%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO932^9 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:48:41 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 26
% Syntax : Number of formulae : 214 ( 78 unt; 0 typ; 12 def)
% Number of atoms : 1737 ( 326 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 2575 ( 123 ~; 275 |; 0 &;1743 @)
% ( 11 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 312 ( 312 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 22 con; 0-4 aty)
% ( 219 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 718 ( 0 sgn 180 !; 1 ?; 718 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vAND: $o > $o > $o ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vIMP: $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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
sK5: $i > $i ).
thf(func_def_51,type,
sK6: $i > $i ).
thf(func_def_52,type,
sK7: $i > $i ).
thf(func_def_53,type,
sK8: $i > individuals ).
thf(func_def_54,type,
sK9: $i > $i ).
thf(func_def_58,type,
sK13: individuals ).
thf(func_def_62,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_63,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_64,type,
sK19: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f10,axiom,
( ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) )
= mall ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mall) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) )
= cs4_atom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_atom) ).
thf(f19,axiom,
( cs4_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ reli @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f22,axiom,
( cs4_all
= ( ^ [X0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_all) ).
thf(f23,axiom,
( cs4_box
= ( ^ [X0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_box) ).
thf(f24,axiom,
( cs4_valid
= ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',cs4_valid_def) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',refl_axiom_i) ).
thf(f27,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL009^0.ax',trans_axiom_i) ).
thf(f30,conjecture,
! [X0: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_atom @ ( X0 @ X1 ) ) ) )
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cs4_cbarcan) ).
thf(f31,negated_conjecture,
~ ! [X0: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_atom @ ( X0 @ X1 ) ) ) )
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f42,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f43,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ Y0 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f49,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f57,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f58,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f60,plain,
~ ! [X0: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [X1: individuals] : ( cs4_atom @ ( X0 @ X1 ) ) ) )
@ ( cs4_all
@ ^ [X2: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f61,plain,
~ ! [X0: individuals > $i > $o] :
( ( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( X0 @ Y0 ) ) ) )
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( ( ^ [X0: individuals > $i > $o,X1: $i] :
! [X2: individuals] : ( X0 @ X2 @ X1 ) )
= mall ),
inference(rectify,[],[f10]) ).
thf(f63,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f65,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f67,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f69,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f71,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f72,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f73,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f75,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f77,plain,
? [X0: individuals > $i > $o] :
( ( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( X0 @ Y0 ) ) ) )
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( X0 @ Y0 ) ) ) ) ) )
!= $true ),
inference(ennf_transformation,[],[f61]) ).
thf(f78,plain,
( $true
!= ( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( sK0 @ Y0 ) ) ) )
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f77]) ).
thf(f79,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ ( mbox @ reli @ ( mbox @ reli @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f81,plain,
( mall
= ( ^ [Y0: individuals > $i > $o,Y1: $i] :
( !! @ individuals
@ ^ [Y2: individuals] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f84,plain,
( $true
!= ( cs4_valid
@ ( cs4_impl
@ ( cs4_box
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_atom @ ( sK0 @ Y0 ) ) ) )
@ ( cs4_all
@ ^ [Y0: individuals] : ( cs4_box @ ( cs4_atom @ ( sK0 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f85,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f86,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f88,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ reli @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f73]) ).
thf(f89,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f92,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f93,plain,
( cs4_box
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f100,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f101,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f102,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f104,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f107,plain,
( cs4_all
= ( ^ [Y0: individuals > $i > $o] : ( mbox @ reli @ ( mall @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
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,[],[f89,f100,f85]) ).
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,[],[f104,f101]) ).
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,[],[f92,f101,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,f101,f81]) ).
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,[],[f93,f101,f101]) ).
thf(f121,plain,
( cs4_valid
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f102,f86]) ).
thf(f122,plain,
! [X0: $i > $o] :
( $true
= ( ^ [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 ) ) ) ) ),
inference(definition_unfolding,[],[f79,f86,f111,f101,f101,f101]) ).
thf(f124,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: $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 ) ) ) )
@ ( ^ [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 ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f84,f121,f116,f120,f119,f113,f119,f120,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,[],[f88,f86,f111,f101]) ).
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: $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 ) ) ) )
@ ( ^ [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 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f129,plain,
sF1 != $true,
inference(definition_folding,[],[f124,f128]) ).
thf(f139,plain,
! [X0: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f140,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X0: $i > $o,X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( X0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X0: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true )
| ( ( X0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( X0 @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( ( reli @ X1 @ ( sK3 @ X1 @ X0 ) )
=> ( X0 @ ( sK3 @ X1 @ X0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK3 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ ( sK3 @ X1 @ X0 ) )
= $true )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f148,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,[],[f122]) ).
thf(f149,plain,
! [X0: $i > $o,X1: $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 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,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,[],[f149]) ).
thf(f151,plain,
! [X0: $i > $o,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,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 ) )
@ ( sK4 @ X1 @ X0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ( reli @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( reli @ X1 @ ( sK4 @ X1 @ X0 ) )
=> ( X0 @ ( sK4 @ X1 @ X0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( $false
= ( ( reli @ X1 @ ( sK4 @ X1 @ X0 ) )
=> ( X0 @ ( sK4 @ X1 @ X0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true )
| ( $false
= ( X0 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( reli @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( ( reli @ X1 @ ( sK4 @ X1 @ X0 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 )
= $true )
| ( ( reli @ X1 @ ( sK4 @ X1 @ X0 ) )
= $true )
| ( ( reli @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( ( reli @ X2 @ X3 )
=> ( X0 @ X3 ) )
= $true )
| ( ( reli @ X1 @ ( sK4 @ X1 @ X0 ) )
= $true )
| ( ( reli @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ ( sK4 @ X1 @ X0 ) )
= $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( ( reli @ X1 @ X2 )
= $false )
| ( $true
= ( X0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 )
= $true )
| ( ( reli @ X1 @ X2 )
= $false )
| ( $false
= ( X0 @ ( sK4 @ X1 @ X0 ) ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f163,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( reli @ X1 @ X2 )
= $false )
| ( $false
= ( X0 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( ( reli @ X2 @ X3 )
=> ( X0 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( reli @ X1 @ X2 )
= $false )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( X0 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [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: $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 ) ) ) )
@ ( ^ [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 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f128]) ).
thf(f228,plain,
( ( sF1 = $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 )
=> ( !! @ individuals
@ ^ [Y5: individuals] :
( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y4 @ Y6 )
=> ( sK0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f229,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 )
=> ( !! @ individuals
@ ^ [Y5: individuals] :
( !! @ $i
@ ^ [Y6: $i] :
( ( reli @ Y4 @ Y6 )
=> ( sK0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK10 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK10 @ Y0 )
=> ( ~ ( !! @ $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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ sK10 @ Y0 )
=> ( ~ ( !! @ $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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $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 ) ) ) ) ) ) ) ) ) ) ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( sF1 = $true )
| ( $false
= ( ( reli @ sK10 @ sK11 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f235,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( sF1 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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,[],[f233]) ).
thf(f237,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( ( reli @ sK11 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( relr @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !! @ individuals
@ ^ [Y2: individuals] :
( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( sK0 @ Y2 @ Y3 ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $true )
| ( ( ( relr @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( reli @ sK11 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( sF1 = $true )
| ( $false
= ( reli @ sK11 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !! @ individuals
@ ^ [Y1: individuals] :
( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) )
@ X3 )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( reli @ sK11 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( sF1 = $true )
| ( ( ( reli @ X2 @ X3 )
=> ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X3 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF1 = $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $true
= ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X3 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ sK11 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X1: $i,X4: individuals] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ X3 @ Y1 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X4 ) )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X1: $i,X4: individuals] :
( ( $false
= ( reli @ sK11 @ X1 ) )
| ( sF1 = $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK0 @ X4 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: $i,X1: $i,X4: individuals,X5: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( sF1 = $true )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( reli @ X3 @ Y0 )
=> ( sK0 @ X4 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X3: $i,X1: $i,X4: individuals,X5: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $true
= ( ( reli @ X3 @ X5 )
=> ( sK0 @ X4 @ X5 ) ) )
| ( sF1 = $true )
| ( $false
= ( reli @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X1: $i,X4: individuals,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X2 @ X3 ) )
| ( sF1 = $true )
| ( $false
= ( reli @ X3 @ X5 ) )
| ( $false
= ( reli @ sK11 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( reli @ sK11 @ 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 ) ) ) ) ) ) ) ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f253,plain,
( ( ( ( reli @ sK11 @ sK12 )
=> ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ sK12 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
( ( sF1 = $true )
| ( $false
= ( !! @ individuals
@ ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ sK12 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f255,plain,
( ( $true
= ( reli @ sK11 @ sK12 ) )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f253]) ).
thf(f256,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: individuals] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ sK12 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( sK0 @ Y0 @ Y3 ) ) ) ) ) ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f254]) ).
thf(f257,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ sK13 @ Y2 ) ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f258,plain,
( ( ( ^ [Y0: $i] :
( ( reli @ sK12 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ sK13 @ Y2 ) ) ) ) ) )
@ sK14 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( sF1 = $true )
| ( ( ( reli @ sK12 @ sK14 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK14 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ sK13 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( relr @ sK14 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ sK13 @ Y1 ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( ( sF1 = $true )
| ( ( reli @ sK12 @ sK14 )
= $true ) ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f262,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( relr @ sK14 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ sK13 @ Y1 ) ) ) )
@ sK15 ) ) ),
inference(sigma_proxy_clausification,[],[f260]) ).
thf(f263,plain,
( ( $false
= ( ( relr @ sK14 @ sK15 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK15 @ Y0 )
=> ( sK0 @ sK13 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f262]) ).
thf(f264,plain,
( ( sF1 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK15 @ Y0 )
=> ( sK0 @ sK13 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ( sF1 = $true )
| ( ( relr @ sK14 @ sK15 )
= $true ) ),
inference(imp_proxy_clausification,[],[f263]) ).
thf(f266,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ( reli @ sK15 @ Y0 )
=> ( sK0 @ sK13 @ Y0 ) )
@ sK16 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f264]) ).
thf(f267,plain,
( ( ( ( reli @ sK15 @ sK16 )
=> ( sK0 @ sK13 @ sK16 ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
( ( $false
= ( sK0 @ sK13 @ sK16 ) )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( ( reli @ sK15 @ sK16 )
= $true )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f334,definition,
( spl20_7
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
thf(f343,definition,
( spl20_9
<=> ! [X2: $i,X3: $i,X4: individuals,X5: $i,X1: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X3 @ X5 ) )
| ( $false
= ( reli @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
thf(f344,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: individuals,X5: $i] :
( ( $false
= ( relr @ X1 @ X2 ) )
| ( $false
= ( reli @ X3 @ X5 ) )
| ( ( sK0 @ X4 @ X5 )
= $true )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $false
= ( reli @ X2 @ X3 ) ) )
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f343]) ).
thf(f345,plain,
( spl20_7
| spl20_9 ),
inference(avatar_split_clause,[],[f251,f343,f334]) ).
thf(f347,definition,
( spl20_10
<=> ( $true
= ( reli @ sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
thf(f349,plain,
( ( $true
= ( reli @ sK11 @ sK12 ) )
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f350,plain,
( spl20_10
| spl20_7 ),
inference(avatar_split_clause,[],[f255,f334,f347]) ).
thf(f352,definition,
( spl20_11
<=> ( ( reli @ sK12 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition]) ).
thf(f354,plain,
( ( ( reli @ sK12 @ sK14 )
= $true )
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f355,plain,
( spl20_7
| spl20_11 ),
inference(avatar_split_clause,[],[f261,f352,f334]) ).
thf(f357,definition,
( spl20_12
<=> ( ( relr @ sK14 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition]) ).
thf(f359,plain,
( ( ( relr @ sK14 @ sK15 )
= $true )
| ~ spl20_12 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f360,plain,
( spl20_7
| spl20_12 ),
inference(avatar_split_clause,[],[f265,f357,f334]) ).
thf(f362,definition,
( spl20_13
<=> ( ( reli @ sK15 @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition]) ).
thf(f364,plain,
( ( ( reli @ sK15 @ sK16 )
= $true )
| ~ spl20_13 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f365,plain,
( spl20_13
| spl20_7 ),
inference(avatar_split_clause,[],[f269,f334,f362]) ).
thf(f367,definition,
( spl20_14
<=> ( $false
= ( sK0 @ sK13 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition]) ).
thf(f369,plain,
( ( $false
= ( sK0 @ sK13 @ sK16 ) )
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f370,plain,
( spl20_7
| spl20_14 ),
inference(avatar_split_clause,[],[f268,f367,f334]) ).
thf(f371,plain,
~ spl20_7,
inference(avatar_split_clause,[],[f129,f334]) ).
thf(f398,plain,
! [X0: $i] :
( ( $false = $true )
| ( $true
= ( reli @ X0 @ X0 ) )
| ( $true
= ( reli @ X0 @ X0 ) ) ),
inference(constrained_superposition,[],[f146,f147]) ).
thf(f399,plain,
! [X0: $i] :
( ( $true
= ( reli @ X0 @ X0 ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[],[f398]) ).
thf(f400,plain,
! [X0: $i] :
( $true
= ( reli @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f399]) ).
thf(f425,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X0 @ X3 ) )
| ( ( reli @ X0 @ X4 )
= $true )
| ( $false = $true )
| ( ( reli @ X0 @ X2 )
= $true )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( ( reli @ X1 @ X2 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false ) ),
inference(constrained_superposition,[],[f164,f161]) ).
thf(f429,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( reli @ X0 @ X3 ) )
| ( ( reli @ X0 @ X2 )
= $true )
| ( ( reli @ X1 @ X2 )
= $false )
| ( ( reli @ X3 @ X4 )
= $false )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( ( reli @ X0 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f425]) ).
thf(f443,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( reli @ sK11 @ sK14 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( reli @ sK15 @ X0 ) ) )
| ~ spl20_9
| ~ spl20_12 ),
inference(constrained_superposition,[],[f344,f359]) ).
thf(f458,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( reli @ sK15 @ X0 ) )
| ( $false
= ( reli @ sK11 @ sK14 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) ) )
| ~ spl20_9
| ~ spl20_12 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f462,definition,
( spl20_15
<=> ( $false
= ( reli @ sK11 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
thf(f464,plain,
( ( $false
= ( reli @ sK11 @ sK14 ) )
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f462]) ).
thf(f466,definition,
( spl20_16
<=> ! [X2: individuals,X0: $i,X1: $i] :
( ( $false
= ( reli @ sK15 @ X0 ) )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
thf(f467,plain,
( ! [X2: individuals,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( reli @ X0 @ X1 ) )
| ( $false
= ( reli @ sK15 @ X0 ) ) )
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f466]) ).
thf(f469,plain,
( spl20_16
| spl20_15
| ~ spl20_9
| ~ spl20_12 ),
inference(avatar_split_clause,[],[f458,f357,f343,f462,f466]) ).
thf(f590,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( reli @ sK11 @ X2 )
= $true )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $true
= ( reli @ sK11 @ X0 ) )
| ( $false = $true )
| ( $false
= ( reli @ X1 @ X0 ) )
| ( $false
= ( reli @ sK12 @ X2 ) ) )
| ~ spl20_10 ),
inference(constrained_superposition,[],[f349,f429]) ).
thf(f612,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( reli @ sK12 @ X2 ) )
| ( ( reli @ sK11 @ X2 )
= $true )
| ( $true
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( reli @ X1 @ X0 ) )
| ( $false
= ( reli @ sK11 @ X1 ) ) )
| ~ spl20_10 ),
inference(trivial_inequality_removal,[],[f590]) ).
thf(f619,definition,
( spl20_19
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $false
= ( reli @ X1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_19])],[avatar_definition]) ).
thf(f620,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( reli @ sK11 @ X1 ) )
| ( $false
= ( reli @ X1 @ X0 ) ) )
| ~ spl20_19 ),
inference(avatar_component_clause,[],[f619]) ).
thf(f622,definition,
( spl20_20
<=> ! [X2: $i] :
( ( ( reli @ sK11 @ X2 )
= $true )
| ( $false
= ( reli @ sK12 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_20])],[avatar_definition]) ).
thf(f623,plain,
( ! [X2: $i] :
( ( $false
= ( reli @ sK12 @ X2 ) )
| ( ( reli @ sK11 @ X2 )
= $true ) )
| ~ spl20_20 ),
inference(avatar_component_clause,[],[f622]) ).
thf(f647,plain,
( spl20_20
| spl20_19
| ~ spl20_10 ),
inference(avatar_split_clause,[],[f612,f347,f619,f622]) ).
thf(f993,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK14 ) ) )
| ~ spl20_15
| ~ spl20_19 ),
inference(constrained_superposition,[],[f620,f464]) ).
thf(f1020,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ sK11 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK14 ) ) )
| ~ spl20_15
| ~ spl20_19 ),
inference(trivial_inequality_removal,[],[f993]) ).
thf(f1048,plain,
( ( $false = $true )
| ( ( reli @ sK12 @ sK14 )
= $false )
| ~ spl20_10
| ~ spl20_15
| ~ spl20_19 ),
inference(constrained_superposition,[],[f349,f1020]) ).
thf(f1057,plain,
( ( ( reli @ sK12 @ sK14 )
= $false )
| ~ spl20_10
| ~ spl20_15
| ~ spl20_19 ),
inference(trivial_inequality_removal,[],[f1048]) ).
thf(f1069,plain,
( ( $false = $true )
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_19 ),
inference(forward_demodulation,[],[f1057,f354]) ).
thf(f1070,plain,
( $false
| ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_19 ),
inference(trivial_inequality_removal,[],[f1069]) ).
thf(f1071,plain,
( ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_19 ),
inference(avatar_contradiction_clause,[],[f1070]) ).
thf(f1080,plain,
( ( $false = $true )
| ( ( reli @ sK11 @ sK14 )
= $true )
| ~ spl20_11
| ~ spl20_20 ),
inference(constrained_superposition,[],[f354,f623]) ).
thf(f1089,plain,
( ( ( reli @ sK11 @ sK14 )
= $true )
| ~ spl20_11
| ~ spl20_20 ),
inference(trivial_inequality_removal,[],[f1080]) ).
thf(f1101,plain,
( ( $false = $true )
| ~ spl20_11
| ~ spl20_15
| ~ spl20_20 ),
inference(forward_demodulation,[],[f1089,f464]) ).
thf(f1102,plain,
( $false
| ~ spl20_11
| ~ spl20_15
| ~ spl20_20 ),
inference(trivial_inequality_removal,[],[f1101]) ).
thf(f1103,plain,
( ~ spl20_11
| ~ spl20_15
| ~ spl20_20 ),
inference(avatar_contradiction_clause,[],[f1102]) ).
thf(f1225,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ X0 @ sK16 ) )
| ( $false
= ( reli @ sK15 @ X0 ) )
| ( $false = $true ) )
| ~ spl20_14
| ~ spl20_16 ),
inference(constrained_superposition,[],[f369,f467]) ).
thf(f1232,plain,
( ! [X0: $i] :
( ( $false
= ( reli @ sK15 @ X0 ) )
| ( $false
= ( reli @ X0 @ sK16 ) ) )
| ~ spl20_14
| ~ spl20_16 ),
inference(trivial_inequality_removal,[],[f1225]) ).
thf(f1244,plain,
( ( ( reli @ sK15 @ sK16 )
= $false )
| ( $false = $true )
| ~ spl20_14
| ~ spl20_16 ),
inference(constrained_superposition,[],[f1232,f400]) ).
thf(f1261,plain,
( ( ( reli @ sK15 @ sK16 )
= $false )
| ~ spl20_14
| ~ spl20_16 ),
inference(trivial_inequality_removal,[],[f1244]) ).
thf(f1274,plain,
( ( $false = $true )
| ~ spl20_13
| ~ spl20_14
| ~ spl20_16 ),
inference(forward_demodulation,[],[f1261,f364]) ).
thf(f1275,plain,
( $false
| ~ spl20_13
| ~ spl20_14
| ~ spl20_16 ),
inference(trivial_inequality_removal,[],[f1274]) ).
thf(f1276,plain,
( ~ spl20_13
| ~ spl20_14
| ~ spl20_16 ),
inference(avatar_contradiction_clause,[],[f1275]) ).
cnf(s7,plain,
( spl20_7
| spl20_9 ),
inference(sat_conversion,[],[f345]) ).
cnf(s8,plain,
( spl20_7
| spl20_10 ),
inference(sat_conversion,[],[f350]) ).
cnf(s9,plain,
( spl20_7
| spl20_11 ),
inference(sat_conversion,[],[f355]) ).
cnf(s10,plain,
( spl20_7
| spl20_12 ),
inference(sat_conversion,[],[f360]) ).
cnf(s11,plain,
( spl20_7
| spl20_13 ),
inference(sat_conversion,[],[f365]) ).
cnf(s12,plain,
( spl20_7
| spl20_14 ),
inference(sat_conversion,[],[f370]) ).
cnf(s13,plain,
~ spl20_7,
inference(sat_conversion,[],[f371]) ).
cnf(s16,plain,
( ~ spl20_9
| ~ spl20_12
| spl20_15
| spl20_16 ),
inference(sat_conversion,[],[f469]) ).
cnf(s24,plain,
( ~ spl20_10
| spl20_19
| spl20_20 ),
inference(sat_conversion,[],[f647]) ).
cnf(s36,plain,
( ~ spl20_10
| ~ spl20_11
| ~ spl20_15
| ~ spl20_19 ),
inference(sat_conversion,[],[f1071]) ).
cnf(s38,plain,
( ~ spl20_11
| ~ spl20_15
| ~ spl20_20 ),
inference(sat_conversion,[],[f1103]) ).
cnf(s45,plain,
( ~ spl20_13
| ~ spl20_14
| ~ spl20_16 ),
inference(sat_conversion,[],[f1276]) ).
cnf(s47,plain,
spl20_14,
inference(rat,[],[s12,s13]) ).
cnf(s48,plain,
spl20_13,
inference(rat,[],[s11,s13]) ).
cnf(s49,plain,
~ spl20_16,
inference(rat,[],[s45,s47,s48]) ).
cnf(s50,plain,
spl20_12,
inference(rat,[],[s10,s13]) ).
cnf(s51,plain,
spl20_11,
inference(rat,[],[s9,s13]) ).
cnf(s52,plain,
spl20_10,
inference(rat,[],[s8,s13]) ).
cnf(s53,plain,
spl20_9,
inference(rat,[],[s7,s13]) ).
cnf(s55,plain,
spl20_15,
inference(rat,[],[s16,s49,s50,s53]) ).
cnf(s56,plain,
~ spl20_20,
inference(rat,[],[s38,s51,s55]) ).
cnf(s57,plain,
~ spl20_19,
inference(rat,[],[s36,s52,s51,s55]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s24,s52,s56,s57]) ).
thf(f1277,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO932^9 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n015.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 17:31:48 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.32 % (3850600)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (3850607)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1317010272:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (3850607)Instruction limit reached!
% 0.21/0.32 % (3850607)------------------------------
% 0.21/0.32 % (3850607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850607)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850607)Termination reason: Instruction limit
% 0.21/0.32 % (3850607)Termination phase: Saturation
% 0.21/0.32 % (3850607)Time elapsed: 0.002 s
% 0.21/0.32 % (3850607)Peak memory usage: 11 MB
% 0.21/0.32 % (3850607)Instructions burned: 10 (million)
% 0.21/0.32 % (3850611)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (3850611)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
% 0.21/0.32 % (3850605)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=868609969:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (3850606)lrs+10_16_si=on:nwc=1.5:random_seed=3665625576:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (3850609)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3260843303:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (3850610)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=637463498:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (3850608)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=1910090307: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)
% 0.21/0.32 % (3850611)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=3197806007:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (3850613)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=813515637:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.32 % (3850613)Instruction limit reached!
% 0.21/0.32 % (3850613)------------------------------
% 0.21/0.32 % (3850613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850613)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850613)Termination reason: Instruction limit
% 0.21/0.32 % (3850613)Termination phase: Function definition elimination
% 0.21/0.32 % (3850613)Time elapsed: 0.001 s
% 0.21/0.32 % (3850613)Peak memory usage: 11 MB
% 0.21/0.32 % (3850613)Instructions burned: 4 (million)
% 0.21/0.32 % (3850606)Instruction limit reached!
% 0.21/0.32 % (3850606)------------------------------
% 0.21/0.32 % (3850606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850606)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850606)Termination reason: Instruction limit
% 0.21/0.32 % (3850606)Termination phase: Saturation
% 0.21/0.32 % (3850606)Time elapsed: 0.009 s
% 0.21/0.32 % (3850606)Peak memory usage: 12 MB
% 0.21/0.32 % (3850606)Instructions burned: 19 (million)
% 0.21/0.32 % (3850609)Instruction limit reached!
% 0.21/0.32 % (3850609)------------------------------
% 0.21/0.32 % (3850609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850609)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850609)Termination reason: Instruction limit
% 0.21/0.32 % (3850609)Termination phase: Saturation
% 0.21/0.32 % (3850609)Time elapsed: 0.014 s
% 0.21/0.32 % (3850609)Peak memory usage: 12 MB
% 0.21/0.32 % (3850609)Instructions burned: 24 (million)
% 0.21/0.32 % (3850621)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2001257870:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.32 % (3850621)Instruction limit reached!
% 0.21/0.32 % (3850621)------------------------------
% 0.21/0.32 % (3850621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850621)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850621)Termination reason: Instruction limit
% 0.21/0.32 % (3850621)Termination phase: Saturation
% 0.21/0.32 % (3850621)Time elapsed: 0.002 s
% 0.21/0.32 % (3850621)Peak memory usage: 11 MB
% 0.21/0.32 % (3850621)Instructions burned: 8 (million)
% 0.21/0.32 % (3850622)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (3850625)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
% 0.21/0.32 % (3850625)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (3850622)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4244521048:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.32 % (3850625)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4113728366:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.32 % (3850623)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=699841072:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.32 % (3850622)Instruction limit reached!
% 0.21/0.32 % (3850622)------------------------------
% 0.21/0.32 % (3850622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850622)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850622)Termination reason: Instruction limit
% 0.21/0.32 % (3850622)Termination phase: Saturation
% 0.21/0.32 % (3850622)Time elapsed: 0.004 s
% 0.21/0.32 % (3850622)Peak memory usage: 11 MB
% 0.21/0.32 % (3850622)Instructions burned: 9 (million)
% 0.21/0.32 % (3850625)Instruction limit reached!
% 0.21/0.32 % (3850625)------------------------------
% 0.21/0.32 % (3850625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850625)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850625)Termination reason: Instruction limit
% 0.21/0.32 % (3850625)Termination phase: Saturation
% 0.21/0.32 % (3850625)Time elapsed: 0.007 s
% 0.21/0.32 % (3850625)Peak memory usage: 12 MB
% 0.21/0.32 % (3850625)Instructions burned: 30 (million)
% 0.21/0.32 % (3850610)Instruction limit reached!
% 0.21/0.32 % (3850610)------------------------------
% 0.21/0.32 % (3850610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850610)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850610)Termination reason: Instruction limit
% 0.21/0.32 % (3850610)Termination phase: Saturation
% 0.21/0.32 % (3850610)Time elapsed: 0.038 s
% 0.21/0.32 % (3850610)Peak memory usage: 12 MB
% 0.21/0.32 % (3850610)Instructions burned: 75 (million)
% 0.21/0.32 % (3850623)Instruction limit reached!
% 0.21/0.32 % (3850623)------------------------------
% 0.21/0.32 % (3850623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850623)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850623)Termination reason: Instruction limit
% 0.21/0.32 % (3850623)Termination phase: Saturation
% 0.21/0.32 % (3850623)Time elapsed: 0.006 s
% 0.21/0.32 % (3850623)Peak memory usage: 11 MB
% 0.21/0.32 % (3850623)Instructions burned: 13 (million)
% 0.21/0.32 % (3850605)Instruction limit reached!
% 0.21/0.32 % (3850605)------------------------------
% 0.21/0.32 % (3850605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850605)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850605)Termination reason: Instruction limit
% 0.21/0.32 % (3850605)Termination phase: Saturation
% 0.21/0.32 % (3850605)Time elapsed: 0.044 s
% 0.21/0.32 % (3850605)Peak memory usage: 12 MB
% 0.21/0.32 % (3850605)Instructions burned: 89 (million)
% 0.21/0.32 % (3850611) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3850600-3850611"...
% 0.21/0.32 % (3850630)lrs+10_1_si=on:cs=on:random_seed=4239642696:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.32 % (3850630)Instruction limit reached!
% 0.21/0.32 % (3850630)------------------------------
% 0.21/0.32 % (3850630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850630)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850630)Termination reason: Instruction limit
% 0.21/0.32 % (3850630)Termination phase: Saturation
% 0.21/0.32 % (3850630)Time elapsed: 0.002 s
% 0.21/0.32 % (3850630)Peak memory usage: 11 MB
% 0.21/0.32 % (3850630)Instructions burned: 8 (million)
% 0.21/0.32 % (3850629)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=1041405075:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.32 % (3850631)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.32 % (3850611)...printing done.
% 0.21/0.32 % (3850611)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (3850611)------------------------------
% 0.21/0.32 % (3850611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3850611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3850611)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3850611)Termination reason: Refutation
% 0.21/0.32 % (3850611)Time elapsed: 0.053 s
% 0.21/0.32 % (3850611)Peak memory usage: 14 MB
% 0.21/0.32 % (3850611)Instructions burned: 106 (million)
% 0.21/0.32 % (3850600)Success in time 0.087 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------