95 !; 0 ?; 544 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: 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,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $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,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
f: mu > $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_53,type,
sK2: $i > mu ).
thf(func_def_54,type,
sK3: $i > mu ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_59,type,
sK8: mu ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f10,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_ind) ).
thf(f12,axiom,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mexists_ind) ).
thf(f19,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( mbox_s5 @ ( f @ X0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( mbox_s5 @ ( f @ X0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X0: mu] : ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f42,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f46,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f65,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f66,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
~ ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( mbox_s5 @ ( f @ X0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [X1: mu] : ( f @ X1 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X2: mu] : ( f @ X2 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f70,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( mbox_s5 @ ( f @ Y0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
inference(rectify,[],[f12]) ).
thf(f72,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f74,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f77,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f78,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) )
= mforall_ind ),
inference(rectify,[],[f10]) ).
thf(f80,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f82,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f83,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f91,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f92,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f96,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f97,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f100,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f101,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( mbox_s5 @ ( f @ Y0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f70]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f104,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f106,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f109,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f113,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f121,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f122,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( mbox_s5 @ ( f @ Y0 ) ) ) ) )
@ ( mdia_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( mbox_s5
@ ( mexists_ind
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f123,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f125,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f128,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f133,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f135,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f136,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f137,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f113,f106,f102,f106,f106]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f123,f102,f106]) ).
thf(f146,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f135,f106,f121,f106]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f133,f106,f137,f106]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f104,f109]) ).
thf(f153,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( f @ Y0 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f122,f136,f142,f141,f137,f121,f142,f137,f150,f146,f137,f146]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f125,f128]) ).
thf(f155,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( f @ Y0 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
sF0 != $true,
inference(definition_folding,[],[f153,f155]) ).
thf(f160,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( f @ Y0 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f205,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s5 @ Y1 @ Y3 ) ) )
| ~ ( f @ Y2 @ Y1 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f206,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
~ ( f @ Y2 @ Y1 ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( f @ Y2 @ Y3 )
| ~ ( rel_s5 @ Y1 @ Y3 ) ) )
| ~ ( f @ Y2 @ Y1 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f210,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK6 ) )
| ~ ( rel_s5 @ sK5 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( ~ ( rel_s5 @ sK5 @ sK6 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK6 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK6 ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: mu] :
( ( $true
= ( ^ [Y0: mu] :
~ ( f @ Y0 @ sK6 )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: mu] :
( ( sF0 = $true )
| ( $true
= ( ~ ( f @ X1 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X1: mu] :
( ( sF0 = $true )
| ( $false
= ( f @ X1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f219,plain,
( ( sF0 = $true )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f220,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f223,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
~ ( f @ Y1 @ Y0 ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK7 ) )
| ~ ( rel_s5 @ sK5 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( rel_s5 @ sK5 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK7 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f229,plain,
( ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK7 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
~ ( f @ Y0 @ sK7 ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $false
= ( ^ [Y0: mu] :
~ ( f @ Y0 @ sK7 )
@ sK8 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( f @ sK8 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
( ( sF0 = $true )
| ( ( f @ sK8 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( ( rel_s5 @ sK5 @ sK7 )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f235,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f236,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s5 @ Y0 @ Y2 ) ) )
| ~ ( f @ Y1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK5 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s5 @ X1 @ Y1 ) ) )
| ~ ( f @ Y0 @ X1 ) ) )
| ~ ( rel_s5 @ sK5 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s5 @ X1 @ Y1 ) ) )
| ~ ( f @ Y0 @ X1 ) ) ) )
| ( sF0 = $true )
| ( $true
= ( ~ ( rel_s5 @ sK5 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: mu,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s5 @ X1 @ Y1 ) ) )
| ~ ( f @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK5 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( ( ^ [Y0: mu] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s5 @ X1 @ Y1 ) ) )
| ~ ( f @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: mu,X1: $i] :
( ( sF0 = $true )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s5 @ X1 @ Y0 ) ) )
| ~ ( f @ X2 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s5 @ X1 @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $true
= ( ~ ( f @ X2 @ X1 ) ) )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s5 @ X1 @ Y0 ) )
@ X3 ) )
| ( sF0 = $true )
| ( $true
= ( ~ ( f @ X2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( f @ X2 @ Y0 )
| ~ ( rel_s5 @ X1 @ Y0 ) )
@ X3 ) )
| ( sF0 = $true )
| ( ( f @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( ( f @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( sF0 = $true )
| ( $true
= ( ( f @ X2 @ X3 )
| ~ ( rel_s5 @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( ( f @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ X1 @ X3 ) )
= $true )
| ( $true
= ( f @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( f @ X2 @ X3 ) )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( ( f @ X2 @ X1 )
= $false )
| ( sF0 = $true )
| ( $false
= ( rel_s5 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f249,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f254,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f255,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X3 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) ) )
| ( $true
= ( rel_s5 @ X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ X2 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f261]) ).
thf(f284,definition,
( spl9_6
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f288,definition,
( spl9_7
<=> ! [X1: mu] :
( $false
= ( f @ X1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f289,plain,
( ! [X1: mu] :
( $false
= ( f @ X1 @ sK6 ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f290,plain,
( spl9_6
| spl9_7 ),
inference(avatar_split_clause,[],[f217,f288,f284]) ).
thf(f292,definition,
( spl9_8
<=> ( ( rel_s5 @ sK5 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f294,plain,
( ( ( rel_s5 @ sK5 @ sK6 )
= $true )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f295,plain,
( spl9_8
| spl9_6 ),
inference(avatar_split_clause,[],[f218,f284,f292]) ).
thf(f297,definition,
( spl9_9
<=> ( ( f @ sK8 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f299,plain,
( ( ( f @ sK8 @ sK7 )
= $true )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f300,plain,
( spl9_9
| spl9_6 ),
inference(avatar_split_clause,[],[f233,f284,f297]) ).
thf(f302,definition,
( spl9_10
<=> ( ( rel_s5 @ sK5 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f304,plain,
( ( ( rel_s5 @ sK5 @ sK7 )
= $true )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,plain,
( spl9_10
| spl9_6 ),
inference(avatar_split_clause,[],[f234,f284,f302]) ).
thf(f307,definition,
( spl9_11
<=> ! [X2: mu,X1: $i,X3: $i] :
( ( $true
= ( f @ X2 @ X3 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( ( f @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f308,plain,
( ! [X2: mu,X3: $i,X1: $i] :
( ( $true
= ( f @ X2 @ X3 ) )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( ( f @ X2 @ X1 )
= $false ) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f309,plain,
( spl9_11
| spl9_6 ),
inference(avatar_split_clause,[],[f247,f284,f307]) ).
thf(f310,plain,
~ spl9_6,
inference(avatar_split_clause,[],[f156,f284]) ).
thf(f329,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK5 ) )
| ( $false = $true )
| ~ spl9_8 ),
inference(constrained_superposition,[],[f294,f253]) ).
thf(f335,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK5 ) )
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f347,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ X2 ) )
| ( $true
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f253,f262]) ).
thf(f350,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f360,plain,
( ! [X0: mu,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ sK6 ) )
| ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( $false = $true )
| ( ( f @ X0 @ X1 )
= $false ) )
| ~ spl9_7
| ~ spl9_11 ),
inference(constrained_superposition,[],[f308,f289]) ).
thf(f363,plain,
( ! [X0: mu,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X1 ) )
| ( $false
= ( rel_s5 @ X1 @ sK6 ) )
| ( ( f @ X0 @ X1 )
= $false ) )
| ~ spl9_7
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f360]) ).
thf(f366,plain,
( ! [X0: mu] :
( ( $false
= ( f @ X0 @ sK7 ) )
| ( ( rel_s5 @ sK7 @ sK6 )
= $false )
| ( $false = $true ) )
| ~ spl9_7
| ~ spl9_10
| ~ spl9_11 ),
inference(constrained_superposition,[],[f363,f304]) ).
thf(f381,plain,
( ! [X0: mu] :
( ( ( rel_s5 @ sK7 @ sK6 )
= $false )
| ( $false
= ( f @ X0 @ sK7 ) ) )
| ~ spl9_7
| ~ spl9_10
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f388,definition,
( spl9_12
<=> ( ( rel_s5 @ sK7 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
thf(f390,plain,
( ( ( rel_s5 @ sK7 @ sK6 )
= $false )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f388]) ).
thf(f392,definition,
( spl9_13
<=> ! [X0: mu] :
( $false
= ( f @ X0 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
thf(f393,plain,
( ! [X0: mu] :
( $false
= ( f @ X0 @ sK7 ) )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f395,plain,
( spl9_13
| spl9_12
| ~ spl9_7
| ~ spl9_10
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f381,f307,f302,f288,f388,f392]) ).
thf(f400,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( ( rel_s5 @ X0 @ sK7 )
= $false )
| ( $false = $true ) )
| ~ spl9_12 ),
inference(constrained_superposition,[],[f390,f350]) ).
thf(f405,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( ( rel_s5 @ X0 @ sK7 )
= $false ) )
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f421,plain,
( ( $false
= ( rel_s5 @ sK5 @ sK7 ) )
| ( $false = $true )
| ~ spl9_8
| ~ spl9_12 ),
inference(constrained_superposition,[],[f335,f405]) ).
thf(f430,plain,
( ( $false
= ( rel_s5 @ sK5 @ sK7 ) )
| ~ spl9_8
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f421]) ).
thf(f437,plain,
( ( $false = $true )
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(forward_demodulation,[],[f430,f304]) ).
thf(f438,plain,
( $false
| ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f437]) ).
thf(f439,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f438]) ).
thf(f446,plain,
( ( $false = $true )
| ~ spl9_9
| ~ spl9_13 ),
inference(constrained_superposition,[],[f393,f299]) ).
thf(f454,plain,
( $false
| ~ spl9_9
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f455,plain,
( ~ spl9_9
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f454]) ).
cnf(s5,plain,
( spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f290]) ).
cnf(s6,plain,
( spl9_6
| spl9_8 ),
inference(sat_conversion,[],[f295]) ).
cnf(s7,plain,
( spl9_6
| spl9_9 ),
inference(sat_conversion,[],[f300]) ).
cnf(s8,plain,
( spl9_6
| spl9_10 ),
inference(sat_conversion,[],[f305]) ).
cnf(s9,plain,
( spl9_6
| spl9_11 ),
inference(sat_conversion,[],[f309]) ).
cnf(s10,plain,
~ spl9_6,
inference(sat_conversion,[],[f310]) ).
cnf(s12,plain,
( ~ spl9_7
| ~ spl9_10
| ~ spl9_11
| spl9_12
| spl9_13 ),
inference(sat_conversion,[],[f395]) ).
cnf(s14,plain,
( ~ spl9_8
| ~ spl9_10
| ~ spl9_12 ),
inference(sat_conversion,[],[f439]) ).
cnf(s16,plain,
( ~ spl9_9
| ~ spl9_13 ),
inference(sat_conversion,[],[f455]) ).
cnf(s17,plain,
spl9_11,
inference(rat,[],[s9,s10]) ).
cnf(s18,plain,
spl9_10,
inference(rat,[],[s8,s10]) ).
cnf(s19,plain,
spl9_9,
inference(rat,[],[s7,s10]) ).
cnf(s20,plain,
~ spl9_13,
inference(rat,[],[s16,s19]) ).
cnf(s21,plain,
spl9_8,
inference(rat,[],[s6,s10]) ).
cnf(s22,plain,
~ spl9_12,
inference(rat,[],[s14,s18,s21]) ).
cnf(s23,plain,
~ spl9_7,
inference(rat,[],[s12,s20,s18,s17,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s5,s23,s10]) ).
thf(f457,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO497^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:10:25 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.19/0.28 % (1035892)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (1035898)lrs+10_16_si=on:nwc=1.5:random_seed=3031931523:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (1035903)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (1035903)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
% 0.19/0.28 % (1035898)Instruction limit reached!
% 0.19/0.28 % (1035898)------------------------------
% 0.19/0.28 % (1035898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1035898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1035898)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1035898)Termination reason: Instruction limit
% 0.19/0.28 % (1035898)Termination phase: Saturation
% 0.19/0.28 % (1035898)Time elapsed: 0.005 s
% 0.19/0.28 % (1035898)Peak memory usage: 12 MB
% 0.19/0.28 % (1035898)Instructions burned: 20 (million)
% 0.19/0.28 % (1035897)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=156596248:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (1035899)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2976436887:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (1035901)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1072965219:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (1035900)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=2920446512: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)
% 0.19/0.28 % (1035902)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=94815096:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (1035903)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=541094864:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (1035899)Instruction limit reached!
% 0.19/0.28 % (1035899)------------------------------
% 0.19/0.28 % (1035899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1035899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1035899)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1035899)Termination reason: Instruction limit
% 0.19/0.28 % (1035899)Termination phase: Property scanning
% 0.19/0.28 % (1035899)Time elapsed: 0.002 s
% 0.19/0.28 % (1035899)Peak memory usage: 10 MB
% 0.19/0.28 % (1035899)Instructions burned: 4 (million)
% 0.19/0.28 % (1035905)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2801005191:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.28 % (1035905)Instruction limit reached!
% 0.19/0.28 % (1035905)------------------------------
% 0.19/0.28 % (1035905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1035905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1035905)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1035905)Termination reason: Instruction limit
% 0.19/0.28 % (1035905)Termination phase: Property scanning
% 0.19/0.28 % (1035905)Time elapsed: 0.001 s
% 0.19/0.28 % (1035905)Peak memory usage: 10 MB
% 0.19/0.28 % (1035905)Instructions burned: 4 (million)
% 0.19/0.28 % (1035903) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1035892-1035903"...
% 0.19/0.28 % (1035901)Instruction limit reached!
% 0.19/0.28 % (1035901)------------------------------
% 0.19/0.28 % (1035901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1035901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1035901)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1035901)Termination reason: Instruction limit
% 0.19/0.28 % (1035901)Termination phase: Saturation
% 0.19/0.28 % (1035901)Time elapsed: 0.013 s
% 0.19/0.28 % (1035901)Peak memory usage: 11 MB
% 0.19/0.28 % (1035901)Instructions burned: 25 (million)
% 0.19/0.28 % (1035903)...printing done.
% 0.19/0.28 % (1035903)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1035903)------------------------------
% 0.19/0.29 % (1035903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1035903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1035903)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1035903)Termination reason: Refutation
% 0.19/0.29 % (1035903)Time elapsed: 0.018 s
% 0.19/0.29 % (1035903)Peak memory usage: 13 MB
% 0.19/0.29 % (1035903)Instructions burned: 35 (million)
% 0.19/0.29 % (1035892)Success in time 0.052 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------