%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV444^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:08 AM UTC 2026
% Result : Theorem 0.63s 0.45s
% Output : Refutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 27
% Syntax : Number of formulae : 208 ( 122 unt; 0 typ; 9 def)
% Number of atoms : 1578 ( 275 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 2426 ( 128 ~; 225 |; 0 &;1661 @)
% ( 9 <=>; 208 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 20 con; 0-4 aty)
% ( 195 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 622 ( 0 sgn 130 !; 2 ?; 622 :)
% 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_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
vIMP: $o > $o > $o ).
thf(func_def_54,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
sK0: individuals ).
thf(func_def_57,type,
sK1: $i > $o ).
thf(func_def_60,type,
sK4: $i > $i ).
thf(func_def_65,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_66,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_67,type,
sK11: $i > ( $i > $o ) > $i ).
thf(func_def_68,type,
sK12: $i > ( $i > $o ) > $i ).
thf(func_def_69,type,
sK13: $i > ( $i > $o ) > $i ).
thf(func_def_70,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_72,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
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,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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(f10,axiom,
( mall
= ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mall) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( cs4_atom
= ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f22,axiom,
( cs4_all
= ( ^ [X0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_all) ).
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(f24,axiom,
( cs4_valid
= ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_valid_def) ).
thf(f30,axiom,
( bl_atom
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_atom) ).
thf(f31,axiom,
( bl_princ
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
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(f40,axiom,
( cs4_valid
@ ( cs4_all
@ ^ [X0: individuals] : ( cs4_impl @ ( princ_inj @ X0 ) @ ( princ_inj @ loca ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',loca_strength) ).
thf(f41,conjecture,
! [X0: individuals,X1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_strength) ).
thf(f42,negated_conjecture,
~ ! [X0: individuals,X1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f45,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f46,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f48,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f51,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f53,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
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(f57,plain,
( mall
= ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f58,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f62,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f69,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f72,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f73,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ Y0 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f74,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f75,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f86,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f87,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f90,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f92,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f93,plain,
( cs4_valid
@ ( cs4_all
@ ^ [X0: individuals] : ( cs4_impl @ ( princ_inj @ X0 ) @ ( princ_inj @ loca ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f94,plain,
( $true
= ( cs4_valid
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_impl @ ( princ_inj @ Y0 ) @ ( princ_inj @ loca ) ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
~ ! [X0: individuals,X1: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f96,plain,
~ ! [X0: individuals,X1: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
? [X0: individuals,X1: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ X1 ) ) @ ( bl_says @ X0 @ ( bl_atom @ X1 ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f96]) ).
thf(f98,plain,
( $true
!= ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( 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(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f104,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f106,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f108,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f110,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f114,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f117,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f120,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f121,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f122,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f128,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f129,plain,
( bl_princ
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f132,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f136,plain,
( bl_says
= ( ^ [Y0: individuals,Y1: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ Y0 ) ) @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f137,plain,
mvalid = bl_valid,
inference(cnf_transformation,[],[f39]) ).
thf(f138,plain,
( $true
= ( cs4_valid
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_impl @ ( princ_inj @ Y0 ) @ ( princ_inj @ loca ) ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f139,plain,
( $true
!= ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ sK1 ) ) @ ( bl_says @ sK0 @ ( bl_atom @ sK1 ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
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,[],[f104,f102,f101]) ).
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,[],[f114,f106]) ).
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,[],[f117,f106,f142]) ).
thf(f150,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ ( ^ [Y1: individuals > $i > $o,Y2: $i] :
( !! @ individuals
@ ^ [Y3: individuals] : ( Y1 @ Y3 @ Y2 ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f120,f106,f108]) ).
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,[],[f121,f106,f106]) ).
thf(f152,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f122,f110]) ).
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,[],[f128,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,[],[f129,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,[],[f132,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,[],[f136,f151,f147,f154]) ).
thf(f160,plain,
( bl_valid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f137,f110]) ).
thf(f168,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: individuals > $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ ( ^ [Y1: individuals > $i > $o,Y2: $i] :
( !! @ individuals
@ ^ [Y3: individuals] : ( Y1 @ Y3 @ Y2 ) )
@ Y0 ) )
@ ^ [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 > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ Y1
@ Y2 ) )
@ ( princ_inj @ Y0 )
@ ( princ_inj @ loca ) ) ) ) ),
inference(definition_unfolding,[],[f138,f152,f150,f147]) ).
thf(f169,plain,
( $true
!= ( ^ [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 ) )
@ loca
@ ( ^ [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 ) ) ) ) ),
inference(definition_unfolding,[],[f139,f160,f157,f159,f153,f159,f153]) ).
thf(f170,plain,
( $true
!= ( !! @ $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 @ loca @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,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 @ loca @ 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 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ loca @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( princ_inj @ loca @ 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 ) ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( $false
= ( ( reli @ sK2 @ sK3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ loca @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ loca @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ loca @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f179,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ loca @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ loca @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( $true
= ( ( reli @ sK3 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ loca @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ loca @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ loca @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $true
= ( ( relr @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ loca @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ loca @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ loca @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( ( reli @ X2 @ X3 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ loca @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ loca @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ loca @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ loca @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ loca @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( princ_inj @ loca @ Y0 ) )
@ ( sK4 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ( reli @ X3 @ X4 )
=> ( sK1 @ X4 ) ) )
| ( $false
= ( ( reli @ X3 @ ( sK4 @ X3 ) )
=> ( princ_inj @ loca @ ( sK4 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( ( reli @ X3 @ ( sK4 @ X3 ) )
=> ( princ_inj @ loca @ ( sK4 @ X3 ) ) ) )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( princ_inj @ loca @ ( sK4 @ X3 ) ) )
| ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( reli @ X3 @ ( sK4 @ X3 ) ) )
| ( $false
= ( reli @ sK3 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X3 @ X4 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( princ_inj @ sK0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK1 @ Y3 ) ) ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f198,plain,
( $false
= ( ( reli @ sK3 @ sK5 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK5 @ 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,[],[f197]) ).
thf(f199,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK5 @ 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,[],[f198]) ).
thf(f200,plain,
( $true
= ( reli @ sK3 @ sK5 ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f201,plain,
( $false
= ( ^ [Y0: $i] :
( ( relr @ sK5 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( princ_inj @ sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) )
@ sK6 ) ),
inference(sigma_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( $false
= ( ( relr @ sK5 @ sK6 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( $true
= ( relr @ sK5 @ sK6 ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( princ_inj @ sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
@ sK7 ) ),
inference(sigma_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( $false
= ( ( reli @ sK6 @ sK7 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( $true
= ( reli @ sK6 @ sK7 ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f210,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f211,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( princ_inj @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X1: $i] :
( $true
= ( ( reli @ sK7 @ X1 )
=> ( princ_inj @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( $false
= ( reli @ sK7 @ X1 ) )
| ( $true
= ( princ_inj @ sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( $false
= ( ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK8 ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f216,plain,
( $false
= ( ( reli @ sK7 @ sK8 )
=> ( sK1 @ sK8 ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( $false
= ( sK1 @ sK8 ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( $true
= ( reli @ sK7 @ sK8 ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( ~ ( princ_inj @ Y2 @ Y3 )
| ( princ_inj @ loca @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f220,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( ~ ( princ_inj @ Y2 @ Y3 )
| ( princ_inj @ loca @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( ~ ( princ_inj @ Y1 @ Y2 )
| ( princ_inj @ loca @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( ~ ( princ_inj @ Y1 @ Y2 )
| ( princ_inj @ loca @ Y2 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( reli @ X1 @ X2 )
=> ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X2 @ Y1 )
=> ( ~ ( princ_inj @ Y0 @ Y1 )
| ( princ_inj @ loca @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $true
= ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X2 @ Y1 )
=> ( ~ ( princ_inj @ Y0 @ Y1 )
| ( princ_inj @ loca @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: individuals,X1: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X2 @ Y1 )
=> ( ~ ( princ_inj @ Y0 @ Y1 )
| ( princ_inj @ loca @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: individuals,X1: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( princ_inj @ X3 @ Y0 )
| ( princ_inj @ loca @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: individuals,X1: $i,X4: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( ~ ( princ_inj @ X3 @ Y0 )
| ( princ_inj @ loca @ Y0 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: individuals,X1: $i,X4: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $true
= ( ( reli @ X2 @ X4 )
=> ( ~ ( princ_inj @ X3 @ X4 )
| ( princ_inj @ loca @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: individuals,X1: $i,X4: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X4 ) )
| ( $true
= ( ~ ( princ_inj @ X3 @ X4 )
| ( princ_inj @ loca @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: individuals,X1: $i,X4: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X4 ) )
| ( $true
= ( princ_inj @ loca @ X4 ) )
| ( $true
= ( ~ ( princ_inj @ X3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: individuals,X1: $i,X4: $i] :
( ( $false
= ( reli @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X4 ) )
| ( $true
= ( princ_inj @ loca @ X4 ) )
| ( $false
= ( princ_inj @ X3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f325,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) )
| ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(constrained_superposition,[],[f195,f218]) ).
thf(f348,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) )
| ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f364,definition,
( spl15_3
<=> ( $true
= ( sK1 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
thf(f366,plain,
( ( $true
= ( sK1 @ sK8 ) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f364]) ).
thf(f368,definition,
( spl15_4
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $false
= ( relr @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
thf(f369,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $false
= ( relr @ X0 @ X1 ) ) )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f368]) ).
thf(f371,definition,
( spl15_5
<=> ( $false
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
thf(f373,plain,
( ( $false
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f395,plain,
( spl15_3
| spl15_4
| spl15_5 ),
inference(avatar_split_clause,[],[f348,f371,f368,f364]) ).
thf(f403,plain,
( ( $false = $true )
| ~ spl15_3 ),
inference(constrained_superposition,[],[f366,f217]) ).
thf(f407,plain,
( $false
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f403]) ).
thf(f408,plain,
~ spl15_3,
inference(avatar_contradiction_clause,[],[f407]) ).
thf(f426,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ sK6 ) ) )
| ~ spl15_4 ),
inference(constrained_superposition,[],[f208,f369]) ).
thf(f427,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ sK6 ) ) )
| ~ spl15_4 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f435,plain,
( ( $false = $true )
| ( $false
= ( reli @ sK3 @ sK5 ) )
| ~ spl15_4 ),
inference(constrained_superposition,[],[f204,f427]) ).
thf(f436,plain,
( ( $false
= ( reli @ sK3 @ sK5 ) )
| ~ spl15_4 ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f440,plain,
( ( $false = $true )
| ~ spl15_4 ),
inference(constrained_superposition,[],[f436,f200]) ).
thf(f446,plain,
( $false
| ~ spl15_4 ),
inference(trivial_inequality_removal,[],[f440]) ).
thf(f447,plain,
~ spl15_4,
inference(avatar_contradiction_clause,[],[f446]) ).
thf(f478,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ sK7 @ X2 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $true
= ( princ_inj @ sK0 @ ( sK4 @ sK7 ) ) ) ),
inference(constrained_superposition,[],[f196,f214]) ).
thf(f485,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( reli @ sK7 @ ( sK4 @ sK7 ) ) )
| ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(constrained_superposition,[],[f196,f218]) ).
thf(f511,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( reli @ sK7 @ ( sK4 @ sK7 ) ) )
| ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f518,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ sK3 @ X0 ) )
| ( $false
= ( relr @ X0 @ X1 ) )
| ( $false
= ( reli @ sK7 @ X2 ) )
| ( $false
= ( reli @ X1 @ sK7 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $true
= ( princ_inj @ sK0 @ ( sK4 @ sK7 ) ) ) ),
inference(trivial_inequality_removal,[],[f478]) ).
thf(f526,definition,
( spl15_12
<=> ( $true
= ( reli @ sK7 @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
thf(f528,plain,
( ( $true
= ( reli @ sK7 @ ( sK4 @ sK7 ) ) )
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f526]) ).
thf(f532,definition,
( spl15_13
<=> ! [X2: $i] :
( ( $false
= ( reli @ sK7 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
thf(f533,plain,
( ! [X2: $i] :
( ( $false
= ( reli @ sK7 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f532]) ).
thf(f535,definition,
( spl15_14
<=> ( $true
= ( princ_inj @ sK0 @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
thf(f537,plain,
( ( $true
= ( princ_inj @ sK0 @ ( sK4 @ sK7 ) ) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f535]) ).
thf(f539,plain,
( spl15_3
| spl15_4
| spl15_12 ),
inference(avatar_split_clause,[],[f511,f526,f368,f364]) ).
thf(f541,plain,
( spl15_14
| spl15_13
| spl15_4 ),
inference(avatar_split_clause,[],[f518,f368,f532,f535]) ).
thf(f576,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK8 ) )
| ~ spl15_13 ),
inference(constrained_superposition,[],[f218,f533]) ).
thf(f577,plain,
( ( $true
= ( sK1 @ sK8 ) )
| ~ spl15_13 ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f584,plain,
( spl15_3
| ~ spl15_13 ),
inference(avatar_split_clause,[],[f577,f532,f364]) ).
thf(f816,plain,
( ! [X0: $i,X1: individuals] :
( ( $false = $true )
| ( $false
= ( reli @ X0 @ sK7 ) )
| ( $true
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) )
| ( $false
= ( princ_inj @ X1 @ ( sK4 @ sK7 ) ) ) )
| ~ spl15_12 ),
inference(constrained_superposition,[],[f231,f528]) ).
thf(f887,plain,
( ! [X0: $i,X1: individuals] :
( ( $false
= ( reli @ X0 @ sK7 ) )
| ( $true
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) )
| ( $false
= ( princ_inj @ X1 @ ( sK4 @ sK7 ) ) ) )
| ~ spl15_12 ),
inference(trivial_inequality_removal,[],[f816]) ).
thf(f900,definition,
( spl15_21
<=> ( $true
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_21])],[avatar_definition]) ).
thf(f902,plain,
( ( $true
= ( princ_inj @ loca @ ( sK4 @ sK7 ) ) )
| ~ spl15_21 ),
inference(avatar_component_clause,[],[f900]) ).
thf(f908,definition,
( spl15_23
<=> ! [X2: individuals] :
( $false
= ( princ_inj @ X2 @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_23])],[avatar_definition]) ).
thf(f909,plain,
( ! [X2: individuals] :
( $false
= ( princ_inj @ X2 @ ( sK4 @ sK7 ) ) )
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f908]) ).
thf(f922,definition,
( spl15_27
<=> ! [X0: $i] :
( $false
= ( reli @ X0 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_27])],[avatar_definition]) ).
thf(f923,plain,
( ! [X0: $i] :
( $false
= ( reli @ X0 @ sK7 ) )
| ~ spl15_27 ),
inference(avatar_component_clause,[],[f922]) ).
thf(f973,plain,
( spl15_23
| spl15_21
| spl15_27
| ~ spl15_12 ),
inference(avatar_split_clause,[],[f887,f526,f922,f900,f908]) ).
thf(f1036,plain,
( ( $false = $true )
| ~ spl15_5
| ~ spl15_21 ),
inference(constrained_superposition,[],[f902,f373]) ).
thf(f1043,plain,
( $false
| ~ spl15_5
| ~ spl15_21 ),
inference(trivial_inequality_removal,[],[f1036]) ).
thf(f1044,plain,
( ~ spl15_5
| ~ spl15_21 ),
inference(avatar_contradiction_clause,[],[f1043]) ).
thf(f1054,plain,
( ( $false = $true )
| ~ spl15_14
| ~ spl15_23 ),
inference(constrained_superposition,[],[f909,f537]) ).
thf(f1063,plain,
( $false
| ~ spl15_14
| ~ spl15_23 ),
inference(trivial_inequality_removal,[],[f1054]) ).
thf(f1064,plain,
( ~ spl15_14
| ~ spl15_23 ),
inference(avatar_contradiction_clause,[],[f1063]) ).
thf(f1066,plain,
( ( $false = $true )
| ~ spl15_27 ),
inference(constrained_superposition,[],[f923,f208]) ).
thf(f1072,plain,
( $false
| ~ spl15_27 ),
inference(trivial_inequality_removal,[],[f1066]) ).
thf(f1073,plain,
~ spl15_27,
inference(avatar_contradiction_clause,[],[f1072]) ).
cnf(s6,plain,
( spl15_3
| spl15_4
| spl15_5 ),
inference(sat_conversion,[],[f395]) ).
cnf(s10,plain,
~ spl15_3,
inference(sat_conversion,[],[f408]) ).
cnf(s12,plain,
~ spl15_4,
inference(sat_conversion,[],[f447]) ).
cnf(s18,plain,
( spl15_3
| spl15_4
| spl15_12 ),
inference(sat_conversion,[],[f539]) ).
cnf(s20,plain,
( spl15_4
| spl15_13
| spl15_14 ),
inference(sat_conversion,[],[f541]) ).
cnf(s24,plain,
( spl15_3
| ~ spl15_13 ),
inference(sat_conversion,[],[f584]) ).
cnf(s50,plain,
( ~ spl15_12
| spl15_21
| spl15_23
| spl15_27 ),
inference(sat_conversion,[],[f973]) ).
cnf(s52,plain,
( ~ spl15_5
| ~ spl15_21 ),
inference(sat_conversion,[],[f1044]) ).
cnf(s54,plain,
( ~ spl15_14
| ~ spl15_23 ),
inference(sat_conversion,[],[f1064]) ).
cnf(s56,plain,
~ spl15_27,
inference(sat_conversion,[],[f1073]) ).
cnf(s57,plain,
( ~ spl15_12
| spl15_21
| spl15_23 ),
inference(rat,[],[s50,s56]) ).
cnf(s61,plain,
~ spl15_13,
inference(rat,[],[s24,s10]) ).
cnf(s62,plain,
spl15_12,
inference(rat,[],[s18,s12,s10]) ).
cnf(s63,plain,
spl15_14,
inference(rat,[],[s20,s12,s61]) ).
cnf(s64,plain,
~ spl15_23,
inference(rat,[],[s54,s63]) ).
cnf(s65,plain,
spl15_21,
inference(rat,[],[s57,s62,s64]) ).
cnf(s66,plain,
~ spl15_5,
inference(rat,[],[s52,s65]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s6,s66,s12,s10]) ).
thf(f1074,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV444^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n026.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:07:12 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.30 Running first-order model finding
% 0.26/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.45 % (788453)Will run a generic schedule for satisfiability detection.
% 0.63/0.45 % (788459)% WARNING: option uhcvi not known.
% 0.63/0.45 % (788460)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2743141296:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.63/0.45 % (788459)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2302357872:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.63/0.45 % (788459)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.45 % (788459)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.63/0.45 % (788458)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3035958478_2999 on theBenchmark for (2999ds/0Mi)
% 0.63/0.45 % (788462)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3962714063:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.63/0.45 % (788463)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3885255010:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.63/0.45 % (788464)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4241898742:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.63/0.45 % (788461)dis+10_1_sil=32000:sp=arity:random_seed=3839703046:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.63/0.45 % (788462)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.45 % Exception at run slice level
% 0.63/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.63/0.45 % (788472)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=381642827:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.63/0.45 % Exception at run slice level
% 0.63/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.63/0.45 % (788475)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=210744771:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.63/0.45 % (788464) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-788453-788464"...
% 0.63/0.45 % (788461)Instruction limit reached!
% 0.63/0.45 % (788461)------------------------------
% 0.63/0.45 % (788461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (788461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (788461)CaDiCaL version: 2.1.3
% 0.63/0.45 % (788461)Termination reason: Instruction limit
% 0.63/0.45 % (788461)Termination phase: Saturation
% 0.63/0.45 % (788461)Time elapsed: 0.090 s
% 0.63/0.45 % (788461)Peak memory usage: 12 MB
% 0.63/0.45 % (788461)Instructions burned: 104 (million)
% 0.63/0.45 % (788462)Instruction limit reached!
% 0.63/0.45 % (788462)------------------------------
% 0.63/0.45 % (788462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (788462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (788462)CaDiCaL version: 2.1.3
% 0.63/0.45 % (788462)Termination reason: Instruction limit
% 0.63/0.45 % (788462)Termination phase: Saturation
% 0.63/0.45 % (788462)Time elapsed: 0.098 s
% 0.63/0.45 % (788462)Peak memory usage: 12 MB
% 0.63/0.45 % (788462)Instructions burned: 116 (million)
% 0.63/0.45 % (788464)...printing done.
% 0.63/0.45 % (788464)Refutation found. Thanks to Tanya!
% 0.63/0.45 % SZS status Theorem for theBenchmark
% 0.63/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.63/0.46 % (788464)------------------------------
% 0.63/0.46 % (788464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.46 % (788464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.46 % (788464)CaDiCaL version: 2.1.3
% 0.63/0.46 % (788464)Termination reason: Refutation
% 0.63/0.46 % (788464)Time elapsed: 0.103 s
% 0.63/0.46 % (788464)Peak memory usage: 13 MB
% 0.63/0.46 % (788464)Instructions burned: 114 (million)
% 0.63/0.46 % (788453)Success in time 0.143 s
% 0.63/0.46 % Vampire exiting
%------------------------------------------------------------------------------