%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO886^9 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:48:34 AM UTC 2026
% Result : Theorem 0.19s 0.33s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 24
% Syntax : Number of formulae : 204 ( 77 unt; 0 typ; 10 def)
% Number of atoms : 1737 ( 318 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2696 ( 139 ~; 287 |; 0 &;1819 @)
% ( 9 <=>; 213 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 359 ( 359 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 71 usr; 20 con; 0-4 aty)
% ( 229 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 779 ( 0 sgn 180 !; 1 ?; 779 :)
% 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_33,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
sK0: individuals > $i > $o ).
thf(func_def_45,type,
sF1: $o ).
thf(func_def_46,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_47,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_49,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_50,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_51,type,
sK7: $i > ( $i > $o ) > $i ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK13: individuals ).
thf(func_def_60,type,
sK15: $i > $i ).
thf(func_def_61,type,
sK16: $i > individuals ).
thf(func_def_62,type,
sK17: $i > $i ).
thf(func_def_63,type,
sK18: $i > $i ).
thf(func_def_64,type,
sK19: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
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,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f10,axiom,
( ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) )
= mall ),
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,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) )
= cs4_atom ),
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,
( ( ^ [X0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ X0 ) ) )
= cs4_all ),
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,
( ( ^ [X0: $i > $o] : ( mvalid @ X0 ) )
= cs4_valid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_valid_def) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',refl_axiom_i) ).
thf(f27,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',trans_axiom_i) ).
thf(f30,conjecture,
! [X0: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ X1 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_atom @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_barcan) ).
thf(f31,negated_conjecture,
~ ! [X0: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ X1 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_atom @ ( X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f35,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ Y0 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f37,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f38,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f41,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f42,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f46,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f50,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f54,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f63,plain,
~ ! [X0: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ X1 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [X2: individuals] : ( cs4_atom @ ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f64,plain,
~ ! [X0: individuals > $i > $o] :
( ( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ Y0 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( X0 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f66,plain,
( ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) )
= mall ),
inference(rectify,[],[f10]) ).
thf(f67,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f69,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f72,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f73,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f76,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f77,plain,
? [X0: individuals > $i > $o] :
( ( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ Y0 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( X0 @ Y0 ) ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f64]) ).
thf(f78,plain,
( $true
!= ( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( sK0 @ Y0 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f77]) ).
thf(f79,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f80,plain,
( $true
!= ( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( sK0 @ Y0 ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f81,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f84,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f87,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f88,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f93,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f95,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f96,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f99,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f101,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f102,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f106,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f107,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f111,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,[],[f96,f87,f93]) ).
thf(f113,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,[],[f101,f84]) ).
thf(f116,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,[],[f81,f84,f111]) ).
thf(f119,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,[],[f107,f84,f88]) ).
thf(f120,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,[],[f79,f84,f84]) ).
thf(f121,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f95,f99]) ).
thf(f122,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ relr
@ Y1 ) )
@ ( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f80,f121,f116,f119,f120,f113,f120,f119,f113]) ).
thf(f125,plain,
! [X0: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ reli
@ X0 )
@ X0 ) )
= $true ),
inference(definition_unfolding,[],[f102,f99,f111,f84]) ).
thf(f127,plain,
! [X0: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ reli
@ X0 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ reli
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ reli
@ X0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f106,f99,f111,f84,f84,f84]) ).
thf(f128,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ relr
@ Y1 ) )
@ ( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f129,plain,
( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ relr
@ Y1 ) )
@ ( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f128]) ).
thf(f130,plain,
$true != sF1,
inference(definition_folding,[],[f122,f129]) ).
thf(f159,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f160,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X0: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK5 @ X1 @ X0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ( reli @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( ( ( reli @ X1 @ ( sK5 @ X1 @ X0 ) )
=> ( X0 @ ( sK5 @ X1 @ X0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true )
| ( ( ( reli @ X1 @ ( sK5 @ X1 @ X0 ) )
=> ( X0 @ ( sK5 @ X1 @ X0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( ( ( reli @ X1 @ ( sK5 @ X1 @ X0 ) )
=> ( X0 @ ( sK5 @ X1 @ X0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 )
= $true )
| ( ( X0 @ ( sK5 @ X1 @ X0 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 )
= $true )
| ( ( reli @ X1 @ X2 )
= $false )
| ( $true
= ( reli @ X1 @ ( sK5 @ X1 @ X0 ) ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( $true
= ( reli @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( ( ( reli @ X2 @ X3 )
=> ( X0 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( reli @ X1 @ ( sK5 @ X1 @ X0 ) ) )
| ( ( reli @ X2 @ X3 )
= $false )
| ( ( X0 @ X3 )
= $true )
| ( ( reli @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( ( reli @ X2 @ X3 )
=> ( X0 @ X3 ) )
= $true )
| ( ( X0 @ ( sK5 @ X1 @ X0 ) )
= $false )
| ( ( reli @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK5 @ X1 @ X0 ) )
= $false )
| ( ( reli @ X2 @ X3 )
= $false )
| ( ( reli @ X1 @ X2 )
= $false )
| ( ( X0 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f193,plain,
! [X0: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f194,plain,
! [X0: $i > $o,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK7 @ X1 @ X0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( ( reli @ X1 @ ( sK7 @ X1 @ X0 ) )
=> ( X0 @ ( sK7 @ X1 @ X0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK7 @ X1 @ X0 ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( reli @ X1 @ ( sK7 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f203,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ relr
@ Y1 ) )
@ ( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) )
@ ( ^ [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 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ ( sK0 @ Y0 ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f129]) ).
thf(f204,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ individuals
@ ^ [Y3: individuals] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK0 @ Y3 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ individuals
@ ^ [Y5: individuals] :
( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y4 @ Y6 )
=> ( sK0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ individuals
@ ^ [Y3: individuals] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( sK0 @ Y3 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !! @ individuals
@ ^ [Y5: individuals] :
( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y4 @ Y6 )
=> ( sK0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK8 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ individuals
@ ^ [Y4: individuals] :
( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y3 @ Y5 )
=> ( sK0 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( ( reli @ sK8 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( sK0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !! @ individuals
@ ^ [Y4: individuals] :
( !! @ $i
@ ^ [Y5: $i] :
( ( reli @ Y3 @ Y5 )
=> ( sK0 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK9 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( ( ( reli @ sK8 @ sK9 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ individuals
@ ^ [Y3: individuals] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( sK0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ individuals
@ ^ [Y3: individuals] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( sK0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f211,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ individuals
@ ^ [Y3: individuals] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( sK0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f212,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f213,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( sK0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) )
@ X1 ) )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( ( ( reli @ sK9 @ X1 )
=> ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) )
= $true )
| ( $true = sF1 )
| ( ( reli @ sK9 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: individuals,X1: $i] :
( ( ( reli @ sK9 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) )
@ X2 ) )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: individuals,X1: $i] :
( ( $true = sF1 )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ X2 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: individuals,X3: $i,X1: $i] :
( ( ( reli @ sK9 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ X2 @ Y2 ) ) ) ) ) )
@ X3 ) )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: individuals,X3: $i,X1: $i] :
( ( $true
= ( ( reli @ X1 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ X2 @ Y1 ) ) ) ) ) ) )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
! [X2: individuals,X3: $i,X1: $i] :
( ( $false
= ( reli @ X1 @ X3 ) )
| ( $true = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ X2 @ Y1 ) ) ) ) ) )
| ( ( reli @ sK9 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: individuals,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X1 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( relr @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ X2 @ Y1 ) ) ) )
@ X4 )
= $true )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: individuals,X3: $i,X1: $i,X4: $i] :
( ( ( reli @ sK9 @ X1 )
= $false )
| ( $true
= ( ( relr @ X3 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( sK0 @ X2 @ Y0 ) ) ) ) )
| ( $true = sF1 )
| ( $false
= ( reli @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: individuals,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( sK0 @ X2 @ Y0 ) ) ) )
| ( $false
= ( reli @ X1 @ X3 ) )
| ( $true = sF1 )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( ( relr @ X3 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: individuals,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( relr @ X3 @ X4 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( sK0 @ X2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( reli @ X1 @ X3 ) )
| ( $true = sF1 )
| ( ( reli @ sK9 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: individuals,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( relr @ X3 @ X4 )
= $false )
| ( $true = sF1 )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( $false
= ( reli @ X1 @ X3 ) )
| ( $true
= ( ( reli @ X4 @ X5 )
=> ( sK0 @ X2 @ X5 ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
! [X2: individuals,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true = sF1 )
| ( ( reli @ X4 @ X5 )
= $false )
| ( ( sK0 @ X2 @ X5 )
= $true )
| ( ( relr @ X3 @ X4 )
= $false )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( $false
= ( reli @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( ( reli @ sK9 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !! @ individuals
@ ^ [Y3: individuals] :
( !! @ $i
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( sK0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
@ sK10 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f229,plain,
( ( $true = sF1 )
| ( ( ( reli @ sK9 @ sK10 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK10 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK10 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $true = sF1 )
| ( $true
= ( reli @ sK9 @ sK10 ) ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f232,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( relr @ sK10 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f233,plain,
( ( ( ( relr @ sK10 @ sK11 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( ( relr @ sK10 @ sK11 )
= $true )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( ( ^ [Y0: $i] :
( ( reli @ sK11 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ sK12 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f237,plain,
( ( ( ( reli @ sK11 @ sK12 )
=> ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ sK12 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
( ( ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ sK12 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $true = sF1 )
| ( $true
= ( reli @ sK11 @ sK12 ) ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f240,plain,
( ( ( ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ sK12 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK13 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f241,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( sK0 @ sK13 @ Y0 ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( sK0 @ sK13 @ Y0 ) )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $true = sF1 )
| ( ( ( reli @ sK12 @ sK14 )
=> ( sK0 @ sK13 @ sK14 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
( ( $true = sF1 )
| ( ( sK0 @ sK13 @ sK14 )
= $false ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( $true = sF1 )
| ( $true
= ( reli @ sK12 @ sK14 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f303,definition,
( spl20_2
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
thf(f308,definition,
( spl20_3
<=> ! [X2: individuals,X3: $i,X4: $i,X5: $i,X1: $i] :
( ( ( reli @ X4 @ X5 )
= $false )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( $false
= ( reli @ X1 @ X3 ) )
| ( ( relr @ X3 @ X4 )
= $false )
| ( ( sK0 @ X2 @ X5 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
thf(f309,plain,
( ! [X2: individuals,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( reli @ X1 @ X3 ) )
| ( ( reli @ sK9 @ X1 )
= $false )
| ( ( reli @ X4 @ X5 )
= $false )
| ( ( relr @ X3 @ X4 )
= $false )
| ( ( sK0 @ X2 @ X5 )
= $true ) )
| ~ spl20_3 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f310,plain,
( spl20_3
| spl20_2 ),
inference(avatar_split_clause,[],[f227,f303,f308]) ).
thf(f312,definition,
( spl20_4
<=> ( $true
= ( reli @ sK9 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
thf(f314,plain,
( ( $true
= ( reli @ sK9 @ sK10 ) )
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f315,plain,
( spl20_2
| spl20_4 ),
inference(avatar_split_clause,[],[f231,f312,f303]) ).
thf(f317,definition,
( spl20_5
<=> ( ( relr @ sK10 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition]) ).
thf(f319,plain,
( ( ( relr @ sK10 @ sK11 )
= $true )
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f317]) ).
thf(f320,plain,
( spl20_2
| spl20_5 ),
inference(avatar_split_clause,[],[f235,f317,f303]) ).
thf(f322,definition,
( spl20_6
<=> ( $true
= ( reli @ sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
thf(f324,plain,
( ( $true
= ( reli @ sK11 @ sK12 ) )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f322]) ).
thf(f325,plain,
( spl20_2
| spl20_6 ),
inference(avatar_split_clause,[],[f239,f322,f303]) ).
thf(f327,definition,
( spl20_7
<=> ( $true
= ( reli @ sK12 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f329,plain,
( ( $true
= ( reli @ sK12 @ sK14 ) )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f327]) ).
thf(f330,plain,
( spl20_7
| spl20_2 ),
inference(avatar_split_clause,[],[f245,f303,f327]) ).
thf(f332,definition,
( spl20_8
<=> ( ( sK0 @ sK13 @ sK14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
thf(f334,plain,
( ( ( sK0 @ sK13 @ sK14 )
= $false )
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f332]) ).
thf(f335,plain,
( spl20_2
| spl20_8 ),
inference(avatar_split_clause,[],[f244,f332,f303]) ).
thf(f360,plain,
~ spl20_2,
inference(avatar_split_clause,[],[f130,f303]) ).
thf(f385,plain,
! [X0: $i] :
( ( ( reli @ X0 @ X0 )
= $true )
| ( $true = $false )
| ( ( reli @ X0 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f201,f200]) ).
thf(f387,plain,
! [X0: $i] :
( ( ( reli @ X0 @ X0 )
= $true )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f385]) ).
thf(f388,plain,
! [X0: $i] :
( ( reli @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f387]) ).
thf(f416,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X0 @ X3 ) )
| ( $true
= ( reli @ X0 @ X4 ) )
| ( ( reli @ X0 @ X1 )
= $false )
| ( ( reli @ X1 @ X2 )
= $false )
| ( $true
= ( reli @ X0 @ X2 ) )
| ( $true = $false )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(constrained_superposition,[],[f174,f172]) ).
thf(f420,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( reli @ X0 @ X4 ) )
| ( $true
= ( reli @ X0 @ X2 ) )
| ( ( reli @ X1 @ X2 )
= $false )
| ( ( reli @ X0 @ X1 )
= $false )
| ( $false
= ( reli @ X0 @ X3 ) )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f416]) ).
thf(f445,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( ( relr @ sK10 @ X0 )
= $false )
| ( ( reli @ X0 @ X1 )
= $false )
| ( $true = $false )
| ( ( reli @ sK9 @ sK9 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $true ) )
| ~ spl20_3
| ~ spl20_4 ),
inference(constrained_superposition,[],[f314,f309]) ).
thf(f453,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( ( reli @ X0 @ X1 )
= $false )
| ( ( relr @ sK10 @ X0 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( reli @ sK9 @ sK9 )
= $false ) )
| ~ spl20_3
| ~ spl20_4 ),
inference(trivial_inequality_removal,[],[f445]) ).
thf(f477,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( reli @ X0 @ X1 )
= $false )
| ( ( relr @ sK10 @ X0 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $true ) )
| ~ spl20_3
| ~ spl20_4 ),
inference(forward_demodulation,[],[f453,f388]) ).
thf(f478,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( reli @ X0 @ X1 )
= $false )
| ( ( relr @ sK10 @ X0 )
= $false ) )
| ~ spl20_3
| ~ spl20_4 ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f551,plain,
( ! [X0: $i] :
( ( ( relr @ sK10 @ X0 )
= $false )
| ( $true = $false )
| ( ( reli @ X0 @ sK14 )
= $false ) )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_8 ),
inference(constrained_superposition,[],[f334,f478]) ).
thf(f561,plain,
( ! [X0: $i] :
( ( ( relr @ sK10 @ X0 )
= $false )
| ( ( reli @ X0 @ sK14 )
= $false ) )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_8 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f574,plain,
( ( $false
= ( reli @ sK11 @ sK14 ) )
| ( $true = $false )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_8 ),
inference(constrained_superposition,[],[f319,f561]) ).
thf(f579,plain,
( ( $false
= ( reli @ sK11 @ sK14 ) )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_8 ),
inference(trivial_inequality_removal,[],[f574]) ).
thf(f592,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( reli @ sK11 @ X0 )
= $true )
| ( $true = $false )
| ( ( reli @ sK11 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ sK14 ) )
| ( ( reli @ sK11 @ X1 )
= $false )
| ( ( reli @ X1 @ X0 )
= $false ) )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_8 ),
inference(constrained_superposition,[],[f420,f579]) ).
thf(f622,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ X2 @ sK14 ) )
| ( ( reli @ X1 @ X0 )
= $false )
| ( ( reli @ sK11 @ X2 )
= $false )
| ( ( reli @ sK11 @ X1 )
= $false )
| ( ( reli @ sK11 @ X0 )
= $true ) )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_8 ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f632,definition,
( spl20_21
<=> ! [X0: $i,X1: $i] :
( ( ( reli @ X1 @ X0 )
= $false )
| ( ( reli @ sK11 @ X1 )
= $false )
| ( ( reli @ sK11 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl20_21])],[avatar_definition]) ).
thf(f633,plain,
( ! [X0: $i,X1: $i] :
( ( ( reli @ sK11 @ X1 )
= $false )
| ( ( reli @ sK11 @ X0 )
= $true )
| ( ( reli @ X1 @ X0 )
= $false ) )
| ~ spl20_21 ),
inference(avatar_component_clause,[],[f632]) ).
thf(f635,definition,
( spl20_22
<=> ! [X2: $i] :
( ( $false
= ( reli @ X2 @ sK14 ) )
| ( ( reli @ sK11 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_22])],[avatar_definition]) ).
thf(f636,plain,
( ! [X2: $i] :
( ( $false
= ( reli @ X2 @ sK14 ) )
| ( ( reli @ sK11 @ X2 )
= $false ) )
| ~ spl20_22 ),
inference(avatar_component_clause,[],[f635]) ).
thf(f638,plain,
( spl20_22
| spl20_21
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_8 ),
inference(avatar_split_clause,[],[f622,f332,f317,f312,f308,f632,f635]) ).
thf(f777,plain,
( ! [X0: $i] :
( ( ( reli @ sK11 @ X0 )
= $true )
| ( ( reli @ sK12 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl20_6
| ~ spl20_21 ),
inference(constrained_superposition,[],[f633,f324]) ).
thf(f794,plain,
( ! [X0: $i] :
( ( ( reli @ sK12 @ X0 )
= $false )
| ( ( reli @ sK11 @ X0 )
= $true ) )
| ~ spl20_6
| ~ spl20_21 ),
inference(trivial_inequality_removal,[],[f777]) ).
thf(f813,plain,
( ( $true = $false )
| ( $true
= ( reli @ sK11 @ sK14 ) )
| ~ spl20_6
| ~ spl20_7
| ~ spl20_21 ),
inference(constrained_superposition,[],[f329,f794]) ).
thf(f830,plain,
( ( $true
= ( reli @ sK11 @ sK14 ) )
| ~ spl20_6
| ~ spl20_7
| ~ spl20_21 ),
inference(trivial_inequality_removal,[],[f813]) ).
thf(f842,plain,
( ( $true = $false )
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_21 ),
inference(forward_demodulation,[],[f830,f579]) ).
thf(f843,plain,
( $false
| ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_21 ),
inference(trivial_inequality_removal,[],[f842]) ).
thf(f844,plain,
( ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_21 ),
inference(avatar_contradiction_clause,[],[f843]) ).
thf(f852,plain,
( ( $true = $false )
| ( $false
= ( reli @ sK11 @ sK12 ) )
| ~ spl20_7
| ~ spl20_22 ),
inference(constrained_superposition,[],[f329,f636]) ).
thf(f858,plain,
( ( $false
= ( reli @ sK11 @ sK12 ) )
| ~ spl20_7
| ~ spl20_22 ),
inference(trivial_inequality_removal,[],[f852]) ).
thf(f863,plain,
( ( $true = $false )
| ~ spl20_6
| ~ spl20_7
| ~ spl20_22 ),
inference(forward_demodulation,[],[f858,f324]) ).
thf(f864,plain,
( $false
| ~ spl20_6
| ~ spl20_7
| ~ spl20_22 ),
inference(trivial_inequality_removal,[],[f863]) ).
thf(f865,plain,
( ~ spl20_6
| ~ spl20_7
| ~ spl20_22 ),
inference(avatar_contradiction_clause,[],[f864]) ).
cnf(s2,plain,
( spl20_2
| spl20_3 ),
inference(sat_conversion,[],[f310]) ).
cnf(s3,plain,
( spl20_2
| spl20_4 ),
inference(sat_conversion,[],[f315]) ).
cnf(s4,plain,
( spl20_2
| spl20_5 ),
inference(sat_conversion,[],[f320]) ).
cnf(s5,plain,
( spl20_2
| spl20_6 ),
inference(sat_conversion,[],[f325]) ).
cnf(s6,plain,
( spl20_2
| spl20_7 ),
inference(sat_conversion,[],[f330]) ).
cnf(s7,plain,
( spl20_2
| spl20_8 ),
inference(sat_conversion,[],[f335]) ).
cnf(s13,plain,
~ spl20_2,
inference(sat_conversion,[],[f360]) ).
cnf(s22,plain,
( ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_8
| spl20_21
| spl20_22 ),
inference(sat_conversion,[],[f638]) ).
cnf(s37,plain,
( ~ spl20_3
| ~ spl20_4
| ~ spl20_5
| ~ spl20_6
| ~ spl20_7
| ~ spl20_8
| ~ spl20_21 ),
inference(sat_conversion,[],[f844]) ).
cnf(s40,plain,
( ~ spl20_6
| ~ spl20_7
| ~ spl20_22 ),
inference(sat_conversion,[],[f865]) ).
cnf(s41,plain,
spl20_8,
inference(rat,[],[s7,s13]) ).
cnf(s43,plain,
spl20_7,
inference(rat,[],[s6,s13]) ).
cnf(s45,plain,
spl20_6,
inference(rat,[],[s5,s13]) ).
cnf(s46,plain,
~ spl20_22,
inference(rat,[],[s40,s43,s45]) ).
cnf(s47,plain,
spl20_5,
inference(rat,[],[s4,s13]) ).
cnf(s48,plain,
spl20_4,
inference(rat,[],[s3,s13]) ).
cnf(s49,plain,
spl20_3,
inference(rat,[],[s2,s13]) ).
cnf(s50,plain,
~ spl20_21,
inference(rat,[],[s37,s48,s41,s43,s45,s47,s49]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s22,s46,s48,s41,s47,s50,s49]) ).
thf(f866,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO886^9 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:26:09 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.33 % (3465016)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.33 % (3465021)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2950786398:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.33 % (3465027)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.33 % (3465027)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.33 % (3465022)lrs+10_16_si=on:nwc=1.5:random_seed=3372629143:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.33 % (3465023)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=333349088:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.33 % (3465025)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1622720934:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.33 % (3465024)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=2892884802:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.33 % (3465026)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4078213810:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.33 % (3465027)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=4042354273:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.33 % (3465023)Instruction limit reached!
% 0.19/0.33 % (3465023)------------------------------
% 0.19/0.33 % (3465023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465023)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465023)Termination reason: Instruction limit
% 0.19/0.33 % (3465023)Termination phase: Function definition elimination
% 0.19/0.33 % (3465023)Time elapsed: 0.002 s
% 0.19/0.33 % (3465023)Peak memory usage: 10 MB
% 0.19/0.33 % (3465023)Instructions burned: 4 (million)
% 0.19/0.33 % (3465022)Instruction limit reached!
% 0.19/0.33 % (3465022)------------------------------
% 0.19/0.33 % (3465022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465022)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465022)Termination reason: Instruction limit
% 0.19/0.33 % (3465022)Termination phase: Saturation
% 0.19/0.33 % (3465022)Time elapsed: 0.009 s
% 0.19/0.33 % (3465022)Peak memory usage: 12 MB
% 0.19/0.33 % (3465022)Instructions burned: 19 (million)
% 0.19/0.33 % (3465025)Instruction limit reached!
% 0.19/0.33 % (3465025)------------------------------
% 0.19/0.33 % (3465025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465025)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465025)Termination reason: Instruction limit
% 0.19/0.33 % (3465025)Termination phase: Saturation
% 0.19/0.33 % (3465025)Time elapsed: 0.015 s
% 0.19/0.33 % (3465025)Peak memory usage: 12 MB
% 0.19/0.33 % (3465025)Instructions burned: 25 (million)
% 0.19/0.33 % (3465021)Instruction limit reached!
% 0.19/0.33 % (3465021)------------------------------
% 0.19/0.33 % (3465021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465021)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465021)Termination reason: Instruction limit
% 0.19/0.33 % (3465021)Termination phase: Saturation
% 0.19/0.33 % (3465021)Time elapsed: 0.024 s
% 0.19/0.33 % (3465021)Peak memory usage: 12 MB
% 0.19/0.33 % (3465021)Instructions burned: 91 (million)
% 0.19/0.33 % (3465035)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2132796259:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.33 % (3465035)Instruction limit reached!
% 0.19/0.33 % (3465035)------------------------------
% 0.19/0.33 % (3465035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465035)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465035)Termination reason: Instruction limit
% 0.19/0.33 % (3465035)Termination phase: Saturation
% 0.19/0.33 % (3465035)Time elapsed: 0.004 s
% 0.19/0.33 % (3465035)Peak memory usage: 11 MB
% 0.19/0.33 % (3465035)Instructions burned: 7 (million)
% 0.19/0.33 % (3465038)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=604359605:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/0.33 % (3465036)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3272559723:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.33 % (3465037)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.33 % (3465036)Instruction limit reached!
% 0.19/0.33 % (3465036)------------------------------
% 0.19/0.33 % (3465036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465036)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465036)Termination reason: Instruction limit
% 0.19/0.33 % (3465036)Termination phase: Property scanning
% 0.19/0.33 % (3465036)Time elapsed: 0.003 s
% 0.19/0.33 % (3465036)Peak memory usage: 11 MB
% 0.19/0.33 % (3465036)Instructions burned: 7 (million)
% 0.19/0.33 % (3465038)Instruction limit reached!
% 0.19/0.33 % (3465038)------------------------------
% 0.19/0.33 % (3465038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465038)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465038)Termination reason: Instruction limit
% 0.19/0.33 % (3465038)Termination phase: Saturation
% 0.19/0.33 % (3465038)Time elapsed: 0.003 s
% 0.19/0.33 % (3465038)Peak memory usage: 12 MB
% 0.19/0.33 % (3465038)Instructions burned: 14 (million)
% 0.19/0.33 % (3465027) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3465016-3465027"...
% 0.19/0.33 % (3465037)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2482616156:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.33 % (3465037)Instruction limit reached!
% 0.19/0.33 % (3465037)------------------------------
% 0.19/0.33 % (3465037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465037)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465037)Termination reason: Instruction limit
% 0.19/0.33 % (3465037)Termination phase: Saturation
% 0.19/0.33 % (3465037)Time elapsed: 0.004 s
% 0.19/0.33 % (3465037)Peak memory usage: 11 MB
% 0.19/0.33 % (3465037)Instructions burned: 8 (million)
% 0.19/0.33 % (3465026)Instruction limit reached!
% 0.19/0.33 % (3465026)------------------------------
% 0.19/0.33 % (3465026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465026)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465026)Termination reason: Instruction limit
% 0.19/0.33 % (3465026)Termination phase: Saturation
% 0.19/0.33 % (3465026)Time elapsed: 0.039 s
% 0.19/0.33 % (3465026)Peak memory usage: 13 MB
% 0.19/0.33 % (3465026)Instructions burned: 75 (million)
% 0.19/0.33 % (3465027)...printing done.
% 0.19/0.33 % (3465040)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.33 % (3465040)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.33 % (3465043)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=386715507:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.19/0.33 % (3465027)Refutation found. Thanks to Tanya!
% 0.19/0.33 % SZS status Theorem for theBenchmark
% 0.19/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.33 % (3465027)------------------------------
% 0.19/0.33 % (3465027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (3465027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (3465027)CaDiCaL version: 2.1.3
% 0.19/0.33 % (3465027)Termination reason: Refutation
% 0.19/0.33 % (3465027)Time elapsed: 0.039 s
% 0.19/0.33 % (3465027)Peak memory usage: 13 MB
% 0.19/0.33 % (3465027)Instructions burned: 75 (million)
% 0.19/0.33 % (3465016)Success in time 0.086 s
% 0.19/0.33 % Vampire exiting
%------------------------------------------------------------------------------