%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV441^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 3.20s 0.85s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 19
% Syntax : Number of formulae : 234 ( 121 unt; 0 typ; 4 def)
% Number of atoms : 2664 ( 466 equ; 0 cnn)
% Maximal formula atoms : 13 ( 11 avg)
% Number of connectives : 4670 ( 215 ~; 462 |; 0 &;3114 @)
% ( 4 <=>; 434 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 346 ( 346 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 15 con; 0-4 aty)
% ( 441 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1024 ( 0 sgn 261 !; 0 ?;1024 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
vOR: $o > $o > $o ).
thf(func_def_54,type,
vNOT: $o > $o ).
thf(func_def_55,type,
vAND: $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,
sK0: individuals ).
thf(func_def_64,type,
sK1: $i > $o ).
thf(func_def_65,type,
sK2: $i > $o ).
thf(func_def_68,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_69,type,
sK6: $i > $i ).
thf(func_def_71,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_76,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_77,type,
sK13: ( $i > $o ) > $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) )
= cs4_atom ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f23,axiom,
( cs4_box
= ( ^ [X0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_box) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',refl_axiom_i) ).
thf(f27,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',trans_axiom_i) ).
thf(f31,axiom,
( ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) )
= bl_princ ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_princ) ).
thf(f34,axiom,
( bl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( cs4_impl @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_says) ).
thf(f39,axiom,
bl_valid = mvalid,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_valid_def) ).
thf(f41,conjecture,
! [X2: $i > $o,X1: $i > $o,X0: individuals] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_impl @ X1 @ X2 ) ) @ ( bl_impl @ ( bl_says @ X0 @ X1 ) @ ( bl_says @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_k) ).
thf(f42,negated_conjecture,
~ ! [X2: $i > $o,X1: $i > $o,X0: individuals] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_impl @ X1 @ X2 ) ) @ ( bl_impl @ ( bl_says @ X0 @ X1 ) @ ( bl_says @ X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f43,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f44,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f45,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f52,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f53,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f59,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f64,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: individuals] : ( bl_valid @ ( bl_impl @ ( bl_says @ X2 @ ( bl_impl @ X1 @ X0 ) ) @ ( bl_impl @ ( bl_says @ X2 @ X1 ) @ ( bl_says @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f65,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ Y0 @ ( bl_impl @ Y1 @ Y2 ) ) @ ( bl_impl @ ( bl_says @ Y0 @ Y1 ) @ ( bl_says @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
mvalid = bl_valid,
inference(fool_elimination,[],[f39]) ).
thf(f67,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f68,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f70,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f71,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ Y0 ) @ ( mbox @ reli @ ( mbox @ reli @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f70]) ).
thf(f75,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f76,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f78,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f82,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f83,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f94,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f98,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f103,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ Y0 ) @ ( mbox @ reli @ ( mbox @ reli @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f71]) ).
thf(f104,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f106,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f114,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f116,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f118,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f119,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ Y0 @ ( bl_impl @ Y1 @ Y2 ) ) @ ( bl_impl @ ( bl_says @ Y0 @ Y1 ) @ ( bl_says @ Y0 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f65]) ).
thf(f120,plain,
mvalid = bl_valid,
inference(cnf_transformation,[],[f66]) ).
thf(f123,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f124,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f127,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f133,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f138,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f139,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f140,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
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,[],[f140,f127,f138]) ).
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,[],[f118,f114]) ).
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,[],[f106,f114,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,[],[f116,f114,f114]) ).
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,[],[f123,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,[],[f139,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,[],[f124,f153,f150,f156]) ).
thf(f162,plain,
( bl_valid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f120,f133]) ).
thf(f164,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 )
@ ( ^ [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 ) ) )
@ reli
@ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f103,f133,f145,f114,f114,f114]) ).
thf(f165,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,[],[f104,f133,f145,f114]) ).
thf(f169,plain,
( $true
= ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ^ [Y3: $i > $o] :
( !! @ $i
@ ^ [Y4: $i] : ( Y3 @ Y4 ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ ( ^ [Y7: $i > $o,Y8: $i > $o] :
( ^ [Y9: $i > $o,Y10: $i > $o,Y11: $i] :
( ( Y9 @ Y11 )
| ( Y10 @ Y11 ) )
@ ( ^ [Y9: $i > $o,Y10: $i] :
~ ( Y9 @ Y10 )
@ Y7 )
@ Y8 )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 )
@ ( ^ [Y3: individuals,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 > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ relr
@ Y5 ) )
@ ( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ ( ^ [Y7: $i > $o,Y8: $i > $o] :
( ^ [Y9: $i > $o,Y10: $i > $o,Y11: $i] :
( ( Y9 @ Y11 )
| ( Y10 @ Y11 ) )
@ ( ^ [Y9: $i > $o,Y10: $i] :
~ ( Y9 @ Y10 )
@ Y7 )
@ Y8 )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i > $o] :
( ^ [Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ Y6 )
@ Y5 )
@ ( princ_inj @ Y3 ) )
@ Y4 ) )
@ Y0
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ ( ^ [Y7: $i > $o,Y8: $i > $o] :
( ^ [Y9: $i > $o,Y10: $i > $o,Y11: $i] :
( ( Y9 @ Y11 )
| ( Y10 @ Y11 ) )
@ ( ^ [Y9: $i > $o,Y10: $i] :
~ ( Y9 @ Y10 )
@ Y7 )
@ Y8 )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 )
@ Y1
@ Y2 ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ ( ^ [Y7: $i > $o,Y8: $i > $o] :
( ^ [Y9: $i > $o,Y10: $i > $o,Y11: $i] :
( ( Y9 @ Y11 )
| ( Y10 @ Y11 ) )
@ ( ^ [Y9: $i > $o,Y10: $i] :
~ ( Y9 @ Y10 )
@ Y7 )
@ Y8 )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 )
@ ( ^ [Y3: individuals,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 > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ relr
@ Y5 ) )
@ ( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ ( ^ [Y7: $i > $o,Y8: $i > $o] :
( ^ [Y9: $i > $o,Y10: $i > $o,Y11: $i] :
( ( Y9 @ Y11 )
| ( Y10 @ Y11 ) )
@ ( ^ [Y9: $i > $o,Y10: $i] :
~ ( Y9 @ Y10 )
@ Y7 )
@ Y8 )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i > $o] :
( ^ [Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ Y6 )
@ Y5 )
@ ( princ_inj @ Y3 ) )
@ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y3: individuals,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 > $i > $o,Y7: $i > $o,Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y8 @ Y9 )
=> ( Y7 @ Y9 ) ) )
@ relr
@ Y5 ) )
@ ( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ ( ^ [Y7: $i > $o,Y8: $i > $o] :
( ^ [Y9: $i > $o,Y10: $i > $o,Y11: $i] :
( ( Y9 @ Y11 )
| ( Y10 @ Y11 ) )
@ ( ^ [Y9: $i > $o,Y10: $i] :
~ ( Y9 @ Y10 )
@ Y7 )
@ Y8 )
@ Y5
@ Y6 ) )
@ ( ^ [Y5: $i > $o] :
( ^ [Y6: $i > $o] :
( ^ [Y7: $i > $i > $o,Y8: $i > $o,Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y9 @ Y10 )
=> ( Y8 @ Y10 ) ) )
@ reli
@ Y6 )
@ Y5 )
@ ( princ_inj @ Y3 ) )
@ Y4 ) )
@ Y0
@ Y2 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f119,f162,f159,f161,f159,f159,f161,f161]) ).
thf(f175,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f177,plain,
( ( ~ ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $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 @ Y0 @ Y8 ) ) )
| ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( ~ ( Y1 @ Y8 )
| ( Y2 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $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 @ Y0 @ Y9 ) ) )
| ( Y1 @ Y8 ) ) ) ) ) ) ) )
| ( !! @ $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 @ Y0 @ Y9 ) ) )
| ( Y2 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f178,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f179,plain,
( ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $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 @ Y0 @ Y8 ) ) )
| ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( ~ ( Y1 @ Y8 )
| ( Y2 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $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 @ Y0 @ Y9 ) ) )
| ( Y1 @ Y8 ) ) ) ) ) ) ) )
| ( !! @ $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 @ Y0 @ Y9 ) ) )
| ( Y2 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( $false
= ( ^ [Y0: individuals] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $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 @ Y0 @ Y8 ) ) )
| ( !! @ $i
@ ^ [Y8: $i] :
( ( reli @ Y7 @ Y8 )
=> ( ~ ( Y1 @ Y8 )
| ( Y2 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( ~ ( !! @ $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 @ Y0 @ Y9 ) ) )
| ( Y1 @ Y8 ) ) ) ) ) ) ) )
| ( !! @ $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 @ Y0 @ Y9 ) ) )
| ( Y2 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $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 @ sK0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( ~ ( Y0 @ Y7 )
| ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $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 ) ) )
| ( Y0 @ Y7 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $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 @ sK0 @ Y7 ) ) )
| ( !! @ $i
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( ~ ( Y0 @ Y7 )
| ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $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 ) ) )
| ( Y0 @ Y7 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( Y1 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,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 )
=> ( ~ ( sK1 @ Y6 )
| ( Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 @ sK0 @ Y7 ) ) )
| ( sK1 @ Y6 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f195,plain,
( ( ^ [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 )
=> ( ~ ( sK1 @ Y6 )
| ( Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 @ sK0 @ Y7 ) ) )
| ( sK1 @ Y6 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( Y0 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f198,plain,
( ( !! @ $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 )
=> ( ~ ( sK1 @ Y5 )
| ( sK2 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK1 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f201,plain,
( $false
= ( ^ [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 )
=> ( ~ ( sK1 @ Y5 )
| ( sK2 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK1 @ Y5 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f203,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ 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 )
=> ( ~ ( sK1 @ Y4 )
| ( sK2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK1 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f207,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK3 @ 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 )
=> ( ~ ( sK1 @ Y4 )
| ( sK2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK1 @ Y4 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f203]) ).
thf(f209,plain,
( $false
= ( ( reli @ sK3 @ sK4 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 ) ) )
| ( sK1 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f211,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 ) ) )
| ( sK1 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f213,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 ) ) )
| ( sK1 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f215,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK4 @ 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 )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( reli @ sK4 @ 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 )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( $true
= ( ( reli @ sK4 @ 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 )
=> ( ~ ( sK1 @ Y2 )
| ( sK2 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $true
= ( !! @ $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 )
=> ( ~ ( sK1 @ Y2 )
| ( sK2 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( reli @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( reli @ sK4 @ X1 ) )
| ( $true
= ( ^ [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 )
=> ( ~ ( sK1 @ Y2 )
| ( sK2 @ Y2 ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f222,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 )
=> ( ~ ( sK1 @ Y1 )
| ( sK2 @ Y1 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ sK4 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( sK1 @ Y1 )
| ( sK2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( sK1 @ Y1 )
| ( sK2 @ Y1 ) ) ) ) ) )
@ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK4 @ X1 ) )
| ( ( ( reli @ X2 @ X3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK4 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( ~ ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) )
@ X4 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( ( ( reli @ X3 @ X4 )
=> ( ~ ( sK1 @ X4 )
| ( sK2 @ X4 ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( ( ~ ( sK1 @ X4 )
| ( sK2 @ X4 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $true
= ( ~ ( sK1 @ X4 ) ) )
| ( $true
= ( sK2 @ X4 ) )
| ( $false
= ( reli @ X3 @ X4 ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( sK1 @ X4 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $true
= ( sK2 @ X4 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f244,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK1 @ X4 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( sK2 @ X4 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ ( sK6 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f237]) ).
thf(f246,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( sK2 @ X4 ) )
| ( $false
= ( sK1 @ X4 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( ( reli @ X3 @ ( sK6 @ X3 ) )
=> ( princ_inj @ sK0 @ ( sK6 @ X3 ) ) ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( princ_inj @ sK0 @ ( sK6 @ X3 ) ) )
| ( $false
= ( sK1 @ X4 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $true
= ( sK2 @ X4 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f249,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( reli @ X3 @ ( sK6 @ X3 ) )
= $true )
| ( $false
= ( sK1 @ X4 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $true
= ( sK2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f250,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f251,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f256,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK4 @ 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 ) ) )
| ( sK1 @ Y3 ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) )
| ( sK2 @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK7 ) ),
inference(sigma_proxy_clausification,[],[f213]) ).
thf(f258,plain,
( $false
= ( ( reli @ sK4 @ sK7 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK1 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK2 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f260,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK1 @ Y2 ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK2 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f261,plain,
( ( reli @ sK4 @ sK7 )
= $true ),
inference(imp_proxy_clausification,[],[f258]) ).
thf(f262,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK2 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f263,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK1 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f264,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f251]) ).
thf(f266,plain,
! [X2: $i,X1: $i > $o] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK8 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f268]) ).
thf(f272,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $false
= ( ( reli @ X2 @ ( sK8 @ X1 @ X2 ) )
=> ( X1 @ ( sK8 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f269]) ).
thf(f273,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( sK8 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( reli @ X2 @ ( sK8 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f277,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK2 @ Y2 ) ) ) ) ) ) )
@ sK9 ) ),
inference(sigma_proxy_clausification,[],[f262]) ).
thf(f279,plain,
( $false
= ( ( reli @ sK7 @ sK9 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( sK2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f281,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( sK2 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f279]) ).
thf(f282,plain,
( $true
= ( reli @ sK7 @ sK9 ) ),
inference(imp_proxy_clausification,[],[f279]) ).
thf(f283,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( sK1 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f264]) ).
thf(f284,plain,
! [X1: $i] :
( ( ( reli @ sK7 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( sK1 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f285,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( sK1 @ Y1 ) ) ) ) ) ) )
| ( ( reli @ sK7 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f284]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( ( reli @ sK7 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( sK1 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f285]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( ( reli @ sK7 @ X1 )
= $false )
| ( ( ( relr @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( sK1 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ sK7 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f294,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( reli @ sK7 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( sK1 @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f290]) ).
thf(f295,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( ( ( reli @ X2 @ X3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( sK1 @ X3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f294]) ).
thf(f296,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( sK1 @ X3 ) )
= $true )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK1 @ X3 )
= $true )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( sK1 @ X3 )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ sK7 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( sK1 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ ( sK6 @ X3 ) ) )
| ( ( reli @ sK7 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f298]) ).
thf(f301,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( ( reli @ X3 @ ( sK6 @ X3 ) )
=> ( princ_inj @ sK0 @ ( sK6 @ X3 ) ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( reli @ sK7 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f303,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( princ_inj @ sK0 @ ( sK6 @ X3 ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f301]) ).
thf(f304,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( reli @ X3 @ ( sK6 @ X3 ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f301]) ).
thf(f315,plain,
( $false
= ( ^ [Y0: $i] :
( ( relr @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( sK2 @ Y1 ) ) ) ) )
@ sK10 ) ),
inference(sigma_proxy_clausification,[],[f281]) ).
thf(f318,plain,
( ( ( relr @ sK9 @ sK10 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK10 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( sK2 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f315]) ).
thf(f319,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK10 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( sK2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f320,plain,
( $true
= ( relr @ sK9 @ sK10 ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f322,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK10 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( sK2 @ Y0 ) ) )
@ sK11 ) ),
inference(sigma_proxy_clausification,[],[f319]) ).
thf(f324,plain,
( $false
= ( ( reli @ sK10 @ sK11 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( sK2 @ sK11 ) ) ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f326,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( sK2 @ sK11 ) ) ),
inference(imp_proxy_clausification,[],[f324]) ).
thf(f327,plain,
( $true
= ( reli @ sK10 @ sK11 ) ),
inference(imp_proxy_clausification,[],[f324]) ).
thf(f328,plain,
( $false
= ( sK2 @ sK11 ) ),
inference(or_proxy_clausification,[],[f326]) ).
thf(f329,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f326]) ).
thf(f330,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f332,plain,
! [X1: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f331]) ).
thf(f335,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f330]) ).
thf(f336,plain,
! [X1: $i] :
( ( ( reli @ sK11 @ X1 )
=> ( princ_inj @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f335]) ).
thf(f337,plain,
! [X1: $i] :
( ( $true
= ( princ_inj @ sK0 @ X1 ) )
| ( $false
= ( reli @ sK11 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f332]) ).
thf(f339,plain,
! [X2: $i,X1: $i > $o] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X1: $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f340]) ).
thf(f344,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK11 @ ( sK6 @ X0 ) ) )
| ( $false = $true )
| ( $true
= ( sK1 @ X0 ) )
| ( $false
= ( reli @ X2 @ X0 ) )
| ( ( reli @ sK7 @ X1 )
= $false ) ),
inference(superposition,[],[f303,f337]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( $false
= ( reli @ sK4 @ X3 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( reli @ X2 @ X0 ) )
| ( $false = $true )
| ( $false
= ( relr @ X3 @ X2 ) )
| ( $false
= ( reli @ sK11 @ ( sK6 @ X0 ) ) )
| ( $false
= ( reli @ X0 @ X1 ) ) ),
inference(superposition,[],[f248,f337]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ sK11 @ ( sK6 @ X0 ) ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( reli @ sK4 @ X3 ) )
| ( ( sK2 @ X1 )
= $true )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( relr @ X3 @ X2 ) )
| ( $false
= ( reli @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ sK11 @ ( sK6 @ X0 ) ) )
| ( $false
= ( reli @ X2 @ X0 ) )
| ( $true
= ( sK1 @ X0 ) )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f344]) ).
thf(f350,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f351,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( ( reli @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f351]) ).
thf(f356,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( reli @ X2 @ sK11 )
= $false )
| ( ( sK1 @ sK11 )
= $true )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ sK7 @ X3 ) )
| ( ( reli @ X1 @ sK11 )
= $false )
| ( $false
= ( relr @ X3 @ X2 ) )
| ( ( sK1 @ sK11 )
= $true )
| ( ( reli @ sK7 @ X0 )
= $false )
| ( $false = $true ) ),
inference(superposition,[],[f304,f347]) ).
thf(f362,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( reli @ X1 @ sK11 )
= $false )
| ( ( reli @ X2 @ sK11 )
= $false )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( relr @ X3 @ X2 ) )
| ( ( reli @ sK7 @ X0 )
= $false )
| ( $false
= ( reli @ sK7 @ X3 ) )
| ( $false = $true )
| ( ( sK1 @ sK11 )
= $true ) ),
inference(duplicate_literal_removal,[],[f356]) ).
thf(f363,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( reli @ X2 @ sK11 )
= $false )
| ( ( reli @ X1 @ sK11 )
= $false )
| ( ( sK1 @ sK11 )
= $true )
| ( ( reli @ sK7 @ X0 )
= $false )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ sK7 @ X3 ) )
| ( $false
= ( relr @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f366,definition,
( spl12_1
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ X2 @ sK11 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f367,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( ( reli @ X2 @ sK11 )
= $false ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f369,definition,
( spl12_2
<=> ! [X4: $i,X3: $i] :
( ( $false
= ( reli @ sK7 @ X4 ) )
| ( $false
= ( relr @ X4 @ X3 ) )
| ( ( reli @ X3 @ sK11 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f370,plain,
( ! [X3: $i,X4: $i] :
( ( $false
= ( relr @ X4 @ X3 ) )
| ( $false
= ( reli @ sK7 @ X4 ) )
| ( ( reli @ X3 @ sK11 )
= $false ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f369]) ).
thf(f372,definition,
( spl12_3
<=> ! [X0: $i] :
( ( $false
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f373,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f372]) ).
thf(f375,definition,
( spl12_4
<=> ( ( sK1 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f377,plain,
( ( ( sK1 @ sK11 )
= $true )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f375]) ).
thf(f381,plain,
( spl12_2
| spl12_4
| spl12_2 ),
inference(avatar_split_clause,[],[f363,f369,f375,f369]) ).
thf(f384,plain,
( ( $false = $true )
| ( $false
= ( reli @ sK7 @ sK9 ) )
| ( $false
= ( reli @ sK10 @ sK11 ) )
| ~ spl12_2 ),
inference(superposition,[],[f320,f370]) ).
thf(f385,plain,
( ( $false
= ( reli @ sK7 @ sK9 ) )
| ( $false
= ( reli @ sK10 @ sK11 ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[],[f384]) ).
thf(f388,plain,
( ( $false
= ( reli @ sK10 @ sK11 ) )
| ( $false = $true )
| ~ spl12_2 ),
inference(forward_demodulation,[],[f385,f282]) ).
thf(f389,plain,
( ( $false
= ( reli @ sK10 @ sK11 ) )
| ~ spl12_2 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f392,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK8 @ X1 @ X2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f352]) ).
thf(f394,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( ( reli @ X2 @ ( sK8 @ X1 @ X2 ) )
=> ( X1 @ ( sK8 @ X1 @ X2 ) ) ) )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f392]) ).
thf(f396,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK8 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f394]) ).
thf(f397,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $true
= ( reli @ X2 @ ( sK8 @ X1 @ X2 ) ) )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f394]) ).
thf(f399,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( reli @ X5 @ sK11 ) )
| ( ( sK2 @ X3 )
= $true )
| ( ( reli @ sK11 @ X3 )
= $false )
| ( $false
= ( relr @ X4 @ X5 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( $false
= ( sK1 @ X3 ) )
| ( $false
= ( reli @ sK4 @ X4 ) )
| ( $true
= ( sK2 @ X0 ) )
| ( $false = $true )
| ( ( reli @ X2 @ sK11 )
= $false )
| ( $false
= ( reli @ sK11 @ X0 ) ) ),
inference(superposition,[],[f346,f249]) ).
thf(f407,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( reli @ sK4 @ X4 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( reli @ sK4 @ X1 ) )
| ( ( reli @ X2 @ sK11 )
= $false )
| ( ( reli @ sK11 @ X3 )
= $false )
| ( $false
= ( sK1 @ X3 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( relr @ X4 @ X5 ) )
| ( $true
= ( sK2 @ X0 ) )
| ( ( sK2 @ X3 )
= $true )
| ( $false
= ( reli @ X5 @ sK11 ) ) ),
inference(trivial_inequality_removal,[],[f399]) ).
thf(f411,plain,
( spl12_3
| spl12_3
| spl12_1
| spl12_1 ),
inference(avatar_split_clause,[],[f407,f366,f366,f372,f372]) ).
thf(f427,plain,
( ( $false = $true )
| ~ spl12_2 ),
inference(superposition,[],[f389,f327]) ).
thf(f432,plain,
( $false
| ~ spl12_2 ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f433,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f432]) ).
thf(f443,plain,
( ( $false
= ( reli @ sK10 @ sK11 ) )
| ( $false = $true )
| ( $false
= ( reli @ sK4 @ sK9 ) )
| ~ spl12_1 ),
inference(superposition,[],[f320,f367]) ).
thf(f444,plain,
( ( $false
= ( reli @ sK10 @ sK11 ) )
| ( $false
= ( reli @ sK4 @ sK9 ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f447,plain,
( ( $false = $true )
| ( $false
= ( reli @ sK4 @ sK9 ) )
| ~ spl12_1 ),
inference(forward_demodulation,[],[f444,f327]) ).
thf(f448,plain,
( ( $false
= ( reli @ sK4 @ sK9 ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f447]) ).
thf(f542,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( reli @ X0 @ X0 )
= $true )
| ( ( reli @ X0 @ X0 )
= $true ) ),
inference(superposition,[],[f273,f274]) ).
thf(f545,plain,
! [X0: $i] :
( ( ( reli @ X0 @ X0 )
= $true )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f542]) ).
thf(f546,plain,
! [X0: $i] :
( ( reli @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f601,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( X1 @ ( sK8 @ X1 @ X2 ) ) )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f602,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ( reli @ X3 @ X4 )
=> ( X1 @ X4 ) ) )
| ( $false
= ( X1 @ ( sK8 @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f601]) ).
thf(f603,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( X1 @ ( sK8 @ X1 @ X2 ) ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( X1 @ X4 ) )
| ( $false
= ( reli @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f602]) ).
thf(f638,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $true
= ( reli @ X2 @ ( sK8 @ X1 @ X2 ) ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f397]) ).
thf(f639,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( reli @ X2 @ ( sK8 @ X1 @ X2 ) ) )
| ( $true
= ( ( reli @ X3 @ X4 )
=> ( X1 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f638]) ).
thf(f640,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $true
= ( reli @ X2 @ ( sK8 @ X1 @ X2 ) ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( X1 @ X4 ) )
| ( $false
= ( reli @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f639]) ).
thf(f673,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( reli @ X1 @ X2 ) )
| ( $false
= ( reli @ X0 @ X3 ) )
| ( ( reli @ X0 @ X4 )
= $true )
| ( ( reli @ X0 @ X2 )
= $true )
| ( $false = $true ) ),
inference(superposition,[],[f603,f640]) ).
thf(f680,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X3 @ X4 ) )
| ( ( reli @ X0 @ X2 )
= $true )
| ( $false
= ( reli @ X1 @ X2 ) )
| ( ( reli @ X0 @ X4 )
= $true )
| ( $false
= ( reli @ X0 @ X3 ) )
| ( $false
= ( reli @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f673]) ).
thf(f1422,plain,
( ( $false = $true )
| ( ( sK1 @ sK11 )
= $false )
| ( ( sK2 @ sK11 )
= $true )
| ~ spl12_3 ),
inference(superposition,[],[f546,f373]) ).
thf(f1624,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ X2 @ X0 ) )
| ( ( reli @ X2 @ X1 )
= $true )
| ( ( reli @ X2 @ X1 )
= $true )
| ( $false != $false )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( reli @ X2 @ X0 ) ) ),
inference(equality_factoring,[],[f680]) ).
thf(f1648,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( reli @ X2 @ X1 )
= $true )
| ( $false
= ( reli @ X2 @ X0 ) )
| ( $false
= ( reli @ X0 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f1624]) ).
thf(f1649,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ X2 @ X0 ) )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( ( reli @ X2 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1648]) ).
thf(f2491,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( reli @ sK7 @ X0 )
= $false )
| ( ( reli @ sK4 @ X0 )
= $true ) ),
inference(superposition,[],[f1649,f261]) ).
thf(f2520,plain,
! [X0: $i] :
( ( ( reli @ sK7 @ X0 )
= $false )
| ( ( reli @ sK4 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f2491]) ).
thf(f2578,plain,
( ( $true
= ( reli @ sK4 @ sK9 ) )
| ( $false = $true ) ),
inference(superposition,[],[f282,f2520]) ).
thf(f2589,plain,
( $true
= ( reli @ sK4 @ sK9 ) ),
inference(trivial_inequality_removal,[],[f2578]) ).
thf(f2634,plain,
( ( $false = $true )
| ~ spl12_1 ),
inference(forward_demodulation,[],[f2589,f448]) ).
thf(f2635,plain,
( $false
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f2634]) ).
thf(f2636,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f2635]) ).
thf(f2665,plain,
( ( ( sK1 @ sK11 )
= $false )
| ( ( sK2 @ sK11 )
= $true )
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f1422]) ).
thf(f2672,plain,
( ( ( sK2 @ sK11 )
= $true )
| ( $false = $true )
| ~ spl12_3
| ~ spl12_4 ),
inference(forward_demodulation,[],[f2665,f377]) ).
thf(f2673,plain,
( ( ( sK2 @ sK11 )
= $true )
| ~ spl12_3
| ~ spl12_4 ),
inference(trivial_inequality_removal,[],[f2672]) ).
thf(f2684,plain,
( ( $false = $true )
| ~ spl12_3
| ~ spl12_4 ),
inference(forward_demodulation,[],[f2673,f328]) ).
thf(f2685,plain,
( $false
| ~ spl12_3
| ~ spl12_4 ),
inference(trivial_inequality_removal,[],[f2684]) ).
thf(f2686,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(avatar_contradiction_clause,[],[f2685]) ).
cnf(s5,plain,
( spl12_2
| spl12_2
| spl12_4 ),
inference(sat_conversion,[],[f381]) ).
cnf(s6,plain,
( spl12_2
| spl12_4 ),
inference(rat,[],[s5]) ).
cnf(s9,plain,
( spl12_1
| spl12_3
| spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f411]) ).
cnf(s10,plain,
( spl12_1
| spl12_3 ),
inference(rat,[],[s9]) ).
cnf(s13,plain,
~ spl12_2,
inference(sat_conversion,[],[f433]) ).
cnf(s114,plain,
~ spl12_1,
inference(sat_conversion,[],[f2636]) ).
cnf(s123,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(sat_conversion,[],[f2686]) ).
cnf(s131,plain,
spl12_3,
inference(rat,[],[s10,s114]) ).
cnf(s132,plain,
~ spl12_4,
inference(rat,[],[s123,s131]) ).
cnf(s134,plain,
$false,
inference(rat,[],[s6,s132,s13]) ).
thf(f2687,plain,
$false,
inference(avatar_sat_refutation,[],[s134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV441^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n001.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 16:10:06 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 Running higher-order theorem proving
% 0.25/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.46 % (1428422)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.69/0.46 % (1428432)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1889082628:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.69/0.46 % (1428433)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.69/0.46 % (1428433)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
% 0.69/0.46 % (1428429)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2537702572:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.69/0.46 % (1428427)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3828225457:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.69/0.46 % (1428428)lrs+10_16_si=on:nwc=1.5:random_seed=3291766081:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.69/0.46 % (1428431)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3451967057:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.69/0.46 % (1428430)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=1460632334: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)
% 0.69/0.46 % (1428433)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=897032241:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.69/0.46 % (1428429)Instruction limit reached!
% 0.69/0.46 % (1428429)------------------------------
% 0.69/0.46 % (1428429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.46 % (1428429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.46 % (1428429)CaDiCaL version: 2.1.3
% 0.69/0.46 % (1428429)Termination reason: Instruction limit
% 0.69/0.46 % (1428429)Termination phase: Property scanning
% 0.69/0.46 % (1428429)Time elapsed: 0.003 s
% 0.69/0.46 % (1428429)Peak memory usage: 10 MB
% 0.69/0.46 % (1428429)Instructions burned: 3 (million)
% 0.69/0.46 % (1428428)Instruction limit reached!
% 0.69/0.46 % (1428428)------------------------------
% 0.69/0.46 % (1428428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.46 % (1428428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.46 % (1428428)CaDiCaL version: 2.1.3
% 0.69/0.46 % (1428428)Termination reason: Instruction limit
% 0.69/0.46 % (1428428)Termination phase: Saturation
% 0.69/0.46 % (1428428)Time elapsed: 0.015 s
% 0.69/0.46 % (1428428)Peak memory usage: 11 MB
% 0.69/0.46 % (1428428)Instructions burned: 19 (million)
% 0.69/0.46 % (1428432)Instruction limit reached!
% 0.69/0.46 % (1428432)------------------------------
% 0.69/0.46 % (1428432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.46 % (1428432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.46 % (1428432)CaDiCaL version: 2.1.3
% 0.69/0.46 % (1428432)Termination reason: Instruction limit
% 0.69/0.46 % (1428432)Termination phase: Saturation
% 0.69/0.46 % (1428432)Time elapsed: 0.036 s
% 0.69/0.46 % (1428432)Peak memory usage: 12 MB
% 0.69/0.46 % (1428432)Instructions burned: 76 (million)
% 0.69/0.46 % (1428431)Instruction limit reached!
% 0.69/0.46 % (1428431)------------------------------
% 0.69/0.46 % (1428431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.46 % (1428431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.46 % (1428431)CaDiCaL version: 2.1.3
% 0.69/0.46 % (1428431)Termination reason: Instruction limit
% 0.69/0.46 % (1428431)Termination phase: Saturation
% 0.69/0.46 % (1428431)Time elapsed: 0.024 s
% 0.69/0.46 % (1428431)Peak memory usage: 11 MB
% 0.69/0.46 % (1428431)Instructions burned: 25 (million)
% 0.69/0.46 % (1428441)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=269885723:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.46 % (1428441)Instruction limit reached!
% 0.69/0.46 % (1428441)------------------------------
% 0.69/0.46 % (1428441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.49 % (1428441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.49 % (1428441)CaDiCaL version: 2.1.3
% 1.39/0.49 % (1428441)Termination reason: Instruction limit
% 1.39/0.49 % (1428441)Termination phase: Property scanning
% 1.39/0.49 % (1428441)Time elapsed: 0.002 s
% 1.39/0.49 % (1428441)Peak memory usage: 10 MB
% 1.39/0.49 % (1428441)Instructions burned: 2 (million)
% 1.39/0.49 % (1428442)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3180800744:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.39/0.49 % (1428443)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.39/0.49 % (1428442)Instruction limit reached!
% 1.39/0.49 % (1428442)------------------------------
% 1.39/0.49 % (1428442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.49 % (1428442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.49 % (1428442)CaDiCaL version: 2.1.3
% 1.39/0.49 % (1428442)Termination reason: Instruction limit
% 1.39/0.49 % (1428442)Termination phase: Function definition elimination
% 1.39/0.49 % (1428442)Time elapsed: 0.005 s
% 1.39/0.49 % (1428442)Peak memory usage: 10 MB
% 1.39/0.49 % (1428442)Instructions burned: 5 (million)
% 1.39/0.49 % (1428443)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=601497888:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.39/0.49 % (1428444)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1786323543:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.39/0.49 % (1428443)Instruction limit reached!
% 1.39/0.49 % (1428443)------------------------------
% 1.39/0.49 % (1428443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.49 % (1428443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.49 % (1428443)CaDiCaL version: 2.1.3
% 1.39/0.49 % (1428443)Termination reason: Instruction limit
% 1.39/0.49 % (1428443)Termination phase: Property scanning
% 1.39/0.49 % (1428443)Time elapsed: 0.006 s
% 1.39/0.49 % (1428443)Peak memory usage: 10 MB
% 1.39/0.49 % (1428443)Instructions burned: 8 (million)
% 1.39/0.49 % (1428446)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
% 1.39/0.49 % (1428446)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.39/0.49 % (1428446)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2480143572:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.39/0.49 % (1428444)Instruction limit reached!
% 1.39/0.49 % (1428444)------------------------------
% 1.39/0.49 % (1428444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.49 % (1428444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.49 % (1428444)CaDiCaL version: 2.1.3
% 1.39/0.49 % (1428444)Termination reason: Instruction limit
% 1.39/0.49 % (1428444)Termination phase: Saturation
% 1.39/0.49 % (1428444)Time elapsed: 0.010 s
% 1.39/0.49 % (1428444)Peak memory usage: 11 MB
% 1.39/0.49 % (1428444)Instructions burned: 12 (million)
% 1.39/0.49 % (1428427)Instruction limit reached!
% 1.39/0.49 % (1428427)------------------------------
% 1.39/0.49 % (1428427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.49 % (1428427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.49 % (1428427)CaDiCaL version: 2.1.3
% 1.39/0.49 % (1428427)Termination reason: Instruction limit
% 1.39/0.49 % (1428427)Termination phase: Saturation
% 1.39/0.49 % (1428427)Time elapsed: 0.072 s
% 1.39/0.49 % (1428427)Peak memory usage: 12 MB
% 1.39/0.49 % (1428427)Instructions burned: 87 (million)
% 1.39/0.49 % (1428448)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=3164279646:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.39/0.49 % (1428433)Instruction limit reached!
% 1.39/0.49 % (1428433)------------------------------
% 1.39/0.49 % (1428433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.53 % (1428433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.53 % (1428433)CaDiCaL version: 2.1.3
% 1.39/0.53 % (1428433)Termination reason: Instruction limit
% 1.39/0.53 % (1428433)Termination phase: Saturation
% 1.39/0.53 % (1428433)Time elapsed: 0.083 s
% 1.39/0.53 % (1428433)Peak memory usage: 12 MB
% 1.39/0.53 % (1428433)Instructions burned: 157 (million)
% 1.39/0.53 % (1428446)Instruction limit reached!
% 1.39/0.53 % (1428446)------------------------------
% 1.39/0.53 % (1428446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.53 % (1428446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.53 % (1428446)CaDiCaL version: 2.1.3
% 1.39/0.53 % (1428446)Termination reason: Instruction limit
% 1.39/0.53 % (1428446)Termination phase: Saturation
% 1.39/0.53 % (1428446)Time elapsed: 0.023 s
% 1.39/0.53 % (1428446)Peak memory usage: 12 MB
% 1.39/0.53 % (1428446)Instructions burned: 28 (million)
% 1.39/0.53 % (1428451)lrs+10_1_si=on:cs=on:random_seed=3644960418:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.39/0.53 % (1428453)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.39/0.53 % (1428456)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1077456597:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.39/0.53 % (1428453)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=1085681737:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.39/0.53 % (1428451)Instruction limit reached!
% 1.39/0.53 % (1428451)------------------------------
% 1.39/0.53 % (1428451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.53 % (1428451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.53 % (1428451)CaDiCaL version: 2.1.3
% 1.39/0.53 % (1428451)Termination reason: Instruction limit
% 1.39/0.53 % (1428451)Termination phase: Property scanning
% 1.39/0.53 % (1428451)Time elapsed: 0.007 s
% 1.39/0.53 % (1428451)Peak memory usage: 10 MB
% 1.39/0.53 % (1428451)Instructions burned: 9 (million)
% 1.39/0.53 % (1428453)Instruction limit reached!
% 1.39/0.53 % (1428453)------------------------------
% 1.39/0.53 % (1428453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.53 % (1428453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.53 % (1428453)CaDiCaL version: 2.1.3
% 1.39/0.53 % (1428453)Termination reason: Instruction limit
% 1.39/0.53 % (1428453)Termination phase: Property scanning
% 1.39/0.53 % (1428453)Time elapsed: 0.002 s
% 1.39/0.53 % (1428453)Peak memory usage: 10 MB
% 1.39/0.53 % (1428453)Instructions burned: 2 (million)
% 1.39/0.53 % (1428454)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1911679090:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.39/0.53 % (1428456)Refutation not found, incomplete strategy
% 1.39/0.53 % (1428456)------------------------------
% 1.39/0.53 % (1428456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.53 % (1428456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.53 % (1428456)CaDiCaL version: 2.1.3
% 1.39/0.53 % (1428456)Termination reason: Refutation not found, incomplete strategy
% 1.39/0.53 % (1428456)Time elapsed: 0.003 s
% 1.39/0.53 % (1428456)Peak memory usage: 12 MB
% 1.39/0.53 % (1428456)Instructions burned: 7 (million)
% 1.39/0.53 % (1428456)------------------------------
% 1.39/0.53 % (1428456)------------------------------
% 1.39/0.53 % (1428454)Refutation not found, incomplete strategy
% 1.39/0.53 % (1428454)------------------------------
% 1.39/0.53 % (1428454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.39/0.53 % (1428454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.39/0.53 % (1428454)CaDiCaL version: 2.1.3
% 1.39/0.53 % (1428454)Termination reason: Refutation not found, incomplete strategy
% 1.39/0.53 % (1428454)Time elapsed: 0.008 s
% 1.39/0.53 % (1428454)Peak memory usage: 12 MB
% 1.39/0.53 % (1428454)Instructions burned: 9 (million)
% 1.39/0.53 % (1428454)------------------------------
% 1.39/0.53 % (1428454)------------------------------
% 1.39/0.53 % (1428457)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=347093900:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.09/0.59 % (1428464)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=117340141:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.09/0.59 % (1428464)Instruction limit reached!
% 2.09/0.59 % (1428464)------------------------------
% 2.09/0.59 % (1428464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.59 % (1428464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.59 % (1428464)CaDiCaL version: 2.1.3
% 2.09/0.59 % (1428464)Termination reason: Instruction limit
% 2.09/0.59 % (1428464)Termination phase: Saturation
% 2.09/0.59 % (1428464)Time elapsed: 0.006 s
% 2.09/0.59 % (1428464)Peak memory usage: 11 MB
% 2.09/0.59 % (1428464)Instructions burned: 14 (million)
% 2.09/0.59 % (1428448)Instruction limit reached!
% 2.09/0.59 % (1428448)------------------------------
% 2.09/0.59 % (1428448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.59 % (1428463)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1343485026:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.09/0.59 % (1428448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.59 % (1428448)CaDiCaL version: 2.1.3
% 2.09/0.59 % (1428448)Termination reason: Instruction limit
% 2.09/0.59 % (1428448)Termination phase: Saturation
% 2.09/0.59 % (1428448)Time elapsed: 0.061 s
% 2.09/0.59 % (1428448)Peak memory usage: 13 MB
% 2.09/0.59 % (1428448)Instructions burned: 87 (million)
% 2.09/0.59 % (1428461)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2912933859:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.09/0.59 % (1428463)Refutation not found, incomplete strategy
% 2.09/0.59 % (1428463)------------------------------
% 2.09/0.59 % (1428463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.59 % (1428463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.59 % (1428463)CaDiCaL version: 2.1.3
% 2.09/0.59 % (1428463)Termination reason: Refutation not found, incomplete strategy
% 2.09/0.59 % (1428463)Time elapsed: 0.011 s
% 2.09/0.59 % (1428463)Peak memory usage: 12 MB
% 2.09/0.59 % (1428463)Instructions burned: 12 (million)
% 2.09/0.59 % (1428463)------------------------------
% 2.09/0.59 % (1428463)------------------------------
% 2.09/0.59 % (1428457)Instruction limit reached!
% 2.09/0.59 % (1428457)------------------------------
% 2.09/0.59 % (1428457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.59 % (1428457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.59 % (1428457)CaDiCaL version: 2.1.3
% 2.09/0.59 % (1428457)Termination reason: Instruction limit
% 2.09/0.59 % (1428457)Termination phase: Saturation
% 2.09/0.59 % (1428457)Time elapsed: 0.024 s
% 2.09/0.59 % (1428457)Peak memory usage: 12 MB
% 2.09/0.59 % (1428457)Instructions burned: 25 (million)
% 2.09/0.59 % (1428465)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3407062316: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)
% 2.09/0.59 % (1428468)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4032456636:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.09/0.59 % (1428465)Instruction limit reached!
% 2.09/0.59 % (1428465)------------------------------
% 2.09/0.59 % (1428465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.59 % (1428465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.59 % (1428465)CaDiCaL version: 2.1.3
% 2.09/0.59 % (1428465)Termination reason: Instruction limit
% 2.09/0.59 % (1428465)Termination phase: shuffling
% 2.09/0.59 % (1428465)Time elapsed: 0.002 s
% 2.09/0.59 % (1428465)Peak memory usage: 9 MB
% 2.09/0.59 % (1428465)Instructions burned: 2 (million)
% 2.09/0.59 % (1428461)Instruction limit reached!
% 2.09/0.59 % (1428461)------------------------------
% 2.09/0.59 % (1428461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.59 % (1428461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.59 % (1428461)CaDiCaL version: 2.1.3
% 2.09/0.59 % (1428461)Termination reason: Instruction limit
% 2.09/0.59 % (1428461)Termination phase: Saturation
% 2.09/0.63 % (1428461)Time elapsed: 0.019 s
% 2.09/0.63 % (1428461)Peak memory usage: 11 MB
% 2.09/0.63 % (1428461)Instructions burned: 15 (million)
% 2.09/0.63 % (1428468)Instruction limit reached!
% 2.09/0.63 % (1428468)------------------------------
% 2.09/0.63 % (1428468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.63 % (1428468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.63 % (1428468)CaDiCaL version: 2.1.3
% 2.09/0.63 % (1428468)Termination reason: Instruction limit
% 2.09/0.63 % (1428468)Termination phase: Saturation
% 2.09/0.63 % (1428468)Time elapsed: 0.011 s
% 2.09/0.63 % (1428468)Peak memory usage: 11 MB
% 2.09/0.63 % (1428468)Instructions burned: 26 (million)
% 2.09/0.63 % (1428471)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3698777349:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.09/0.63 % (1428475)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
% 2.09/0.63 % (1428475)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.09/0.63 % (1428476)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.09/0.63 % (1428472)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3217312528:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.09/0.63 % (1428475)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=1922394690:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.09/0.63 % (1428478)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2942852967:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.09/0.63 % (1428477)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=1947173368:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.09/0.63 % (1428476)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=2449868529:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.09/0.63 % (1428478)Instruction limit reached!
% 2.09/0.63 % (1428478)------------------------------
% 2.09/0.63 % (1428478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.63 % (1428478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.63 % (1428478)CaDiCaL version: 2.1.3
% 2.09/0.63 % (1428478)Termination reason: Instruction limit
% 2.09/0.63 % (1428478)Termination phase: Property scanning
% 2.09/0.63 % (1428478)Time elapsed: 0.004 s
% 2.09/0.63 % (1428478)Peak memory usage: 10 MB
% 2.09/0.63 % (1428478)Instructions burned: 7 (million)
% 2.09/0.63 % (1428476)Instruction limit reached!
% 2.09/0.63 % (1428476)------------------------------
% 2.09/0.63 % (1428476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.63 % (1428476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.63 % (1428476)CaDiCaL version: 2.1.3
% 2.09/0.63 % (1428476)Termination reason: Instruction limit
% 2.09/0.63 % (1428476)Termination phase: Property scanning
% 2.09/0.63 % (1428476)Time elapsed: 0.007 s
% 2.09/0.63 % (1428476)Peak memory usage: 11 MB
% 2.09/0.63 % (1428476)Instructions burned: 8 (million)
% 2.09/0.63 % (1428471)Instruction limit reached!
% 2.09/0.63 % (1428471)------------------------------
% 2.09/0.63 % (1428471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.09/0.63 % (1428471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/0.63 % (1428471)CaDiCaL version: 2.1.3
% 2.09/0.63 % (1428471)Termination reason: Instruction limit
% 2.09/0.63 % (1428471)Termination phase: Saturation
% 2.09/0.63 % (1428471)Time elapsed: 0.020 s
% 2.09/0.63 % (1428471)Peak memory usage: 11 MB
% 2.09/0.63 % (1428471)Instructions burned: 24 (million)
% 2.09/0.63 % (1428475)Instruction limit reached!
% 2.09/0.63 % (1428475)------------------------------
% 2.09/0.63 % (1428475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.73 % (1428475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.73 % (1428475)CaDiCaL version: 2.1.3
% 2.77/0.73 % (1428475)Termination reason: Instruction limit
% 2.77/0.73 % (1428475)Termination phase: Saturation
% 2.77/0.73 % (1428475)Time elapsed: 0.012 s
% 2.77/0.73 % (1428475)Peak memory usage: 11 MB
% 2.77/0.73 % (1428475)Instructions burned: 14 (million)
% 2.77/0.73 % (1428487)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1507187712:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.77/0.73 % (1428477)Instruction limit reached!
% 2.77/0.73 % (1428477)------------------------------
% 2.77/0.73 % (1428477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.73 % (1428477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.73 % (1428477)CaDiCaL version: 2.1.3
% 2.77/0.73 % (1428477)Termination reason: Instruction limit
% 2.77/0.73 % (1428477)Termination phase: Saturation
% 2.77/0.73 % (1428477)Time elapsed: 0.030 s
% 2.77/0.73 % (1428477)Peak memory usage: 12 MB
% 2.77/0.73 % (1428477)Instructions burned: 31 (million)
% 2.77/0.73 % (1428486)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2713973786:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.77/0.73 % (1428487)Instruction limit reached!
% 2.77/0.73 % (1428487)------------------------------
% 2.77/0.73 % (1428487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.73 % (1428487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.73 % (1428487)CaDiCaL version: 2.1.3
% 2.77/0.73 % (1428487)Termination reason: Instruction limit
% 2.77/0.73 % (1428487)Termination phase: Saturation
% 2.77/0.73 % (1428487)Time elapsed: 0.011 s
% 2.77/0.73 % (1428487)Peak memory usage: 12 MB
% 2.77/0.73 % (1428487)Instructions burned: 21 (million)
% 2.77/0.73 % (1428489)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2293849984:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.77/0.73 % (1428488)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2396711463:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.77/0.73 % (1428486)Instruction limit reached!
% 2.77/0.73 % (1428486)------------------------------
% 2.77/0.73 % (1428486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.73 % (1428486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.73 % (1428486)CaDiCaL version: 2.1.3
% 2.77/0.73 % (1428486)Termination reason: Instruction limit
% 2.77/0.73 % (1428486)Termination phase: Saturation
% 2.77/0.73 % (1428486)Time elapsed: 0.020 s
% 2.77/0.73 % (1428486)Peak memory usage: 11 MB
% 2.77/0.73 % (1428486)Instructions burned: 23 (million)
% 2.77/0.73 % (1428472)Instruction limit reached!
% 2.77/0.73 % (1428472)------------------------------
% 2.77/0.73 % (1428472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.73 % (1428472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.73 % (1428472)CaDiCaL version: 2.1.3
% 2.77/0.73 % (1428472)Termination reason: Instruction limit
% 2.77/0.73 % (1428472)Termination phase: Saturation
% 2.77/0.73 % (1428472)Time elapsed: 0.054 s
% 2.77/0.73 % (1428472)Peak memory usage: 12 MB
% 2.77/0.73 % (1428472)Instructions burned: 60 (million)
% 2.77/0.73 % (1428494)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2605001600:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.77/0.73 % (1428493)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1410865997:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.77/0.73 % (1428493)Refutation not found, incomplete strategy
% 2.77/0.73 % (1428493)------------------------------
% 2.77/0.73 % (1428493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.73 % (1428493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.73 % (1428493)CaDiCaL version: 2.1.3
% 2.77/0.73 % (1428493)Termination reason: Refutation not found, incomplete strategy
% 2.77/0.73 % (1428493)Time elapsed: 0.009 s
% 2.77/0.73 % (1428493)Peak memory usage: 12 MB
% 2.77/0.73 % (1428493)Instructions burned: 9 (million)
% 2.77/0.73 % (1428494)Instruction limit reached!
% 2.77/0.73 % (1428494)------------------------------
% 2.77/0.73 % (1428494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.84 % (1428494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.84 % (1428494)CaDiCaL version: 2.1.3
% 3.20/0.84 % (1428494)Termination reason: Instruction limit
% 3.20/0.84 % (1428494)Termination phase: Saturation
% 3.20/0.84 % (1428494)Time elapsed: 0.018 s
% 3.20/0.84 % (1428494)Peak memory usage: 12 MB
% 3.20/0.84 % (1428494)Instructions burned: 45 (million)
% 3.20/0.84 % (1428493)------------------------------
% 3.20/0.84 % (1428493)------------------------------
% 3.20/0.84 % (1428497)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.20/0.84 % (1428497)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=918558378:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 3.20/0.84 % (1428498)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1560061838:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 3.20/0.84 % (1428502)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=2021302681:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 3.20/0.84 % (1428497)Instruction limit reached!
% 3.20/0.84 % (1428497)------------------------------
% 3.20/0.84 % (1428497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.84 % (1428497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.84 % (1428497)CaDiCaL version: 2.1.3
% 3.20/0.84 % (1428497)Termination reason: Instruction limit
% 3.20/0.84 % (1428497)Termination phase: Property scanning
% 3.20/0.84 % (1428497)Time elapsed: 0.006 s
% 3.20/0.84 % (1428497)Peak memory usage: 10 MB
% 3.20/0.84 % (1428497)Instructions burned: 7 (million)
% 3.20/0.84 % (1428502)Refutation not found, incomplete strategy
% 3.20/0.84 % (1428502)------------------------------
% 3.20/0.84 % (1428502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.84 % (1428502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.84 % (1428502)CaDiCaL version: 2.1.3
% 3.20/0.84 % (1428502)Termination reason: Refutation not found, incomplete strategy
% 3.20/0.84 % (1428502)Time elapsed: 0.003 s
% 3.20/0.84 % (1428502)Peak memory usage: 12 MB
% 3.20/0.84 % (1428502)Instructions burned: 10 (million)
% 3.20/0.84 % (1428502)------------------------------
% 3.20/0.84 % (1428502)------------------------------
% 3.20/0.84 % (1428498)Refutation not found, incomplete strategy
% 3.20/0.84 % (1428498)------------------------------
% 3.20/0.84 % (1428498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.84 % (1428498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.84 % (1428498)CaDiCaL version: 2.1.3
% 3.20/0.84 % (1428498)Termination reason: Refutation not found, incomplete strategy
% 3.20/0.84 % (1428498)Time elapsed: 0.009 s
% 3.20/0.84 % (1428498)Peak memory usage: 12 MB
% 3.20/0.84 % (1428498)Instructions burned: 8 (million)
% 3.20/0.84 % (1428498)------------------------------
% 3.20/0.84 % (1428498)------------------------------
% 3.20/0.84 % (1428507)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=321240721:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.20/0.84 % (1428503)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.20/0.84 % (1428507)Instruction limit reached!
% 3.20/0.84 % (1428507)------------------------------
% 3.20/0.84 % (1428507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.84 % (1428507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.84 % (1428507)CaDiCaL version: 2.1.3
% 3.20/0.84 % (1428507)Termination reason: Instruction limit
% 3.20/0.84 % (1428507)Termination phase: Saturation
% 3.20/0.84 % (1428507)Time elapsed: 0.007 s
% 3.20/0.84 % (1428507)Peak memory usage: 12 MB
% 3.20/0.84 % (1428507)Instructions burned: 26 (million)
% 3.20/0.84 % (1428503)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3695486380:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 3.20/0.84 % (1428503)Instruction limit reached!
% 3.20/0.84 % (1428503)------------------------------
% 3.20/0.85 % (1428503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428503)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428503)Termination reason: Instruction limit
% 3.20/0.85 % (1428503)Termination phase: Property scanning
% 3.20/0.85 % (1428503)Time elapsed: 0.005 s
% 3.20/0.85 % (1428503)Peak memory usage: 10 MB
% 3.20/0.85 % (1428503)Instructions burned: 6 (million)
% 3.20/0.85 % (1428513)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=3925589580:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.20/0.85 % (1428508)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2301539334:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.20/0.85 % (1428510)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=267995530:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.20/0.85 % (1428508)Instruction limit reached!
% 3.20/0.85 % (1428508)------------------------------
% 3.20/0.85 % (1428508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428508)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428508)Termination reason: Instruction limit
% 3.20/0.85 % (1428508)Termination phase: Saturation
% 3.20/0.85 % (1428508)Time elapsed: 0.016 s
% 3.20/0.85 % (1428508)Peak memory usage: 12 MB
% 3.20/0.85 % (1428508)Instructions burned: 19 (million)
% 3.20/0.85 % (1428514)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=4222810093:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.20/0.85 % (1428489)Instruction limit reached!
% 3.20/0.85 % (1428489)------------------------------
% 3.20/0.85 % (1428489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428489)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428489)Termination reason: Instruction limit
% 3.20/0.85 % (1428489)Termination phase: Saturation
% 3.20/0.85 % (1428489)Time elapsed: 0.121 s
% 3.20/0.85 % (1428489)Peak memory usage: 13 MB
% 3.20/0.85 % (1428489)Instructions burned: 143 (million)
% 3.20/0.85 % (1428518)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2966688065:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.20/0.85 % (1428518)Refutation not found, incomplete strategy
% 3.20/0.85 % (1428518)------------------------------
% 3.20/0.85 % (1428518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428518)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428518)Termination reason: Refutation not found, incomplete strategy
% 3.20/0.85 % (1428518)Time elapsed: 0.008 s
% 3.20/0.85 % (1428518)Peak memory usage: 12 MB
% 3.20/0.85 % (1428518)Instructions burned: 8 (million)
% 3.20/0.85 % (1428518)------------------------------
% 3.20/0.85 % (1428518)------------------------------
% 3.20/0.85 % (1428514)Instruction limit reached!
% 3.20/0.85 % (1428514)------------------------------
% 3.20/0.85 % (1428514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428514)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428514)Termination reason: Instruction limit
% 3.20/0.85 % (1428514)Termination phase: Saturation
% 3.20/0.85 % (1428514)Time elapsed: 0.040 s
% 3.20/0.85 % (1428514)Peak memory usage: 12 MB
% 3.20/0.85 % (1428514)Instructions burned: 46 (million)
% 3.20/0.85 % (1428520)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2936950743:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.20/0.85 % (1428522)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.20/0.85 % (1428520)Instruction limit reached!
% 3.20/0.85 % (1428520)------------------------------
% 3.20/0.85 % (1428520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428520)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428520)Termination reason: Instruction limit
% 3.20/0.85 % (1428520)Termination phase: Saturation
% 3.20/0.85 % (1428520)Time elapsed: 0.018 s
% 3.20/0.85 % (1428520)Peak memory usage: 12 MB
% 3.20/0.85 % (1428520)Instructions burned: 21 (million)
% 3.20/0.85 % (1428522)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3751417163:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 3.20/0.85 % (1428523)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1104879687:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.20/0.85 % (1428525)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1271004341:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 3.20/0.85 % (1428523)Instruction limit reached!
% 3.20/0.85 % (1428523)------------------------------
% 3.20/0.85 % (1428523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428523)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428523)Termination reason: Instruction limit
% 3.20/0.85 % (1428523)Termination phase: Saturation
% 3.20/0.85 % (1428523)Time elapsed: 0.014 s
% 3.20/0.85 % (1428523)Peak memory usage: 12 MB
% 3.20/0.85 % (1428523)Instructions burned: 13 (million)
% 3.20/0.85 % (1428525)Instruction limit reached!
% 3.20/0.85 % (1428525)------------------------------
% 3.20/0.85 % (1428525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428525)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428525)Termination reason: Instruction limit
% 3.20/0.85 % (1428525)Termination phase: Saturation
% 3.20/0.85 % (1428525)Time elapsed: 0.019 s
% 3.20/0.85 % (1428525)Peak memory usage: 13 MB
% 3.20/0.85 % (1428525)Instructions burned: 69 (million)
% 3.20/0.85 % (1428530)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2896079000:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.20/0.85 % (1428530)Instruction limit reached!
% 3.20/0.85 % (1428530)------------------------------
% 3.20/0.85 % (1428530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428530)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428530)Termination reason: Instruction limit
% 3.20/0.85 % (1428530)Termination phase: Saturation
% 3.20/0.85 % (1428530)Time elapsed: 0.009 s
% 3.20/0.85 % (1428530)Peak memory usage: 12 MB
% 3.20/0.85 % (1428530)Instructions burned: 33 (million)
% 3.20/0.85 % (1428529)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=225825897:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 3.20/0.85 % (1428532)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=214942173:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.20/0.85 % (1428529)Refutation not found, incomplete strategy
% 3.20/0.85 % (1428529)------------------------------
% 3.20/0.85 % (1428529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428529)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428529)Termination reason: Refutation not found, incomplete strategy
% 3.20/0.85 % (1428529)Time elapsed: 0.027 s
% 3.20/0.85 % (1428529)Peak memory usage: 12 MB
% 3.20/0.85 % (1428529)Instructions burned: 31 (million)
% 3.20/0.85 % (1428529)------------------------------
% 3.20/0.85 % (1428529)------------------------------
% 3.20/0.85 % (1428488) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1428422-1428488"...
% 3.20/0.85 % (1428532)Instruction limit reached!
% 3.20/0.85 % (1428532)------------------------------
% 3.20/0.85 % (1428532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.85 % (1428532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.85 % (1428532)CaDiCaL version: 2.1.3
% 3.20/0.85 % (1428532)Termination reason: Instruction limit
% 3.20/0.85 % (1428532)Termination phase: Saturation
% 3.20/0.85 % (1428532)Time elapsed: 0.042 s
% 3.20/0.85 % (1428532)Peak memory usage: 13 MB
% 3.20/0.85 % (1428532)Instructions burned: 140 (million)
% 3.20/0.85 % (1428488)...printing done.
% 3.20/0.85 % (1428488)Refutation found. Thanks to Tanya!
% 3.20/0.85 % SZS status Theorem for theBenchmark
% 3.20/0.85 % SZS output start Proof for theBenchmark
% See solution above
% 3.20/0.86 % (1428488)------------------------------
% 3.20/0.86 % (1428488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.20/0.86 % (1428488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.20/0.86 % (1428488)CaDiCaL version: 2.1.3
% 3.20/0.86 % (1428488)Termination reason: Refutation
% 3.20/0.86 % (1428488)Time elapsed: 0.282 s
% 3.20/0.86 % (1428488)Peak memory usage: 15 MB
% 3.20/0.86 % (1428488)Instructions burned: 326 (million)
% 3.20/0.86 % (1428422)Success in time 0.554 s
% 3.20/0.86 % Vampire exiting
%------------------------------------------------------------------------------