%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV443^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 0.30s 0.41s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 16
% Syntax : Number of formulae : 134 ( 94 unt; 0 typ; 2 def)
% Number of atoms : 1209 ( 209 equ; 0 cnn)
% Maximal formula atoms : 11 ( 9 avg)
% Number of connectives : 1956 ( 78 ~; 158 |; 0 &;1360 @)
% ( 2 <=>; 190 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 207 ( 207 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 13 con; 0-4 aty)
% ( 168 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 504 ( 0 sgn 90 !; 2 ?; 504 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vNOT: $o > $o ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
sK0: individuals ).
thf(func_def_57,type,
sK1: $i > $o ).
thf(func_def_58,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_59,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_61,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_62,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_63,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_66,type,
sK10: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) )
= cs4_atom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_atom) ).
thf(f19,axiom,
( cs4_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ reli @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f23,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X0 ) ) )
= cs4_box ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_box) ).
thf(f30,axiom,
( bl_atom
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_atom) ).
thf(f31,axiom,
( bl_princ
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_princ) ).
thf(f34,axiom,
( bl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( cs4_impl @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_impl) ).
thf(f38,axiom,
( ( ^ [X0: individuals,X1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ X0 ) ) @ X1 ) ) )
= bl_says ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_says) ).
thf(f39,axiom,
bl_valid = mvalid,
file('/export/starexec/sandbox/benchmark/Axioms/SWV010^0.ax',bl_valid_def) ).
thf(f41,conjecture,
! [X0: individuals,X1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bl_id2) ).
thf(f42,negated_conjecture,
~ ! [X0: individuals,X1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f45,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f46,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f53,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f61,plain,
~ ! [X0: individuals,X1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f62,plain,
~ ! [X1: $i > $o,X0: individuals] :
( ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f61]) ).
thf(f65,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f68,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f76,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f77,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f84,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f85,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f86,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f88,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f90,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f94,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f96,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f97,plain,
? [X0: individuals,X1: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f62]) ).
thf(f98,plain,
( $true
!= ( bl_valid @ ( bl_impl @ ( bl_says @ sK0 @ ( bl_atom @ sK1 ) ) @ ( bl_says @ sK0 @ ( bl_atom @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f97]) ).
thf(f100,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f102,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f108,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f114,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f116,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f117,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f119,plain,
( $true
!= ( bl_valid @ ( bl_impl @ ( bl_says @ sK0 @ ( bl_atom @ sK1 ) ) @ ( bl_says @ sK0 @ ( bl_atom @ sK1 ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f121,plain,
mvalid = bl_valid,
inference(cnf_transformation,[],[f39]) ).
thf(f123,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f124,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f126,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f131,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f134,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f137,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f142,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,[],[f100,f134,f102]) ).
thf(f144,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,[],[f108,f124]) ).
thf(f147,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,[],[f123,f124,f142]) ).
thf(f151,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,[],[f131,f124,f124]) ).
thf(f153,plain,
( bl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f117,f144]) ).
thf(f154,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,[],[f126,f144]) ).
thf(f157,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,[],[f137,f147]) ).
thf(f159,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,[],[f116,f151,f147,f154]) ).
thf(f160,plain,
( bl_valid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f121,f114]) ).
thf(f164,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [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 ) )
@ sK0
@ ( ^ [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 )
@ sK1 ) )
@ ( ^ [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 ) )
@ sK0
@ ( ^ [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 )
@ sK1 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f119,f160,f157,f159,f153,f159,f153]) ).
thf(f257,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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f258,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( princ_inj @ sK0 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK1 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK8 )
= $false ),
inference(sigma_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ 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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK8 @ 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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) )
@ sK9 ) ),
inference(sigma_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( $false
= ( ( reli @ sK8 @ sK9 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ 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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ 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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f264,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f265,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f266,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( reli @ sK9 @ 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 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X1: $i] :
( ( ( reli @ sK9 @ 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 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f269,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 ) ) ) ) ) ) ) ) )
| ( $false
= ( reli @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( ^ [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 ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f269]) ).
thf(f271,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 ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ sK9 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( 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 ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
@ X3 )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( ( reli @ X2 @ X3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( reli @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $true )
| ( ( reli @ X2 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK9 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X4 ) )
| ( ( reli @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( reli @ X2 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X4 ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ ( sK10 @ X3 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X4 ) )
| ( ( reli @ X2 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( reli @ X3 @ X4 )
=> ( sK1 @ X4 ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( reli @ X2 @ X3 )
= $false )
| ( $false
= ( ( reli @ X3 @ ( sK10 @ X3 ) )
=> ( princ_inj @ sK0 @ ( sK10 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ X2 @ X3 )
= $false )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( sK1 @ X4 )
= $true )
| ( $false
= ( ( reli @ X3 @ ( sK10 @ X3 ) )
=> ( princ_inj @ sK0 @ ( sK10 @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( princ_inj @ sK0 @ ( sK10 @ X3 ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ X2 @ X3 )
= $false )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( sK1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( reli @ X3 @ ( sK10 @ X3 ) )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( ( reli @ X3 @ X4 )
= $false )
| ( ( reli @ X2 @ X3 )
= $false )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( sK1 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f281]) ).
thf(f284,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK9 @ 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 ) ) ) ) ) ) ) ) )
@ sK11 ) ),
inference(sigma_proxy_clausification,[],[f264]) ).
thf(f285,plain,
( $false
= ( ( reli @ sK9 @ sK11 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK11 @ 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 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK11 @ 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 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( $true
= ( reli @ sK9 @ sK11 ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f288,plain,
( $false
= ( ^ [Y0: $i] :
( ( relr @ sK11 @ 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 ) ) ) ) ) ) )
@ sK12 ) ),
inference(sigma_proxy_clausification,[],[f286]) ).
thf(f289,plain,
( $false
= ( ( relr @ sK11 @ sK12 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( relr @ sK11 @ sK12 )
= $true ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f292,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
@ sK13 ) ),
inference(sigma_proxy_clausification,[],[f290]) ).
thf(f293,plain,
( $false
= ( ( reli @ sK12 @ sK13 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f294,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( ( reli @ sK12 @ sK13 )
= $true ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f296,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f298,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X1: $i] :
( ( ( reli @ sK13 @ X1 )
=> ( princ_inj @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
! [X1: $i] :
( ( $true
= ( princ_inj @ sK0 @ X1 ) )
| ( $false
= ( reli @ sK13 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK13 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK14 ) ),
inference(sigma_proxy_clausification,[],[f296]) ).
thf(f303,plain,
( $false
= ( ( reli @ sK13 @ sK14 )
=> ( sK1 @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f302]) ).
thf(f304,plain,
( $false
= ( sK1 @ sK14 ) ),
inference(imp_proxy_clausification,[],[f303]) ).
thf(f305,plain,
( ( reli @ sK13 @ sK14 )
= $true ),
inference(imp_proxy_clausification,[],[f303]) ).
thf(f306,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ X0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true )
| ( $false = $true )
| ( $false
= ( reli @ sK13 @ ( sK10 @ X0 ) ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( $false
= ( reli @ X2 @ X0 ) )
| ( $false
= ( relr @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f282,f301]) ).
thf(f311,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ sK13 @ ( sK10 @ X0 ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X0 ) )
| ( $false
= ( reli @ X0 @ X3 ) )
| ( $false
= ( reli @ sK9 @ X1 ) )
| ( ( sK1 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[],[f306]) ).
thf(f339,definition,
( spl15_3
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( reli @ X1 @ sK13 ) )
| ( $false
= ( reli @ sK9 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
thf(f340,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ X1 @ sK13 ) )
| ( $false
= ( reli @ sK9 @ X0 ) ) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f339]) ).
thf(f346,definition,
( spl15_5
<=> ! [X2: $i] :
( ( ( sK1 @ X2 )
= $true )
| ( $false
= ( reli @ sK13 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
thf(f347,plain,
( ! [X2: $i] :
( ( $false
= ( reli @ sK13 @ X2 ) )
| ( ( sK1 @ X2 )
= $true ) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f350,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ X4 @ sK13 ) )
| ( $false
= ( reli @ sK9 @ X3 ) )
| ( $false = $true )
| ( ( sK1 @ X5 )
= $true )
| ( $false
= ( relr @ X3 @ X4 ) )
| ( $false
= ( reli @ X1 @ sK13 ) )
| ( $false
= ( reli @ sK9 @ X0 ) )
| ( $false
= ( reli @ sK13 @ X5 ) )
| ( ( sK1 @ X2 )
= $true )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ sK13 @ X2 ) ) ),
inference(constrained_superposition,[],[f311,f283]) ).
thf(f366,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ sK13 @ X2 ) )
| ( $false
= ( reli @ sK9 @ X0 ) )
| ( $false
= ( relr @ X3 @ X4 ) )
| ( $false
= ( reli @ sK13 @ X5 ) )
| ( $false
= ( reli @ X4 @ sK13 ) )
| ( $false
= ( reli @ sK9 @ X3 ) )
| ( ( sK1 @ X2 )
= $true )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ X1 @ sK13 ) )
| ( ( sK1 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[],[f350]) ).
thf(f380,plain,
( spl15_5
| spl15_3
| spl15_3
| spl15_5 ),
inference(avatar_split_clause,[],[f366,f346,f339,f339,f346]) ).
thf(f383,plain,
( ( $false
= ( reli @ sK9 @ sK11 ) )
| ( $false = $true )
| ( ( reli @ sK12 @ sK13 )
= $false )
| ~ spl15_3 ),
inference(constrained_superposition,[],[f291,f340]) ).
thf(f385,plain,
( ( $false
= ( reli @ sK9 @ sK11 ) )
| ( ( reli @ sK12 @ sK13 )
= $false )
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f388,plain,
( ( $false = $true )
| ( ( reli @ sK12 @ sK13 )
= $false )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f385,f287]) ).
thf(f389,plain,
( ( ( reli @ sK12 @ sK13 )
= $false )
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f393,plain,
( ( $false = $true )
| ~ spl15_3 ),
inference(forward_demodulation,[],[f389,f295]) ).
thf(f394,plain,
( $false
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f395,plain,
~ spl15_3,
inference(avatar_contradiction_clause,[],[f394]) ).
thf(f403,plain,
( ( ( sK1 @ sK14 )
= $true )
| ( $false = $true )
| ~ spl15_5 ),
inference(constrained_superposition,[],[f305,f347]) ).
thf(f406,plain,
( ( ( sK1 @ sK14 )
= $true )
| ~ spl15_5 ),
inference(trivial_inequality_removal,[],[f403]) ).
thf(f411,plain,
( ( $false = $true )
| ~ spl15_5 ),
inference(forward_demodulation,[],[f406,f304]) ).
thf(f412,plain,
( $false
| ~ spl15_5 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f413,plain,
~ spl15_5,
inference(avatar_contradiction_clause,[],[f412]) ).
cnf(s6,plain,
( spl15_3
| spl15_5
| spl15_3
| spl15_5 ),
inference(sat_conversion,[],[f380]) ).
cnf(s7,plain,
( spl15_3
| spl15_5 ),
inference(rat,[],[s6]) ).
cnf(s10,plain,
~ spl15_3,
inference(sat_conversion,[],[f395]) ).
cnf(s12,plain,
~ spl15_5,
inference(sat_conversion,[],[f413]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s7,s12,s10]) ).
thf(f414,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV443^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n016.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 16:09:19 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running higher-order theorem proving
% 0.23/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.41 % (532705)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.41 % (532711)lrs+10_16_si=on:nwc=1.5:random_seed=3049653446:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.41 % (532716)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.41 % (532716)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
% 0.30/0.41 % (532711)Instruction limit reached!
% 0.30/0.41 % (532711)------------------------------
% 0.30/0.41 % (532711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (532711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (532711)CaDiCaL version: 2.1.3
% 0.30/0.41 % (532711)Termination reason: Instruction limit
% 0.30/0.41 % (532711)Termination phase: Saturation
% 0.30/0.41 % (532711)Time elapsed: 0.008 s
% 0.30/0.41 % (532711)Peak memory usage: 12 MB
% 0.30/0.41 % (532711)Instructions burned: 18 (million)
% 0.30/0.41 % (532712)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2800311402:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.41 % (532714)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1260767100:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.41 % (532713)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=3632573150: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)
% 0.30/0.41 % (532715)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2802808553:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.41 % (532716)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=2215909864:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.41 % (532710)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1944575864:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.41 % (532712)Instruction limit reached!
% 0.30/0.41 % (532712)------------------------------
% 0.30/0.41 % (532712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (532712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (532712)CaDiCaL version: 2.1.3
% 0.30/0.41 % (532712)Termination reason: Instruction limit
% 0.30/0.41 % (532712)Termination phase: Property scanning
% 0.30/0.41 % (532712)Time elapsed: 0.003 s
% 0.30/0.41 % (532712)Peak memory usage: 10 MB
% 0.30/0.41 % (532712)Instructions burned: 3 (million)
% 0.30/0.41 % (532718)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2143717025:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.41 % (532718)Instruction limit reached!
% 0.30/0.41 % (532718)------------------------------
% 0.30/0.41 % (532718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (532718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (532718)CaDiCaL version: 2.1.3
% 0.30/0.41 % (532718)Termination reason: Instruction limit
% 0.30/0.41 % (532718)Termination phase: Property scanning
% 0.30/0.41 % (532718)Time elapsed: 0.001 s
% 0.30/0.41 % (532718)Peak memory usage: 10 MB
% 0.30/0.41 % (532718)Instructions burned: 2 (million)
% 0.30/0.41 % (532714)Instruction limit reached!
% 0.30/0.41 % (532714)------------------------------
% 0.30/0.41 % (532714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (532714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (532714)CaDiCaL version: 2.1.3
% 0.30/0.41 % (532714)Termination reason: Instruction limit
% 0.30/0.41 % (532714)Termination phase: Saturation
% 0.30/0.41 % (532714)Time elapsed: 0.024 s
% 0.30/0.41 % (532714)Peak memory usage: 12 MB
% 0.30/0.41 % (532714)Instructions burned: 25 (million)
% 0.30/0.41 % (532725)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3786504593:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.30/0.41 % (532727)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.41 % (532725)Instruction limit reached!
% 0.30/0.41 % (532725)------------------------------
% 0.30/0.41 % (532725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (532725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (532725)CaDiCaL version: 2.1.3
% 0.30/0.41 % (532725)Termination reason: Instruction limit
% 0.30/0.41 % (532725)Termination phase: Property scanning
% 0.30/0.41 % (532725)Time elapsed: 0.003 s
% 0.30/0.41 % (532725)Peak memory usage: 11 MB
% 0.30/0.41 % (532725)Instructions burned: 6 (million)
% 0.30/0.41 % (532727)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1512260110:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/0.41 % (532710) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-532705-532710"...
% 0.30/0.41 % (532727)Instruction limit reached!
% 0.30/0.41 % (532727)------------------------------
% 0.30/0.41 % (532727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.41 % (532727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.41 % (532727)CaDiCaL version: 2.1.3
% 0.30/0.41 % (532727)Termination reason: Instruction limit
% 0.30/0.41 % (532727)Termination phase: Property scanning
% 0.30/0.41 % (532727)Time elapsed: 0.003 s
% 0.30/0.41 % (532727)Peak memory usage: 10 MB
% 0.30/0.41 % (532727)Instructions burned: 7 (million)
% 0.30/0.41 % (532710)...printing done.
% 0.30/0.41 % (532710)Refutation found. Thanks to Tanya!
% 0.30/0.41 % SZS status Theorem for theBenchmark
% 0.30/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.42 % (532710)------------------------------
% 0.30/0.42 % (532710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.42 % (532710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.42 % (532710)CaDiCaL version: 2.1.3
% 0.30/0.42 % (532710)Termination reason: Refutation
% 0.30/0.42 % (532710)Time elapsed: 0.043 s
% 0.30/0.42 % (532710)Peak memory usage: 13 MB
% 0.30/0.42 % (532710)Instructions burned: 47 (million)
% 0.30/0.42 % (532705)Success in time 0.084 s
% 0.30/0.42 % Vampire exiting
%------------------------------------------------------------------------------