%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV445^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:40:00 AM UTC 2026
% Result : Theorem 1.52s 0.52s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 20
% Syntax : Number of formulae : 216 ( 119 unt; 0 typ; 4 def)
% Number of atoms : 2750 ( 510 equ; 0 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 4699 ( 158 ~; 464 |; 0 &;3215 @)
% ( 4 <=>; 430 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 76 usr; 14 con; 0-4 aty)
% ( 428 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1030 ( 0 sgn 298 !; 0 ?;1030 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
reli: $i > $i > $o ).
thf(func_def_21,type,
relr: $i > $i > $o ).
thf(func_def_22,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
cs4_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
cs4_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
cs4_true: $i > $o ).
thf(func_def_27,type,
cs4_false: $i > $o ).
thf(func_def_28,type,
cs4_all: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_29,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(func_def_30,type,
cs4_valid: ( $i > $o ) > $o ).
thf(func_def_31,type,
princ_inj: individuals > $i > $o ).
thf(func_def_32,type,
bl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_33,type,
bl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
bl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
bl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_37,type,
bl_all: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_38,type,
bl_true: $i > $o ).
thf(func_def_39,type,
bl_false: $i > $o ).
thf(func_def_40,type,
bl_says: individuals > ( $i > $o ) > $i > $o ).
thf(func_def_41,type,
bl_valid: ( $i > $o ) > $o ).
thf(func_def_42,type,
loca: individuals ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_62,type,
db10:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
db11:
!>[X0: $tType] : X0 ).
thf(func_def_64,type,
sK0: individuals ).
thf(func_def_65,type,
sK1: $i > $o ).
thf(func_def_69,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_71,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_74,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_75,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) )
= cs4_atom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_atom) ).
thf(f19,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ reli @ ( mimpl @ X0 @ X1 ) ) )
= cs4_impl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f23,axiom,
( cs4_box
= ( ^ [X0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_box) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',refl_axiom_i) ).
thf(f26,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',refl_axiom_r) ).
thf(f30,axiom,
( ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) )
= bl_atom ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_atom) ).
thf(f31,axiom,
( bl_princ
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_princ) ).
thf(f34,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( cs4_impl @ X0 @ X1 ) )
= bl_impl ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_impl) ).
thf(f38,axiom,
( bl_says
= ( ^ [X0: individuals,X1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ X0 ) ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_says) ).
thf(f39,axiom,
bl_valid = mvalid,
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_valid_def) ).
thf(f41,conjecture,
! [X1: $i > $o,X0: individuals] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_c4) ).
thf(f42,negated_conjecture,
~ ! [X1: $i > $o,X0: individuals] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f43,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f44,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f45,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ Y0 ) @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f49,plain,
~ ! [X0: $i > $o,X1: individuals] : ( bl_valid @ ( bl_impl @ ( bl_says @ X1 @ ( bl_says @ X1 @ ( bl_atom @ X0 ) ) ) @ ( bl_says @ X1 @ ( bl_atom @ X0 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f50,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ Y0 @ ( bl_says @ Y0 @ ( bl_atom @ Y1 ) ) ) @ ( bl_says @ Y0 @ ( bl_atom @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f52,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f58,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f59,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f65,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f68,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f69,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f80,plain,
mvalid = bl_valid,
inference(fool_elimination,[],[f39]) ).
thf(f83,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f84,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f85,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f88,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f96,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ X0 ) @ X0 ) ),
inference(rectify,[],[f26]) ).
thf(f99,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ Y0 ) @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f98]) ).
thf(f102,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f106,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f110,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f111,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f113,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f115,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f119,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ Y0 ) @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f99]) ).
thf(f123,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f126,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f127,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ Y0 ) @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f45]) ).
thf(f128,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f130,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f131,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f138,plain,
mvalid = bl_valid,
inference(cnf_transformation,[],[f80]) ).
thf(f141,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ Y0 @ ( bl_says @ Y0 @ ( bl_atom @ Y1 ) ) ) @ ( bl_says @ Y0 @ ( bl_atom @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f142,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f145,plain,
( mimpl
= ( ^ [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,[],[f126,f123,f102]) ).
thf(f147,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ Y0 ) ) ),
inference(definition_unfolding,[],[f111,f113]) ).
thf(f150,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f110,f113,f145]) ).
thf(f153,plain,
( cs4_box
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ relr
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f128,f113,f113]) ).
thf(f155,plain,
( bl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f115,f147]) ).
thf(f156,plain,
( bl_princ
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f131,f147]) ).
thf(f159,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f106,f150]) ).
thf(f161,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] :
( ^ [Y2: $i > $o] :
( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ reli
@ ( ^ [Y3: $i > $i > $o,Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ relr
@ Y2 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ ( ^ [Y2: $i > $o] :
( ^ [Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ Y3 )
@ Y2 )
@ ( princ_inj @ Y0 ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f142,f153,f150,f156]) ).
thf(f162,plain,
( bl_valid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f138,f130]) ).
thf(f163,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ relr
@ Y0 )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f119,f130,f145,f113]) ).
thf(f167,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ Y0 )
@ Y0 ) ) )
= $true ),
inference(definition_unfolding,[],[f127,f130,f145,f113]) ).
thf(f171,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ ( ^ [Y6: $i > $o,Y7: $i > $o] :
( ^ [Y8: $i > $o,Y9: $i > $o,Y10: $i] :
( ( Y8 @ Y10 )
| ( Y9 @ Y10 ) )
@ ( ^ [Y8: $i > $o,Y9: $i] :
~ ( Y8 @ Y9 )
@ Y6 )
@ Y7 )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: individuals,Y3: $i > $o] :
( ^ [Y4: $i > $o] :
( ^ [Y5: $i > $i > $o,Y6: $i > $o,Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y8 ) ) )
@ reli
@ ( ^ [Y5: $i > $i > $o,Y6: $i > $o,Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y8 ) ) )
@ relr
@ Y4 ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ ( ^ [Y6: $i > $o,Y7: $i > $o] :
( ^ [Y8: $i > $o,Y9: $i > $o,Y10: $i] :
( ( Y8 @ Y10 )
| ( Y9 @ Y10 ) )
@ ( ^ [Y8: $i > $o,Y9: $i] :
~ ( Y8 @ Y9 )
@ Y6 )
@ Y7 )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i > $o] :
( ^ [Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ Y5 )
@ Y4 )
@ ( princ_inj @ Y2 ) )
@ Y3 ) )
@ Y0
@ ( ^ [Y2: individuals,Y3: $i > $o] :
( ^ [Y4: $i > $o] :
( ^ [Y5: $i > $i > $o,Y6: $i > $o,Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y8 ) ) )
@ reli
@ ( ^ [Y5: $i > $i > $o,Y6: $i > $o,Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y8 ) ) )
@ relr
@ Y4 ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ ( ^ [Y6: $i > $o,Y7: $i > $o] :
( ^ [Y8: $i > $o,Y9: $i > $o,Y10: $i] :
( ( Y8 @ Y10 )
| ( Y9 @ Y10 ) )
@ ( ^ [Y8: $i > $o,Y9: $i] :
~ ( Y8 @ Y9 )
@ Y6 )
@ Y7 )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i > $o] :
( ^ [Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ Y5 )
@ Y4 )
@ ( princ_inj @ Y2 ) )
@ Y3 ) )
@ Y0
@ ( ^ [Y2: $i > $o] :
( ^ [Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ Y3 )
@ Y2 )
@ Y1 ) ) )
@ ( ^ [Y2: individuals,Y3: $i > $o] :
( ^ [Y4: $i > $o] :
( ^ [Y5: $i > $i > $o,Y6: $i > $o,Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y8 ) ) )
@ reli
@ ( ^ [Y5: $i > $i > $o,Y6: $i > $o,Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y8 )
=> ( Y6 @ Y8 ) ) )
@ relr
@ Y4 ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ ( ^ [Y6: $i > $o,Y7: $i > $o] :
( ^ [Y8: $i > $o,Y9: $i > $o,Y10: $i] :
( ( Y8 @ Y10 )
| ( Y9 @ Y10 ) )
@ ( ^ [Y8: $i > $o,Y9: $i] :
~ ( Y8 @ Y9 )
@ Y6 )
@ Y7 )
@ Y4
@ Y5 ) )
@ ( ^ [Y4: $i > $o] :
( ^ [Y5: $i > $o] :
( ^ [Y6: $i > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ reli
@ Y5 )
@ Y4 )
@ ( princ_inj @ Y2 ) )
@ Y3 ) )
@ Y0
@ ( ^ [Y2: $i > $o] :
( ^ [Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ Y3 )
@ Y2 )
@ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f141,f162,f159,f161,f161,f155,f161,f155]) ).
thf(f173,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ Y0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( !! @ $i
@ ^ [Y8: $i] :
( ( relr @ Y7 @ Y8 )
=> ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( ~ ( !! @ $i
@ ^ [Y10: $i] :
( ( reli @ Y9 @ Y10 )
=> ( princ_inj @ Y0 @ Y10 ) ) )
| ( !! @ $i
@ ^ [Y10: $i] :
( ( reli @ Y9 @ Y10 )
=> ( Y1 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ Y0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f177,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f178,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f179,plain,
( ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ Y0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( !! @ $i
@ ^ [Y8: $i] :
( ( relr @ Y7 @ Y8 )
=> ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( ~ ( !! @ $i
@ ^ [Y10: $i] :
( ( reli @ Y9 @ Y10 )
=> ( princ_inj @ Y0 @ Y10 ) ) )
| ( !! @ $i
@ ^ [Y10: $i] :
( ( reli @ Y9 @ Y10 )
=> ( Y1 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ Y0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f180,plain,
( ( ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ Y0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( !! @ $i
@ ^ [Y8: $i] :
( ( relr @ Y7 @ Y8 )
=> ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( ~ ( !! @ $i
@ ^ [Y10: $i] :
( ( reli @ Y9 @ Y10 )
=> ( princ_inj @ Y0 @ Y10 ) ) )
| ( !! @ $i
@ ^ [Y10: $i] :
( ( reli @ Y9 @ Y10 )
=> ( Y1 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ Y0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( !! @ $i
@ ^ [Y7: $i] :
( ( relr @ Y6 @ Y7 )
=> ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( ~ ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( princ_inj @ sK0 @ Y9 ) ) )
| ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( Y0 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( !! @ $i
@ ^ [Y7: $i] :
( ( relr @ Y6 @ Y7 )
=> ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( ~ ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( princ_inj @ sK0 @ Y9 ) ) )
| ( !! @ $i
@ ^ [Y9: $i] :
( ( reli @ Y8 @ Y9 )
=> ( Y0 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( relr @ Y5 @ Y6 )
=> ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( princ_inj @ sK0 @ Y8 ) ) )
| ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( sK1 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f195,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( relr @ Y5 @ Y6 )
=> ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( ~ ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( princ_inj @ sK0 @ Y8 ) ) )
| ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( sK1 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f197,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ sK0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( sK1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f201,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( princ_inj @ sK0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( sK1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f204,plain,
( $false
= ( ( reli @ sK2 @ sK3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f205,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f207,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f208,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f209,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f214,plain,
( ( ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f216,plain,
( ( ( reli @ sK3 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f218,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( reli @ sK3 @ sK4 )
= $true ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f220,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f221,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( princ_inj @ sK0 @ Y6 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f223,plain,
! [X1: $i] :
( ( ( reli @ sK3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f226,plain,
! [X2: $i,X1: $i > $o] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( ( reli @ sK3 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( ( ( relr @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK5 @ X1 @ X2 ) )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f228]) ).
thf(f234,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ( reli @ X2 @ ( sK5 @ X1 @ X2 ) )
=> ( X1 @ ( sK5 @ X1 @ X2 ) ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f236,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ ( sK5 @ X1 @ X2 ) )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f237,plain,
! [X2: $i,X1: $i > $o] :
( ( ( reli @ X2 @ ( sK5 @ X1 @ X2 ) )
= $true )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f238,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ sK0 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f231]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( reli @ X2 @ X3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f244,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( ( ^ [Y0: $i] :
( ( relr @ sK4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f218]) ).
thf(f248,plain,
( $false
= ( ( relr @ sK4 @ sK6 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f249,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( relr @ sK4 @ sK6 )
= $true ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f242]) ).
thf(f252,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( ( reli @ X3 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( reli @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f244]) ).
thf(f255,plain,
! [X2: $i,X1: $i > $o] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ( ( X1 @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( relr @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f259,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( ( relr @ X4 @ X5 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X5 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X5 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( relr @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK7 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f257]) ).
thf(f264,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( ( relr @ X2 @ ( sK7 @ X1 @ X2 ) )
=> ( X1 @ ( sK7 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f265,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ ( sK7 @ X1 @ X2 ) )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i > $o] :
( ( ( relr @ X2 @ ( sK7 @ X1 @ X2 ) )
= $true )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f264]) ).
thf(f267,plain,
( ( ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
@ sK8 )
= $false ),
inference(sigma_proxy_clausification,[],[f249]) ).
thf(f269,plain,
( $false
= ( ( reli @ sK6 @ sK8 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f271,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f272,plain,
( ( reli @ sK6 @ sK8 )
= $true ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f273,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f274,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f275,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X5 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
@ X6 )
= $true )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(pi_proxy_clausification,[],[f260]) ).
thf(f277,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( ( reli @ X5 @ X6 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( relr @ X4 @ X5 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $true )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f283,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ X5 @ X6 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f280]) ).
thf(f286,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
=> ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) ) )
= $false )
| ( ( relr @ X4 @ X5 )
= $false ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f292,plain,
( ( ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( sK1 @ Y0 ) )
@ ( sK5 @ sK1 @ sK8 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f273]) ).
thf(f295,plain,
( $false
= ( ( reli @ sK8 @ ( sK5 @ sK1 @ sK8 ) )
=> ( sK1 @ ( sK5 @ sK1 @ sK8 ) ) ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f296,plain,
( ( sK1 @ ( sK5 @ sK1 @ sK8 ) )
= $false ),
inference(imp_proxy_clausification,[],[f295]) ).
thf(f297,plain,
( ( reli @ sK8 @ ( sK5 @ sK1 @ sK8 ) )
= $true ),
inference(imp_proxy_clausification,[],[f295]) ).
thf(f300,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f287]) ).
thf(f303,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( ( reli @ X3 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
=> ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f300]) ).
thf(f304,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $false )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f303]) ).
thf(f308,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f288]) ).
thf(f310,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( reli @ X3 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
=> ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) ) )
= $false )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f308]) ).
thf(f313,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $true )
| ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true )
| ( ( reli @ X3 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f319,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f275]) ).
thf(f320,plain,
! [X1: $i] :
( ( ( reli @ sK8 @ X1 )
=> ( princ_inj @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f319]) ).
thf(f321,plain,
! [X1: $i] :
( ( $false
= ( reli @ sK8 @ X1 ) )
| ( ( princ_inj @ sK0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X7 )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f323,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $false )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( relr @ X4 @ X5 )
= $false )
| ( ( ( reli @ X6 @ X7 )
=> ( sK1 @ X7 ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ X6 @ X7 ) )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $false )
| ( ( sK1 @ X7 )
= $true )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false ) ),
inference(imp_proxy_clausification,[],[f323]) ).
thf(f329,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( relr @ X5 @ X3 )
= $false )
| ( $false
= ( relr @ X2 @ X1 ) )
| ( $false
= ( reli @ X0 @ X2 ) )
| ( $false
= ( reli @ sK3 @ X5 ) )
| ( $false
= ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X0 ) ) )
| ( ( reli @ X1 @ X0 )
= $false )
| ( ( sK1 @ X4 )
= $true )
| ( ( reli @ X0 @ X4 )
= $false )
| ( $false != $false )
| ( ( reli @ X3 @ X0 )
= $false ) ),
inference(equality_factoring,[],[f324]) ).
thf(f330,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X0 ) ) )
| ( ( sK1 @ X4 )
= $true )
| ( $false
= ( relr @ X2 @ X1 ) )
| ( ( reli @ X1 @ X0 )
= $false )
| ( ( reli @ X3 @ X0 )
= $false )
| ( ( relr @ X5 @ X3 )
= $false )
| ( ( reli @ X0 @ X4 )
= $false )
| ( $false
= ( reli @ sK3 @ X5 ) )
| ( $false
= ( reli @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f382,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( relr @ X4 @ X5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X7 )
= $true )
| ( ( reli @ X3 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f313]) ).
thf(f383,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ( reli @ X6 @ X7 )
=> ( sK1 @ X7 ) )
= $true )
| ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true )
| ( ( reli @ X3 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( reli @ X6 @ ( sK5 @ ( princ_inj @ sK0 ) @ X6 ) )
= $true )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ X3 @ ( sK5 @ ( princ_inj @ sK0 ) @ X3 ) )
= $true )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( reli @ X6 @ X7 ) )
| ( ( sK1 @ X7 )
= $true )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( relr @ X4 @ X5 )
= $false )
| ( $false
= ( reli @ X5 @ X6 ) )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f383]) ).
thf(f388,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( reli @ X0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X0 ) )
= $true )
| ( ( relr @ X2 @ X4 )
= $false )
| ( ( sK1 @ X3 )
= $true )
| ( $true != $true )
| ( ( relr @ X1 @ X5 )
= $false )
| ( $false
= ( reli @ X0 @ X3 ) )
| ( $false
= ( reli @ X5 @ X0 ) )
| ( ( reli @ sK3 @ X2 )
= $false )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( reli @ X4 @ X0 ) ) ),
inference(equality_factoring,[],[f384]) ).
thf(f393,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( reli @ X0 @ ( sK5 @ ( princ_inj @ sK0 ) @ X0 ) )
= $true )
| ( $false
= ( reli @ X5 @ X0 ) )
| ( ( relr @ X2 @ X4 )
= $false )
| ( $false
= ( reli @ X0 @ X3 ) )
| ( $false
= ( reli @ X4 @ X0 ) )
| ( ( reli @ sK3 @ X2 )
= $false )
| ( ( sK1 @ X3 )
= $true )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( ( relr @ X1 @ X5 )
= $false ) ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f396,definition,
( spl9_3
<=> ! [X3: $i] :
( ( ( reli @ sK8 @ X3 )
= $false )
| ( ( sK1 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f397,plain,
( ! [X3: $i] :
( ( ( reli @ sK8 @ X3 )
= $false )
| ( ( sK1 @ X3 )
= $true ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f396]) ).
thf(f399,definition,
( spl9_4
<=> ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ sK8 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f401,plain,
( ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ sK8 ) )
= $true )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f399]) ).
thf(f412,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( reli @ sK8 @ X4 )
= $false )
| ( ( reli @ X2 @ sK8 )
= $false )
| ( ( sK1 @ X3 )
= $true )
| ( $false
= ( relr @ X4 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK8 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ sK8 ) )
= $true )
| ( $false = $true )
| ( ( reli @ sK8 @ X3 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ),
inference(superposition,[],[f321,f393]) ).
thf(f417,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK8 @ X3 )
= $false )
| ( $false
= ( relr @ X4 @ X0 ) )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( $false
= ( reli @ X0 @ sK8 ) )
| ( ( princ_inj @ sK0 @ ( sK5 @ ( princ_inj @ sK0 ) @ sK8 ) )
= $true )
| ( ( reli @ sK8 @ X4 )
= $false )
| ( ( reli @ X2 @ sK8 )
= $false )
| ( ( sK1 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f419,definition,
( spl9_6
<=> ! [X4: $i,X0: $i] :
( ( ( reli @ sK8 @ X4 )
= $false )
| ( $false
= ( reli @ X0 @ sK8 ) )
| ( $false
= ( relr @ X4 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f420,plain,
( ! [X0: $i,X4: $i] :
( ( $false
= ( relr @ X4 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK8 ) )
| ( ( reli @ sK8 @ X4 )
= $false ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f422,definition,
( spl9_7
<=> ! [X2: $i,X1: $i] :
( ( ( reli @ X2 @ sK8 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( relr @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f423,plain,
( ! [X2: $i,X1: $i] :
( ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ sK3 @ X1 )
= $false )
| ( ( reli @ X2 @ sK8 )
= $false ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f422]) ).
thf(f425,plain,
( spl9_4
| spl9_3
| spl9_6
| spl9_7 ),
inference(avatar_split_clause,[],[f417,f422,f419,f396,f399]) ).
thf(f429,plain,
( ( ( sK1 @ ( sK5 @ sK1 @ sK8 ) )
= $true )
| ( $false = $true )
| ~ spl9_3 ),
inference(superposition,[],[f397,f297]) ).
thf(f439,plain,
( ( ( sK1 @ ( sK5 @ sK1 @ sK8 ) )
= $true )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f446,plain,
( ( $false = $true )
| ~ spl9_3 ),
inference(forward_demodulation,[],[f439,f296]) ).
thf(f447,plain,
( $false
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f448,plain,
~ spl9_3,
inference(avatar_contradiction_clause,[],[f447]) ).
thf(f449,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK8 @ X1 ) )
| ( $false = $true )
| ( ( reli @ X2 @ sK8 )
= $false )
| ( ( sK1 @ X0 )
= $true )
| ( $false
= ( reli @ sK8 @ X0 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ sK3 @ X4 ) )
| ( ( relr @ X4 @ X3 )
= $false )
| ( ( reli @ X3 @ sK8 )
= $false ) )
| ~ spl9_4 ),
inference(superposition,[],[f401,f330]) ).
thf(f464,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK8 @ X1 ) )
| ( $false
= ( reli @ sK8 @ X0 ) )
| ( ( relr @ X4 @ X3 )
= $false )
| ( ( reli @ X2 @ sK8 )
= $false )
| ( ( sK1 @ X0 )
= $true )
| ( $false
= ( reli @ sK3 @ X4 ) )
| ( ( relr @ X1 @ X2 )
= $false )
| ( ( reli @ X3 @ sK8 )
= $false ) )
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f484,plain,
( spl9_6
| spl9_3
| spl9_7
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f464,f399,f422,f396,f419]) ).
thf(f494,plain,
( ( ( reli @ sK6 @ sK8 )
= $false )
| ( $false = $true )
| ( ( reli @ sK3 @ sK4 )
= $false )
| ~ spl9_7 ),
inference(superposition,[],[f250,f423]) ).
thf(f495,plain,
( ( ( reli @ sK6 @ sK8 )
= $false )
| ( ( reli @ sK3 @ sK4 )
= $false )
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f498,plain,
( ( $false = $true )
| ( ( reli @ sK3 @ sK4 )
= $false )
| ~ spl9_7 ),
inference(forward_demodulation,[],[f495,f272]) ).
thf(f499,plain,
( ( ( reli @ sK3 @ sK4 )
= $false )
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f498]) ).
thf(f519,plain,
( ( $false = $true )
| ~ spl9_7 ),
inference(superposition,[],[f219,f499]) ).
thf(f523,plain,
( $false
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f519]) ).
thf(f524,plain,
~ spl9_7,
inference(avatar_contradiction_clause,[],[f523]) ).
thf(f645,plain,
! [X0: $i] :
( ( ( reli @ X0 @ X0 )
= $true )
| ( ( reli @ X0 @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f236,f237]) ).
thf(f646,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( reli @ X0 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f645]) ).
thf(f647,plain,
! [X0: $i] :
( ( reli @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f687,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( relr @ X0 @ X0 )
= $true )
| ( ( relr @ X0 @ X0 )
= $true ) ),
inference(superposition,[],[f266,f265]) ).
thf(f690,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( relr @ X0 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f687]) ).
thf(f691,plain,
! [X0: $i] :
( ( relr @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f690]) ).
thf(f1206,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ sK8 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK8 ) )
| ( $false = $true ) )
| ~ spl9_6 ),
inference(superposition,[],[f420,f691]) ).
thf(f1207,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ sK8 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK8 ) ) )
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f1206]) ).
thf(f1228,plain,
( ( $false != $false )
| ( ( reli @ sK8 @ sK8 )
= $false )
| ~ spl9_6 ),
inference(equality_factoring,[],[f1207]) ).
thf(f1250,plain,
( ( ( reli @ sK8 @ sK8 )
= $false )
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f1228]) ).
thf(f1254,plain,
( ( $false = $true )
| ~ spl9_6 ),
inference(forward_demodulation,[],[f1250,f647]) ).
thf(f1255,plain,
( $false
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f1254]) ).
thf(f1256,plain,
~ spl9_6,
inference(avatar_contradiction_clause,[],[f1255]) ).
cnf(s6,plain,
( spl9_3
| spl9_4
| spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f425]) ).
cnf(s8,plain,
~ spl9_3,
inference(sat_conversion,[],[f448]) ).
cnf(s14,plain,
( spl9_3
| ~ spl9_4
| spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f484]) ).
cnf(s20,plain,
~ spl9_7,
inference(sat_conversion,[],[f524]) ).
cnf(s69,plain,
~ spl9_6,
inference(sat_conversion,[],[f1256]) ).
cnf(s86,plain,
( spl9_3
| ~ spl9_4 ),
inference(rat,[],[s14,s20,s69]) ).
cnf(s90,plain,
~ spl9_4,
inference(rat,[],[s86,s8]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s6,s20,s69,s90,s8]) ).
thf(f1257,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV445^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:10:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.36 % (1429605)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (1429610)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=723973373:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (1429616)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (1429616)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
% 0.22/0.36 % (1429611)lrs+10_16_si=on:nwc=1.5:random_seed=3581405686:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (1429612)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2152586627:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (1429616)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=1483983568:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (1429613)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=2923071123: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)
% 0.22/0.36 % (1429614)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2974074962:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (1429615)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=822589977:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (1429612)Instruction limit reached!
% 0.22/0.36 % (1429612)------------------------------
% 0.22/0.36 % (1429612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1429612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1429612)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1429612)Termination reason: Instruction limit
% 0.22/0.36 % (1429612)Termination phase: Property scanning
% 0.22/0.36 % (1429612)Time elapsed: 0.002 s
% 0.22/0.36 % (1429612)Peak memory usage: 10 MB
% 0.22/0.36 % (1429612)Instructions burned: 4 (million)
% 0.22/0.36 % (1429611)Instruction limit reached!
% 0.22/0.36 % (1429611)------------------------------
% 0.22/0.36 % (1429611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1429611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1429611)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1429611)Termination reason: Instruction limit
% 0.22/0.36 % (1429611)Termination phase: Saturation
% 0.22/0.36 % (1429611)Time elapsed: 0.008 s
% 0.22/0.36 % (1429611)Peak memory usage: 11 MB
% 0.22/0.36 % (1429611)Instructions burned: 19 (million)
% 0.22/0.36 % (1429610)Instruction limit reached!
% 0.22/0.36 % (1429610)------------------------------
% 0.22/0.36 % (1429610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1429610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1429610)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1429610)Termination reason: Instruction limit
% 0.22/0.36 % (1429610)Termination phase: Saturation
% 0.22/0.36 % (1429610)Time elapsed: 0.022 s
% 0.22/0.36 % (1429610)Peak memory usage: 12 MB
% 0.22/0.36 % (1429610)Instructions burned: 89 (million)
% 0.22/0.36 % (1429614)Instruction limit reached!
% 0.22/0.36 % (1429614)------------------------------
% 0.22/0.36 % (1429614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1429614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1429614)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1429614)Termination reason: Instruction limit
% 0.22/0.36 % (1429614)Termination phase: Saturation
% 0.22/0.36 % (1429614)Time elapsed: 0.014 s
% 0.22/0.36 % (1429614)Peak memory usage: 12 MB
% 0.22/0.36 % (1429614)Instructions burned: 24 (million)
% 0.22/0.36 % (1429624)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3328880344:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.36 % (1429626)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.79/0.38 % (1429624)Instruction limit reached!
% 0.79/0.38 % (1429624)------------------------------
% 0.79/0.38 % (1429624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.38 % (1429624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.38 % (1429624)CaDiCaL version: 2.1.3
% 0.79/0.38 % (1429624)Termination reason: Instruction limit
% 0.79/0.38 % (1429624)Termination phase: Property scanning
% 0.79/0.38 % (1429624)Time elapsed: 0.002 s
% 0.79/0.38 % (1429624)Peak memory usage: 10 MB
% 0.79/0.38 % (1429624)Instructions burned: 4 (million)
% 0.79/0.38 % (1429626)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3365196790:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.79/0.38 % (1429626)Instruction limit reached!
% 0.79/0.38 % (1429626)------------------------------
% 0.79/0.38 % (1429626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.38 % (1429626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.38 % (1429626)CaDiCaL version: 2.1.3
% 0.79/0.38 % (1429626)Termination reason: Instruction limit
% 0.79/0.38 % (1429626)Termination phase: Saturation
% 0.79/0.38 % (1429626)Time elapsed: 0.002 s
% 0.79/0.38 % (1429626)Peak memory usage: 10 MB
% 0.79/0.38 % (1429626)Instructions burned: 9 (million)
% 0.79/0.38 % (1429625)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=364259341:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.79/0.38 % (1429625)Instruction limit reached!
% 0.79/0.38 % (1429625)------------------------------
% 0.79/0.38 % (1429625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.38 % (1429625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.38 % (1429625)CaDiCaL version: 2.1.3
% 0.79/0.38 % (1429625)Termination reason: Instruction limit
% 0.79/0.38 % (1429625)Termination phase: Property scanning
% 0.79/0.38 % (1429625)Time elapsed: 0.003 s
% 0.79/0.38 % (1429625)Peak memory usage: 10 MB
% 0.79/0.38 % (1429625)Instructions burned: 6 (million)
% 0.79/0.38 % (1429627)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3781947830:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.79/0.38 % (1429631)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=389331003:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.79/0.38 % (1429630)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
% 0.79/0.38 % (1429630)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.79/0.38 % (1429615)Instruction limit reached!
% 0.79/0.38 % (1429615)------------------------------
% 0.79/0.38 % (1429615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.38 % (1429615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.38 % (1429615)CaDiCaL version: 2.1.3
% 0.79/0.38 % (1429615)Termination reason: Instruction limit
% 0.79/0.38 % (1429615)Termination phase: Saturation
% 0.79/0.38 % (1429615)Time elapsed: 0.038 s
% 0.79/0.38 % (1429615)Peak memory usage: 12 MB
% 0.79/0.38 % (1429615)Instructions burned: 77 (million)
% 0.79/0.38 % (1429627)Instruction limit reached!
% 0.79/0.38 % (1429627)------------------------------
% 0.79/0.38 % (1429627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.38 % (1429627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.38 % (1429627)CaDiCaL version: 2.1.3
% 0.79/0.38 % (1429627)Termination reason: Instruction limit
% 0.79/0.38 % (1429627)Termination phase: Saturation
% 0.79/0.38 % (1429627)Time elapsed: 0.006 s
% 0.79/0.38 % (1429627)Peak memory usage: 11 MB
% 0.79/0.38 % (1429627)Instructions burned: 13 (million)
% 0.79/0.38 % (1429630)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4258805314:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.79/0.38 % (1429633)lrs+10_1_si=on:cs=on:random_seed=3116953341:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.79/0.38 % (1429636)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.79/0.41 % (1429633)Instruction limit reached!
% 0.79/0.41 % (1429633)------------------------------
% 0.79/0.41 % (1429633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (1429633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (1429633)CaDiCaL version: 2.1.3
% 0.79/0.41 % (1429633)Termination reason: Instruction limit
% 0.79/0.41 % (1429633)Termination phase: Property scanning
% 0.79/0.41 % (1429633)Time elapsed: 0.004 s
% 0.79/0.41 % (1429633)Peak memory usage: 10 MB
% 0.79/0.41 % (1429633)Instructions burned: 8 (million)
% 0.79/0.41 % (1429630)Instruction limit reached!
% 0.79/0.41 % (1429630)------------------------------
% 0.79/0.41 % (1429630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (1429630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (1429630)CaDiCaL version: 2.1.3
% 0.79/0.41 % (1429630)Termination reason: Instruction limit
% 0.79/0.41 % (1429630)Termination phase: Saturation
% 0.79/0.41 % (1429630)Time elapsed: 0.013 s
% 0.79/0.41 % (1429630)Peak memory usage: 12 MB
% 0.79/0.41 % (1429630)Instructions burned: 29 (million)
% 0.79/0.41 % (1429636)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=1547717408:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.79/0.41 % (1429631)Instruction limit reached!
% 0.79/0.41 % (1429631)------------------------------
% 0.79/0.41 % (1429631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (1429631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (1429631)CaDiCaL version: 2.1.3
% 0.79/0.41 % (1429631)Termination reason: Instruction limit
% 0.79/0.41 % (1429631)Termination phase: Saturation
% 0.79/0.41 % (1429631)Time elapsed: 0.023 s
% 0.79/0.41 % (1429631)Peak memory usage: 13 MB
% 0.79/0.41 % (1429631)Instructions burned: 86 (million)
% 0.79/0.41 % (1429638)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2105181972:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.79/0.41 % (1429636)Instruction limit reached!
% 0.79/0.41 % (1429636)------------------------------
% 0.79/0.41 % (1429636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (1429636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (1429636)CaDiCaL version: 2.1.3
% 0.79/0.41 % (1429636)Termination reason: Instruction limit
% 0.79/0.41 % (1429636)Termination phase: Function definition elimination
% 0.79/0.41 % (1429636)Time elapsed: 0.002 s
% 0.79/0.41 % (1429636)Peak memory usage: 10 MB
% 0.79/0.41 % (1429636)Instructions burned: 4 (million)
% 0.79/0.41 % (1429638)Refutation not found, incomplete strategy
% 0.79/0.41 % (1429638)------------------------------
% 0.79/0.41 % (1429638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (1429638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (1429638)CaDiCaL version: 2.1.3
% 0.79/0.41 % (1429638)Termination reason: Refutation not found, incomplete strategy
% 0.79/0.41 % (1429638)Time elapsed: 0.005 s
% 0.79/0.41 % (1429638)Peak memory usage: 12 MB
% 0.79/0.41 % (1429638)Instructions burned: 8 (million)
% 0.79/0.41 % (1429638)------------------------------
% 0.79/0.41 % (1429638)------------------------------
% 0.79/0.41 % (1429640)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=737847622:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.79/0.41 % (1429640)Refutation not found, incomplete strategy
% 0.79/0.41 % (1429640)------------------------------
% 0.79/0.41 % (1429640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (1429640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (1429640)CaDiCaL version: 2.1.3
% 0.79/0.41 % (1429640)Termination reason: Refutation not found, incomplete strategy
% 0.79/0.41 % (1429640)Time elapsed: 0.002 s
% 0.79/0.41 % (1429640)Peak memory usage: 12 MB
% 0.79/0.41 % (1429640)Instructions burned: 6 (million)
% 0.79/0.41 % (1429640)------------------------------
% 0.79/0.41 % (1429640)------------------------------
% 0.79/0.41 % (1429641)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2157223304:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.79/0.45 % (1429643)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1807966488:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.79/0.45 % (1429645)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=487724362:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.79/0.45 % (1429616)Instruction limit reached!
% 0.79/0.45 % (1429616)------------------------------
% 0.79/0.45 % (1429616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.45 % (1429616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.45 % (1429648)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3788512945:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.79/0.45 % (1429616)CaDiCaL version: 2.1.3
% 0.79/0.45 % (1429616)Termination reason: Instruction limit
% 0.79/0.45 % (1429616)Termination phase: Saturation
% 0.79/0.45 % (1429616)Time elapsed: 0.081 s
% 0.79/0.45 % (1429616)Peak memory usage: 12 MB
% 0.79/0.45 % (1429616)Instructions burned: 158 (million)
% 0.79/0.45 % (1429648)Instruction limit reached!
% 0.79/0.45 % (1429648)------------------------------
% 0.79/0.45 % (1429648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.45 % (1429648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.45 % (1429648)CaDiCaL version: 2.1.3
% 0.79/0.45 % (1429648)Termination reason: Instruction limit
% 0.79/0.45 % (1429648)Termination phase: Property scanning
% 0.79/0.45 % (1429648)Time elapsed: 0.002 s
% 0.79/0.45 % (1429648)Peak memory usage: 11 MB
% 0.79/0.45 % (1429648)Instructions burned: 8 (million)
% 0.79/0.45 % (1429646)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=462200479:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.79/0.45 % (1429643)Instruction limit reached!
% 0.79/0.45 % (1429643)------------------------------
% 0.79/0.45 % (1429643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.45 % (1429645)Refutation not found, incomplete strategy
% 0.79/0.45 % (1429645)------------------------------
% 0.79/0.45 % (1429645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.45 % (1429643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.45 % (1429645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.45 % (1429643)CaDiCaL version: 2.1.3
% 0.79/0.45 % (1429643)Termination reason: Instruction limit
% 0.79/0.45 % (1429643)Termination phase: Saturation
% 0.79/0.45 % (1429645)CaDiCaL version: 2.1.3
% 0.79/0.45 % (1429643)Time elapsed: 0.006 s
% 0.79/0.45 % (1429645)Termination reason: Refutation not found, incomplete strategy
% 0.79/0.45 % (1429645)Time elapsed: 0.006 s
% 0.79/0.45 % (1429643)Peak memory usage: 12 MB
% 0.79/0.45 % (1429645)Peak memory usage: 12 MB
% 0.79/0.45 % (1429643)Instructions burned: 14 (million)
% 0.79/0.45 % (1429645)Instructions burned: 11 (million)
% 0.79/0.45 % (1429645)------------------------------
% 0.79/0.45 % (1429645)------------------------------
% 0.79/0.45 % (1429641)Instruction limit reached!
% 0.79/0.45 % (1429641)------------------------------
% 0.79/0.45 % (1429641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.45 % (1429641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.45 % (1429641)CaDiCaL version: 2.1.3
% 0.79/0.45 % (1429641)Termination reason: Instruction limit
% 0.79/0.45 % (1429641)Termination phase: Saturation
% 0.79/0.45 % (1429641)Time elapsed: 0.015 s
% 0.79/0.45 % (1429641)Peak memory usage: 12 MB
% 0.79/0.45 % (1429641)Instructions burned: 26 (million)
% 0.79/0.45 % (1429646)Instruction limit reached!
% 0.79/0.45 % (1429646)------------------------------
% 0.79/0.45 % (1429646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.45 % (1429646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.45 % (1429646)CaDiCaL version: 2.1.3
% 0.79/0.45 % (1429646)Termination reason: Instruction limit
% 0.79/0.45 % (1429646)Termination phase: Saturation
% 0.79/0.45 % (1429646)Time elapsed: 0.006 s
% 0.79/0.45 % (1429646)Peak memory usage: 12 MB
% 0.79/0.45 % (1429646)Instructions burned: 14 (million)
% 0.79/0.45 % (1429654)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1515907704:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.52/0.47 % (1429653)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2327247990:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.52/0.47 % (1429654)Instruction limit reached!
% 1.52/0.47 % (1429654)------------------------------
% 1.52/0.47 % (1429654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.47 % (1429654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.47 % (1429654)CaDiCaL version: 2.1.3
% 1.52/0.47 % (1429654)Termination reason: Instruction limit
% 1.52/0.47 % (1429654)Termination phase: Saturation
% 1.52/0.47 % (1429654)Time elapsed: 0.006 s
% 1.52/0.47 % (1429654)Peak memory usage: 11 MB
% 1.52/0.47 % (1429654)Instructions burned: 26 (million)
% 1.52/0.47 % (1429657)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
% 1.52/0.47 % (1429657)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.52/0.47 % (1429658)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.52/0.47 % (1429656)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3525894657:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.52/0.47 % (1429657)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=372620369:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.52/0.47 % (1429658)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=2421575207:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.52/0.47 % (1429659)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=3050548034:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.52/0.47 % (1429657)Instruction limit reached!
% 1.52/0.47 % (1429657)------------------------------
% 1.52/0.47 % (1429657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.47 % (1429657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.47 % (1429657)CaDiCaL version: 2.1.3
% 1.52/0.47 % (1429657)Termination reason: Instruction limit
% 1.52/0.47 % (1429657)Termination phase: Saturation
% 1.52/0.47 % (1429657)Time elapsed: 0.006 s
% 1.52/0.47 % (1429657)Peak memory usage: 11 MB
% 1.52/0.47 % (1429657)Instructions burned: 14 (million)
% 1.52/0.47 % (1429653)Instruction limit reached!
% 1.52/0.47 % (1429653)------------------------------
% 1.52/0.47 % (1429653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.47 % (1429653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.47 % (1429653)CaDiCaL version: 2.1.3
% 1.52/0.47 % (1429653)Termination reason: Instruction limit
% 1.52/0.47 % (1429653)Termination phase: Saturation
% 1.52/0.47 % (1429653)Time elapsed: 0.012 s
% 1.52/0.47 % (1429653)Peak memory usage: 11 MB
% 1.52/0.47 % (1429653)Instructions burned: 26 (million)
% 1.52/0.47 % (1429658)Instruction limit reached!
% 1.52/0.47 % (1429658)------------------------------
% 1.52/0.47 % (1429658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.47 % (1429658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.47 % (1429658)CaDiCaL version: 2.1.3
% 1.52/0.47 % (1429658)Termination reason: Instruction limit
% 1.52/0.47 % (1429658)Termination phase: Saturation
% 1.52/0.47 % (1429658)Time elapsed: 0.005 s
% 1.52/0.47 % (1429658)Peak memory usage: 11 MB
% 1.52/0.47 % (1429658)Instructions burned: 10 (million)
% 1.52/0.47 % (1429662)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3476690940:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.52/0.47 % (1429662)Instruction limit reached!
% 1.52/0.47 % (1429662)------------------------------
% 1.52/0.47 % (1429662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.47 % (1429662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429662)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429662)Termination reason: Instruction limit
% 1.52/0.52 % (1429662)Termination phase: Property scanning
% 1.52/0.52 % (1429662)Time elapsed: 0.004 s
% 1.52/0.52 % (1429662)Peak memory usage: 11 MB
% 1.52/0.52 % (1429662)Instructions burned: 9 (million)
% 1.52/0.52 % (1429667)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2774581929:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.52/0.52 % (1429667)Instruction limit reached!
% 1.52/0.52 % (1429667)------------------------------
% 1.52/0.52 % (1429667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429667)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429667)Termination reason: Instruction limit
% 1.52/0.52 % (1429667)Termination phase: Saturation
% 1.52/0.52 % (1429667)Time elapsed: 0.005 s
% 1.52/0.52 % (1429667)Peak memory usage: 12 MB
% 1.52/0.52 % (1429667)Instructions burned: 24 (million)
% 1.52/0.52 % (1429659)Instruction limit reached!
% 1.52/0.52 % (1429659)------------------------------
% 1.52/0.52 % (1429659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429659)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429659)Termination reason: Instruction limit
% 1.52/0.52 % (1429659)Termination phase: Saturation
% 1.52/0.52 % (1429659)Time elapsed: 0.017 s
% 1.52/0.52 % (1429659)Peak memory usage: 12 MB
% 1.52/0.52 % (1429659)Instructions burned: 32 (million)
% 1.52/0.52 % (1429668)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3885472213:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.52/0.52 % (1429669)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=805702269:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.52/0.52 % (1429656)Instruction limit reached!
% 1.52/0.52 % (1429656)------------------------------
% 1.52/0.52 % (1429656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429656)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429656)Termination reason: Instruction limit
% 1.52/0.52 % (1429656)Termination phase: Saturation
% 1.52/0.52 % (1429656)Time elapsed: 0.032 s
% 1.52/0.52 % (1429656)Peak memory usage: 12 MB
% 1.52/0.52 % (1429656)Instructions burned: 62 (million)
% 1.52/0.52 % (1429673)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1141056283:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.52/0.52 % (1429672)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1553898816:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.52/0.52 % (1429673)Refutation not found, incomplete strategy
% 1.52/0.52 % (1429673)------------------------------
% 1.52/0.52 % (1429673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429673)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429673)Termination reason: Refutation not found, incomplete strategy
% 1.52/0.52 % (1429673)Time elapsed: 0.003 s
% 1.52/0.52 % (1429673)Peak memory usage: 12 MB
% 1.52/0.52 % (1429673)Instructions burned: 9 (million)
% 1.52/0.52 % (1429673)------------------------------
% 1.52/0.52 % (1429673)------------------------------
% 1.52/0.52 % (1429668)Instruction limit reached!
% 1.52/0.52 % (1429668)------------------------------
% 1.52/0.52 % (1429668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429668)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429668)Termination reason: Instruction limit
% 1.52/0.52 % (1429668)Termination phase: Saturation
% 1.52/0.52 % (1429668)Time elapsed: 0.012 s
% 1.52/0.52 % (1429668)Peak memory usage: 12 MB
% 1.52/0.52 % (1429668)Instructions burned: 20 (million)
% 1.52/0.52 % (1429674)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3360350949:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.52/0.52 % (1429677)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.52/0.52 % (1429677)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1923729671:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.52/0.52 % (1429680)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2189670297:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 1.52/0.52 % (1429677)Instruction limit reached!
% 1.52/0.52 % (1429677)------------------------------
% 1.52/0.52 % (1429677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429677)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429677)Termination reason: Instruction limit
% 1.52/0.52 % (1429677)Termination phase: Property scanning
% 1.52/0.52 % (1429677)Time elapsed: 0.004 s
% 1.52/0.52 % (1429677)Peak memory usage: 10 MB
% 1.52/0.52 % (1429677)Instructions burned: 9 (million)
% 1.52/0.52 % (1429681)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=388021971:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/169Mi)
% 1.52/0.52 % (1429680)Refutation not found, incomplete strategy
% 1.52/0.52 % (1429680)------------------------------
% 1.52/0.52 % (1429680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429680)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429680)Termination reason: Refutation not found, incomplete strategy
% 1.52/0.52 % (1429680)Time elapsed: 0.004 s
% 1.52/0.52 % (1429680)Peak memory usage: 12 MB
% 1.52/0.52 % (1429680)Instructions burned: 8 (million)
% 1.52/0.52 % (1429680)------------------------------
% 1.52/0.52 % (1429680)------------------------------
% 1.52/0.52 % (1429674)Instruction limit reached!
% 1.52/0.52 % (1429674)------------------------------
% 1.52/0.52 % (1429674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429674)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429674)Termination reason: Instruction limit
% 1.52/0.52 % (1429674)Termination phase: Saturation
% 1.52/0.52 % (1429674)Time elapsed: 0.021 s
% 1.52/0.52 % (1429674)Peak memory usage: 12 MB
% 1.52/0.52 % (1429674)Instructions burned: 44 (million)
% 1.52/0.52 % (1429681)Refutation not found, incomplete strategy
% 1.52/0.52 % (1429681)------------------------------
% 1.52/0.52 % (1429681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429681)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429681)Termination reason: Refutation not found, incomplete strategy
% 1.52/0.52 % (1429681)Time elapsed: 0.005 s
% 1.52/0.52 % (1429681)Peak memory usage: 12 MB
% 1.52/0.52 % (1429681)Instructions burned: 9 (million)
% 1.52/0.52 % (1429681)------------------------------
% 1.52/0.52 % (1429681)------------------------------
% 1.52/0.52 % (1429685)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.52/0.52 % (1429685)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2806123270:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2998 on theBenchmark for (2998ds/6Mi)
% 1.52/0.52 % (1429672)Instruction limit reached!
% 1.52/0.52 % (1429672)------------------------------
% 1.52/0.52 % (1429672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429672)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429672)Termination reason: Instruction limit
% 1.52/0.52 % (1429672)Termination phase: Saturation
% 1.52/0.52 % (1429672)Time elapsed: 0.041 s
% 1.52/0.52 % (1429672)Peak memory usage: 13 MB
% 1.52/0.52 % (1429672)Instructions burned: 145 (million)
% 1.52/0.52 % (1429685)Instruction limit reached!
% 1.52/0.52 % (1429685)------------------------------
% 1.52/0.52 % (1429685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429685)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429685)Termination reason: Instruction limit
% 1.52/0.52 % (1429685)Termination phase: Property scanning
% 1.52/0.52 % (1429685)Time elapsed: 0.003 s
% 1.52/0.52 % (1429685)Peak memory usage: 11 MB
% 1.52/0.52 % (1429685)Instructions burned: 8 (million)
% 1.52/0.52 % (1429687)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=948847581:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.52/0.52 % (1429688)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2233006181:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.52/0.52 % (1429689)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4249671121:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 1.52/0.52 % (1429691)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3678747278:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 1.52/0.52 % (1429688)Instruction limit reached!
% 1.52/0.52 % (1429688)------------------------------
% 1.52/0.52 % (1429688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429688)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429688)Termination reason: Instruction limit
% 1.52/0.52 % (1429688)Termination phase: Saturation
% 1.52/0.52 % (1429688)Time elapsed: 0.009 s
% 1.52/0.52 % (1429688)Peak memory usage: 12 MB
% 1.52/0.52 % (1429688)Instructions burned: 20 (million)
% 1.52/0.52 % (1429687)Instruction limit reached!
% 1.52/0.52 % (1429687)------------------------------
% 1.52/0.52 % (1429687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429687)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429687)Termination reason: Instruction limit
% 1.52/0.52 % (1429687)Termination phase: Saturation
% 1.52/0.52 % (1429687)Time elapsed: 0.010 s
% 1.52/0.52 % (1429687)Peak memory usage: 12 MB
% 1.52/0.52 % (1429687)Instructions burned: 22 (million)
% 1.52/0.52 % (1429692)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=4072696155:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 1.52/0.52 % (1429669) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1429605-1429669"...
% 1.52/0.52 % (1429697)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2294100380:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 1.52/0.52 % (1429698)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=904249659:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2997 on theBenchmark for (2997ds/21Mi)
% 1.52/0.52 % (1429697)Refutation not found, incomplete strategy
% 1.52/0.52 % (1429697)------------------------------
% 1.52/0.52 % (1429697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429697)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429697)Termination reason: Refutation not found, incomplete strategy
% 1.52/0.52 % (1429697)Time elapsed: 0.004 s
% 1.52/0.52 % (1429697)Peak memory usage: 12 MB
% 1.52/0.52 % (1429697)Instructions burned: 8 (million)
% 1.52/0.52 % (1429697)------------------------------
% 1.52/0.52 % (1429697)------------------------------
% 1.52/0.52 % (1429669)...printing done.
% 1.52/0.52 % (1429669)Refutation found. Thanks to Tanya!
% 1.52/0.52 % SZS status Theorem for theBenchmark
% 1.52/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.52 % (1429669)------------------------------
% 1.52/0.52 % (1429669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.52 % (1429669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.52 % (1429669)CaDiCaL version: 2.1.3
% 1.52/0.52 % (1429669)Termination reason: Refutation
% 1.52/0.52 % (1429669)Time elapsed: 0.089 s
% 1.52/0.52 % (1429669)Peak memory usage: 14 MB
% 1.52/0.52 % (1429669)Instructions burned: 174 (million)
% 1.52/0.52 % (1429605)Success in time 0.262 s
% 1.52/0.52 % Vampire exiting
%------------------------------------------------------------------------------