%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:14:38 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 31
% Syntax : Number of formulae : 260 ( 78 unt; 0 typ; 18 def)
% Number of atoms : 2188 ( 399 equ; 0 cnn)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 3225 ( 346 ~; 582 |; 26 &;2000 @)
% ( 16 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 437 ( 437 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 81 usr; 27 con; 0-4 aty)
% ( 235 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 784 ( 0 sgn 149 !; 0 ?; 784 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
ra: $i > $i > $o ).
thf(func_def_33,type,
rb: $i > $i > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
sF0: $o ).
thf(func_def_50,type,
sF1: $o ).
thf(func_def_52,type,
sK3: $i > $o ).
thf(func_def_53,type,
sK4: $i > $o ).
thf(func_def_56,type,
sK7: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(func_def_57,type,
sK8: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(func_def_58,type,
sK9: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
sK11: $i > $o ).
thf(func_def_61,type,
sK12: $i > $o ).
thf(func_def_64,type,
sK15: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(func_def_65,type,
sK16: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(func_def_66,type,
sK17: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
mreflexive @ ra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f33,axiom,
mreflexive @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(f36,axiom,
meuclidean @ ra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(f37,axiom,
meuclidean @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(f38,conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ ra @ X1 ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ rb @ X0 ) @ ( mbox @ rb @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f39,negated_conjecture,
~ ( ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ ra @ X1 ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ rb @ X0 ) @ ( mbox @ rb @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
thf(f46,plain,
mreflexive @ rb,
inference(rectify,[],[f33]) ).
thf(f47,plain,
( ( mreflexive @ rb )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f49,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f51,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f52,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f54,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f55,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f64,plain,
meuclidean @ ra,
inference(rectify,[],[f36]) ).
thf(f65,plain,
( ( meuclidean @ ra )
= $true ),
inference(fool_elimination,[],[f64]) ).
thf(f77,plain,
mreflexive @ ra,
inference(rectify,[],[f32]) ).
thf(f78,plain,
( ( mreflexive @ ra )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f82,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f83,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f86,plain,
~ ( ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ ra @ X1 ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] :
( mforall_prop
@ ^ [X3: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ X2 ) @ ( mbox @ rb @ X3 ) ) ) @ ( mor @ ( mbox @ rb @ X2 ) @ ( mbox @ rb @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f87,plain,
~ ( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ rb @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) ) ) ) )
& ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ ra @ Y1 ) ) ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f86]) ).
thf(f90,plain,
meuclidean @ rb,
inference(rectify,[],[f37]) ).
thf(f91,plain,
( ( meuclidean @ rb )
= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f95,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f96,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f98,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f103,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f104,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ ra @ Y1 ) ) ) ) ) )
!= $true )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ rb @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f109,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f110,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f115,plain,
( ( meuclidean @ ra )
= $true ),
inference(cnf_transformation,[],[f65]) ).
thf(f123,plain,
( ( meuclidean @ rb )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f124,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ ra @ Y1 ) ) ) ) ) )
!= $true )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ rb @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f125,plain,
( ( mreflexive @ rb )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f127,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f134,plain,
( ( mreflexive @ ra )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f135,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f136,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f137,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f140,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f147,plain,
( mimplies
= ( ^ [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,[],[f107,f110,f127]) ).
thf(f156,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ra )
= $true ),
inference(definition_unfolding,[],[f115,f137]) ).
thf(f158,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rb )
= $true ),
inference(definition_unfolding,[],[f123,f137]) ).
thf(f159,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) ) ) ) )
!= $true ) ),
inference(definition_unfolding,[],[f124,f136,f109,f109,f147,f140,f110,f140,f140,f110,f140,f140,f136,f109,f109,f147,f140,f110,f140,f140,f110,f140,f140]) ).
thf(f160,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rb ) ),
inference(definition_unfolding,[],[f125,f135]) ).
thf(f161,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ ra ) ),
inference(definition_unfolding,[],[f134,f135]) ).
thf(f162,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f163,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y1 ) ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f162]) ).
thf(f164,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f165,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f164]) ).
thf(f166,plain,
( ( $true != sF1 )
| ( $true != sF0 ) ),
inference(definition_folding,[],[f159,f165,f163]) ).
thf(f167,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rb @ Y2 @ Y0 )
& ( rb @ Y2 @ Y1 ) )
=> ( rb @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f168,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rb @ Y2 @ Y0 )
& ( rb @ Y2 @ Y1 ) )
=> ( rb @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rb @ Y1 @ X1 )
& ( rb @ Y1 @ Y0 ) )
=> ( rb @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rb @ Y1 @ X1 )
& ( rb @ Y1 @ Y0 ) )
=> ( rb @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rb @ Y0 @ X1 )
& ( rb @ Y0 @ X2 ) )
=> ( rb @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rb @ Y0 @ X1 )
& ( rb @ Y0 @ X2 ) )
=> ( rb @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rb @ X3 @ X1 )
& ( rb @ X3 @ X2 ) )
=> ( rb @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ X2 @ X1 ) )
| ( ( ( rb @ X3 @ X1 )
& ( rb @ X3 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ X2 @ X1 ) )
| ( ( rb @ X3 @ X1 )
= $false )
| ( $false
= ( rb @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f186,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y1 ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f163]) ).
thf(f187,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( ra @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rb @ Y3 @ Y4 ) ) )
| ~ ( ra @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( ra @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( ra @ Y0 @ Y3 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( ra @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rb @ Y3 @ Y4 ) ) )
| ~ ( ra @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( ra @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( ra @ Y0 @ Y3 ) ) ) ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( ra @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rb @ Y2 @ Y3 ) ) )
| ~ ( ra @ sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( ra @ sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( ra @ sK2 @ Y2 ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( ra @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rb @ Y2 @ Y3 ) ) )
| ~ ( ra @ sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( ra @ sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( ra @ sK2 @ Y2 ) ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( ra @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rb @ Y1 @ Y2 ) ) )
| ~ ( ra @ sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( ra @ sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( ra @ sK2 @ Y1 ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( sK3 @ Y2 )
| ~ ( ra @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rb @ Y1 @ Y2 ) ) )
| ~ ( ra @ sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( ra @ sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( ra @ sK2 @ Y1 ) ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( ra @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $true = sF0 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( ra @ sK2 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( ra @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK3 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK4 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( ra @ sK2 @ Y0 ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) )
| ~ ( ra @ sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( ( ~ ( ra @ sK2 @ X1 ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) ) )
= $true )
| ( ( ra @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( ( ra @ sK2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) )
= $true )
| ( $true = sF0 )
| ( ( ra @ sK2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) )
@ X3 ) )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK3 @ X2 )
| ~ ( ra @ X1 @ X2 ) )
= $true )
| ( $true
= ( ( sK4 @ X3 )
| ~ ( rb @ X1 @ X3 ) ) )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( sK4 @ X3 )
| ~ ( rb @ X1 @ X3 ) ) )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ~ ( ra @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK4 @ X3 )
= $true )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( $true = sF0 )
| ( $true
= ( ~ ( ra @ X1 @ X2 ) ) )
| ( ( sK3 @ X2 )
= $true )
| ( $true
= ( ~ ( rb @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rb @ X1 @ X3 ) ) )
| ( ( ra @ X1 @ X2 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( $true = sF0 )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( ( sK4 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rb @ X1 @ X3 ) )
| ( $true = sF0 )
| ( ( ra @ X1 @ X2 )
= $false )
| ( ( sK4 @ X3 )
= $true )
| ( ( sK3 @ X2 )
= $true )
| ( ( ra @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f210,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) ) )
= $false )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f211,plain,
( ( ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) )
@ sK5 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( ( ( sK3 @ sK5 )
| ~ ( ra @ sK2 @ sK5 ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
( ( $true = sF0 )
| ( ( ~ ( ra @ sK2 @ sK5 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $true = sF0 )
| ( ( sK3 @ sK5 )
= $false ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f215,plain,
( ( ( ra @ sK2 @ sK5 )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
| ~ ( ra @ sK2 @ Y0 ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f217,plain,
( ( $true = sF0 )
| ( ( ( sK4 @ sK6 )
| ~ ( ra @ sK2 @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
( ( $true = sF0 )
| ( ( ~ ( ra @ sK2 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f220,plain,
( ( $true
= ( ra @ sK2 @ sK6 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f257,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ra @ Y2 @ Y0 )
& ( ra @ Y2 @ Y1 ) )
=> ( ra @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f258,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ra @ Y2 @ Y0 )
& ( ra @ Y2 @ Y1 ) )
=> ( ra @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ra @ Y1 @ X1 )
& ( ra @ Y1 @ Y0 ) )
=> ( ra @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ra @ Y1 @ X1 )
& ( ra @ Y1 @ Y0 ) )
=> ( ra @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ra @ Y0 @ X1 )
& ( ra @ Y0 @ X2 ) )
=> ( ra @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( ra @ Y0 @ X1 )
& ( ra @ Y0 @ X2 ) )
=> ( ra @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( ra @ X3 @ X1 )
& ( ra @ X3 @ X2 ) )
=> ( ra @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ra @ X2 @ X1 ) )
| ( ( ( ra @ X3 @ X1 )
& ( ra @ X3 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ra @ X2 @ X1 ) )
| ( ( ra @ X3 @ X1 )
= $false )
| ( $false
= ( ra @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( ra @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f267,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ra @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X1: $i] :
( ( ra @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f270,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) )
@ rb
@ Y1 ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f165]) ).
thf(f271,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( ra @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rb @ Y3 @ Y4 ) ) )
| ~ ( rb @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rb @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( rb @ Y0 @ Y3 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( ra @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rb @ Y3 @ Y4 ) ) )
| ~ ( rb @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rb @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
| ~ ( rb @ Y0 @ Y3 ) ) ) ) ) )
@ sK10 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f271]) ).
thf(f273,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( ra @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rb @ Y2 @ Y3 ) ) )
| ~ ( rb @ sK10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rb @ sK10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( rb @ sK10 @ Y2 ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
| ~ ( ra @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rb @ Y2 @ Y3 ) ) )
| ~ ( rb @ sK10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rb @ sK10 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( rb @ sK10 @ Y2 ) ) ) ) )
@ sK11 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f273]) ).
thf(f275,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ Y2 )
| ~ ( ra @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rb @ Y1 @ Y2 ) ) )
| ~ ( rb @ sK10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK11 @ Y1 )
| ~ ( rb @ sK10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( rb @ sK10 @ Y1 ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f276,plain,
( ( ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ Y2 )
| ~ ( ra @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rb @ Y1 @ Y2 ) ) )
| ~ ( rb @ sK10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK11 @ Y1 )
| ~ ( rb @ sK10 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( rb @ sK10 @ Y1 ) ) ) )
@ sK12 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f275]) ).
thf(f277,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK11 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK12 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( rb @ sK10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f276]) ).
thf(f278,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK11 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK12 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( rb @ sK10 @ Y0 ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f277]) ).
thf(f280,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK11 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK12 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( rb @ sK10 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK11 @ Y1 )
| ~ ( ra @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK12 @ Y1 )
| ~ ( rb @ Y0 @ Y1 ) ) )
| ~ ( rb @ sK10 @ Y0 ) )
@ X1 ) )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X1: $i] :
( ( $true = sF1 )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) )
| ~ ( rb @ sK10 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( rb @ sK10 @ X1 ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rb @ sK10 @ X1 ) ) )
| ( $true = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( $true = sF1 )
| ( $true
= ( ~ ( rb @ sK10 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) ) ) )
| ( $true = sF1 )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = sF1 )
| ( $true
= ( ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( ra @ X1 @ Y0 ) )
@ X3 ) )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = sF1 )
| ( $true
= ( ( sK11 @ X3 )
| ~ ( ra @ X1 @ X3 ) ) )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( $true
= ( ( sK12 @ X2 )
| ~ ( rb @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK12 @ X2 )
| ~ ( rb @ X1 @ X2 ) ) )
| ( ( ~ ( ra @ X1 @ X3 ) )
= $true )
| ( ( sK11 @ X3 )
= $true )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = sF1 )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( ( sK11 @ X3 )
= $true )
| ( $true
= ( sK12 @ X2 ) )
| ( ( ~ ( ra @ X1 @ X3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( ra @ X1 @ X3 ) )
= $true )
| ( ( sK11 @ X3 )
= $true )
| ( $true
= ( sK12 @ X2 ) )
| ( ( rb @ X1 @ X2 )
= $false )
| ( $true = sF1 )
| ( ( rb @ sK10 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK11 @ X3 )
= $true )
| ( ( rb @ X1 @ X2 )
= $false )
| ( ( ra @ X1 @ X3 )
= $false )
| ( $true
= ( sK12 @ X2 ) )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f293,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f294,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f295,plain,
( ( ( ^ [Y0: $i] :
( ( sK11 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) )
@ sK13 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( ( ( sK11 @ sK13 )
| ~ ( rb @ sK10 @ sK13 ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f297,plain,
( ( ( ~ ( rb @ sK10 @ sK13 ) )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( ( $true = sF1 )
| ( ( sK11 @ sK13 )
= $false ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f299,plain,
( ( $true = sF1 )
| ( $true
= ( rb @ sK10 @ sK13 ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f300,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( ( sK12 @ Y0 )
| ~ ( rb @ sK10 @ Y0 ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f293]) ).
thf(f301,plain,
( ( $true = sF1 )
| ( ( ( sK12 @ sK14 )
| ~ ( rb @ sK10 @ sK14 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f300]) ).
thf(f302,plain,
( ( $true = sF1 )
| ( ( ~ ( rb @ sK10 @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( $true = sF1 )
| ( ( sK12 @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f304,plain,
( ( $true
= ( rb @ sK10 @ sK14 ) )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f340,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rb @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f341,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rb @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X1: $i] :
( ( rb @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f353,definition,
( spl18_1
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
thf(f357,definition,
( spl18_2
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f360,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f166,f357,f353]) ).
thf(f362,definition,
( spl18_3
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( rb @ X1 @ X3 ) )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( ( sK3 @ X2 )
= $true )
| ( ( sK4 @ X3 )
= $true )
| ( ( ra @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
thf(f363,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rb @ X1 @ X3 ) )
| ( ( ra @ sK2 @ X1 )
= $false )
| ( ( sK4 @ X3 )
= $true )
| ( ( sK3 @ X2 )
= $true )
| ( ( ra @ X1 @ X2 )
= $false ) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f364,plain,
( spl18_3
| spl18_2 ),
inference(avatar_split_clause,[],[f208,f357,f362]) ).
thf(f366,definition,
( spl18_4
<=> ( ( sK3 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
thf(f368,plain,
( ( ( sK3 @ sK5 )
= $false )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f369,plain,
( spl18_4
| spl18_2 ),
inference(avatar_split_clause,[],[f214,f357,f366]) ).
thf(f371,definition,
( spl18_5
<=> ( ( ra @ sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
thf(f373,plain,
( ( ( ra @ sK2 @ sK5 )
= $true )
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f374,plain,
( spl18_5
| spl18_2 ),
inference(avatar_split_clause,[],[f215,f357,f371]) ).
thf(f376,definition,
( spl18_6
<=> ( $false
= ( sK4 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
thf(f378,plain,
( ( $false
= ( sK4 @ sK6 ) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f379,plain,
( spl18_6
| spl18_2 ),
inference(avatar_split_clause,[],[f219,f357,f376]) ).
thf(f381,definition,
( spl18_7
<=> ( $true
= ( ra @ sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
thf(f383,plain,
( ( $true
= ( ra @ sK2 @ sK6 ) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f384,plain,
( spl18_2
| spl18_7 ),
inference(avatar_split_clause,[],[f220,f381,f357]) ).
thf(f410,definition,
( spl18_14
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK11 @ X3 )
= $true )
| ( ( rb @ sK10 @ X1 )
= $false )
| ( $true
= ( sK12 @ X2 ) )
| ( ( rb @ X1 @ X2 )
= $false )
| ( ( ra @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_14])],[avatar_definition]) ).
thf(f411,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( rb @ sK10 @ X1 )
= $false )
| ( $true
= ( sK12 @ X2 ) )
| ( ( sK11 @ X3 )
= $true )
| ( ( rb @ X1 @ X2 )
= $false )
| ( ( ra @ X1 @ X3 )
= $false ) )
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f410]) ).
thf(f412,plain,
( spl18_14
| spl18_1 ),
inference(avatar_split_clause,[],[f292,f353,f410]) ).
thf(f414,definition,
( spl18_15
<=> ( ( sK11 @ sK13 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_15])],[avatar_definition]) ).
thf(f416,plain,
( ( ( sK11 @ sK13 )
= $false )
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f414]) ).
thf(f417,plain,
( spl18_1
| spl18_15 ),
inference(avatar_split_clause,[],[f298,f414,f353]) ).
thf(f419,definition,
( spl18_16
<=> ( $true
= ( rb @ sK10 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_16])],[avatar_definition]) ).
thf(f421,plain,
( ( $true
= ( rb @ sK10 @ sK13 ) )
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f422,plain,
( spl18_16
| spl18_1 ),
inference(avatar_split_clause,[],[f299,f353,f419]) ).
thf(f424,definition,
( spl18_17
<=> ( ( sK12 @ sK14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_17])],[avatar_definition]) ).
thf(f426,plain,
( ( ( sK12 @ sK14 )
= $false )
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f427,plain,
( spl18_17
| spl18_1 ),
inference(avatar_split_clause,[],[f303,f353,f424]) ).
thf(f429,definition,
( spl18_18
<=> ( $true
= ( rb @ sK10 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_18])],[avatar_definition]) ).
thf(f431,plain,
( ( $true
= ( rb @ sK10 @ sK14 ) )
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f432,plain,
( spl18_1
| spl18_18 ),
inference(avatar_split_clause,[],[f304,f429,f353]) ).
thf(f512,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( ra @ sK13 @ X1 )
= $false )
| ( ( rb @ sK13 @ X0 )
= $false )
| ( ( sK11 @ X1 )
= $true )
| ( $true
= ( sK12 @ X0 ) ) )
| ~ spl18_14
| ~ spl18_16 ),
inference(constrained_superposition,[],[f421,f411]) ).
thf(f525,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK11 @ X1 )
= $true )
| ( ( ra @ sK13 @ X1 )
= $false )
| ( $true
= ( sK12 @ X0 ) )
| ( ( rb @ sK13 @ X0 )
= $false ) )
| ~ spl18_14
| ~ spl18_16 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f531,definition,
( spl18_25
<=> ! [X0: $i] :
( ( ( rb @ sK10 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_25])],[avatar_definition]) ).
thf(f532,plain,
( ! [X0: $i] :
( ( ( rb @ sK10 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) ) )
| ~ spl18_25 ),
inference(avatar_component_clause,[],[f531]) ).
thf(f547,definition,
( spl18_29
<=> ! [X0: $i] :
( ( ( rb @ sK13 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_29])],[avatar_definition]) ).
thf(f548,plain,
( ! [X0: $i] :
( ( ( rb @ sK13 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) ) )
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f547]) ).
thf(f550,definition,
( spl18_30
<=> ! [X1: $i] :
( ( ( ra @ sK13 @ X1 )
= $false )
| ( ( sK11 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl18_30])],[avatar_definition]) ).
thf(f551,plain,
( ! [X1: $i] :
( ( ( ra @ sK13 @ X1 )
= $false )
| ( ( sK11 @ X1 )
= $true ) )
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f550]) ).
thf(f553,plain,
( spl18_29
| spl18_30
| ~ spl18_14
| ~ spl18_16 ),
inference(avatar_split_clause,[],[f525,f419,f410,f550,f547]) ).
thf(f608,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK12 @ X0 ) )
| ( ( rb @ X1 @ X0 )
= $false )
| ( $true = $false )
| ( ( rb @ X1 @ sK13 )
= $false ) )
| ~ spl18_29 ),
inference(constrained_superposition,[],[f548,f175]) ).
thf(f614,plain,
( ! [X0: $i,X1: $i] :
( ( ( rb @ X1 @ sK13 )
= $false )
| ( ( rb @ X1 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) ) )
| ~ spl18_29 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f663,plain,
( ! [X0: $i] :
( ( ( rb @ sK10 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) )
| ( $true = $false ) )
| ~ spl18_16
| ~ spl18_29 ),
inference(constrained_superposition,[],[f614,f421]) ).
thf(f675,plain,
( ! [X0: $i] :
( ( ( rb @ sK10 @ X0 )
= $false )
| ( $true
= ( sK12 @ X0 ) ) )
| ~ spl18_16
| ~ spl18_29 ),
inference(trivial_inequality_removal,[],[f663]) ).
thf(f680,plain,
( spl18_25
| ~ spl18_16
| ~ spl18_29 ),
inference(avatar_split_clause,[],[f675,f547,f419,f531]) ).
thf(f688,plain,
( ( $true = $false )
| ( $true
= ( sK12 @ sK14 ) )
| ~ spl18_18
| ~ spl18_25 ),
inference(constrained_superposition,[],[f431,f532]) ).
thf(f701,plain,
( ( $true
= ( sK12 @ sK14 ) )
| ~ spl18_18
| ~ spl18_25 ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f707,plain,
( ( $true = $false )
| ~ spl18_17
| ~ spl18_18
| ~ spl18_25 ),
inference(forward_demodulation,[],[f701,f426]) ).
thf(f708,plain,
( $false
| ~ spl18_17
| ~ spl18_18
| ~ spl18_25 ),
inference(trivial_inequality_removal,[],[f707]) ).
thf(f709,plain,
( ~ spl18_17
| ~ spl18_18
| ~ spl18_25 ),
inference(avatar_contradiction_clause,[],[f708]) ).
thf(f715,plain,
( ( $true = $false )
| ( $true
= ( sK11 @ sK13 ) )
| ~ spl18_30 ),
inference(constrained_superposition,[],[f268,f551]) ).
thf(f725,plain,
( ( $true
= ( sK11 @ sK13 ) )
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f715]) ).
thf(f731,plain,
( ( $true = $false )
| ~ spl18_15
| ~ spl18_30 ),
inference(forward_demodulation,[],[f725,f416]) ).
thf(f732,plain,
( $false
| ~ spl18_15
| ~ spl18_30 ),
inference(trivial_inequality_removal,[],[f731]) ).
thf(f733,plain,
( ~ spl18_15
| ~ spl18_30 ),
inference(avatar_contradiction_clause,[],[f732]) ).
thf(f789,plain,
( ! [X0: $i,X1: $i] :
( ( ( ra @ X0 @ X1 )
= $false )
| ( $true
= ( sK4 @ X0 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( ra @ sK2 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl18_3 ),
inference(constrained_superposition,[],[f342,f363]) ).
thf(f795,plain,
( ! [X0: $i,X1: $i] :
( ( ( ra @ sK2 @ X0 )
= $false )
| ( $true
= ( sK4 @ X0 ) )
| ( ( sK3 @ X1 )
= $true )
| ( ( ra @ X0 @ X1 )
= $false ) )
| ~ spl18_3 ),
inference(trivial_inequality_removal,[],[f789]) ).
thf(f997,definition,
( spl18_39
<=> ! [X0: $i] :
( ( ( ra @ sK2 @ X0 )
= $false )
| ( $true
= ( sK3 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_39])],[avatar_definition]) ).
thf(f998,plain,
( ! [X0: $i] :
( ( ( ra @ sK2 @ X0 )
= $false )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl18_39 ),
inference(avatar_component_clause,[],[f997]) ).
thf(f1086,plain,
( ! [X0: $i] :
( ( $true
= ( sK3 @ X0 ) )
| ( $true = $false )
| ( $true
= ( sK4 @ sK6 ) )
| ( ( ra @ sK6 @ X0 )
= $false ) )
| ~ spl18_3
| ~ spl18_7 ),
inference(constrained_superposition,[],[f383,f795]) ).
thf(f1096,plain,
( ! [X0: $i] :
( ( $true
= ( sK4 @ sK6 ) )
| ( ( ra @ sK6 @ X0 )
= $false )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl18_3
| ~ spl18_7 ),
inference(trivial_inequality_removal,[],[f1086]) ).
thf(f1123,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK3 @ X0 ) )
| ( ( ra @ sK6 @ X0 )
= $false ) )
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(forward_demodulation,[],[f1096,f378]) ).
thf(f1124,plain,
( ! [X0: $i] :
( ( ( ra @ sK6 @ X0 )
= $false )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(trivial_inequality_removal,[],[f1123]) ).
thf(f1178,plain,
( ! [X0: $i,X1: $i] :
( ( ( ra @ X1 @ sK6 )
= $false )
| ( $true = $false )
| ( $true
= ( sK3 @ X0 ) )
| ( ( ra @ X1 @ X0 )
= $false ) )
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(constrained_superposition,[],[f265,f1124]) ).
thf(f1180,plain,
( ! [X0: $i,X1: $i] :
( ( ( ra @ X1 @ sK6 )
= $false )
| ( $true
= ( sK3 @ X0 ) )
| ( ( ra @ X1 @ X0 )
= $false ) )
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(trivial_inequality_removal,[],[f1178]) ).
thf(f1235,plain,
( ! [X0: $i] :
( ( ( ra @ sK2 @ X0 )
= $false )
| ( $true
= ( sK3 @ X0 ) )
| ( $true = $false ) )
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(constrained_superposition,[],[f1180,f383]) ).
thf(f1259,plain,
( ! [X0: $i] :
( ( ( ra @ sK2 @ X0 )
= $false )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(trivial_inequality_removal,[],[f1235]) ).
thf(f1272,plain,
( spl18_39
| ~ spl18_3
| ~ spl18_6
| ~ spl18_7 ),
inference(avatar_split_clause,[],[f1259,f381,f376,f362,f997]) ).
thf(f1284,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ( $true = $false )
| ~ spl18_5
| ~ spl18_39 ),
inference(constrained_superposition,[],[f373,f998]) ).
thf(f1298,plain,
( ( $true
= ( sK3 @ sK5 ) )
| ~ spl18_5
| ~ spl18_39 ),
inference(trivial_inequality_removal,[],[f1284]) ).
thf(f1315,plain,
( ( $true = $false )
| ~ spl18_4
| ~ spl18_5
| ~ spl18_39 ),
inference(forward_demodulation,[],[f1298,f368]) ).
thf(f1316,plain,
( $false
| ~ spl18_4
| ~ spl18_5
| ~ spl18_39 ),
inference(trivial_inequality_removal,[],[f1315]) ).
thf(f1317,plain,
( ~ spl18_4
| ~ spl18_5
| ~ spl18_39 ),
inference(avatar_contradiction_clause,[],[f1316]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f360]) ).
cnf(s2,plain,
( spl18_2
| spl18_3 ),
inference(sat_conversion,[],[f364]) ).
cnf(s3,plain,
( spl18_2
| spl18_4 ),
inference(sat_conversion,[],[f369]) ).
cnf(s4,plain,
( spl18_2
| spl18_5 ),
inference(sat_conversion,[],[f374]) ).
cnf(s5,plain,
( spl18_2
| spl18_6 ),
inference(sat_conversion,[],[f379]) ).
cnf(s6,plain,
( spl18_2
| spl18_7 ),
inference(sat_conversion,[],[f384]) ).
cnf(s12,plain,
( spl18_1
| spl18_14 ),
inference(sat_conversion,[],[f412]) ).
cnf(s13,plain,
( spl18_1
| spl18_15 ),
inference(sat_conversion,[],[f417]) ).
cnf(s14,plain,
( spl18_1
| spl18_16 ),
inference(sat_conversion,[],[f422]) ).
cnf(s15,plain,
( spl18_1
| spl18_17 ),
inference(sat_conversion,[],[f427]) ).
cnf(s16,plain,
( spl18_1
| spl18_18 ),
inference(sat_conversion,[],[f432]) ).
cnf(s26,plain,
( ~ spl18_14
| ~ spl18_16
| spl18_29
| spl18_30 ),
inference(sat_conversion,[],[f553]) ).
cnf(s30,plain,
( ~ spl18_16
| spl18_25
| ~ spl18_29 ),
inference(sat_conversion,[],[f680]) ).
cnf(s35,plain,
( ~ spl18_17
| ~ spl18_18
| ~ spl18_25 ),
inference(sat_conversion,[],[f709]) ).
cnf(s37,plain,
( ~ spl18_15
| ~ spl18_30 ),
inference(sat_conversion,[],[f733]) ).
cnf(s60,plain,
( ~ spl18_3
| ~ spl18_6
| ~ spl18_7
| spl18_39 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s66,plain,
( ~ spl18_4
| ~ spl18_5
| ~ spl18_39 ),
inference(sat_conversion,[],[f1317]) ).
cnf(s71,plain,
spl18_1,
inference(rat,[],[s30,s26,s37,s35,s12,s13,s14,s15,s16]) ).
cnf(s73,plain,
~ spl18_2,
inference(rat,[],[s1,s71]) ).
cnf(s80,plain,
spl18_7,
inference(rat,[],[s6,s73]) ).
cnf(s81,plain,
spl18_6,
inference(rat,[],[s5,s73]) ).
cnf(s82,plain,
spl18_5,
inference(rat,[],[s4,s73]) ).
cnf(s83,plain,
spl18_4,
inference(rat,[],[s3,s73]) ).
cnf(s84,plain,
spl18_3,
inference(rat,[],[s2,s73]) ).
cnf(s85,plain,
~ spl18_39,
inference(rat,[],[s66,s82,s83]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s60,s81,s80,s85,s84]) ).
thf(f1320,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 10:18:21 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.22/0.36 % (1911003)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (1911012)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3471969260:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (1911008)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=252808376:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (1911009)lrs+10_16_si=on:nwc=1.5:random_seed=140848473:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (1911010)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1991824341:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (1911011)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=3331780265: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)
% 0.22/0.36 % (1911010)Instruction limit reached!
% 0.22/0.36 % (1911010)------------------------------
% 0.22/0.36 % (1911010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911010)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911010)Termination reason: Instruction limit
% 0.22/0.36 % (1911010)Termination phase: Function definition elimination
% 0.22/0.36 % (1911010)Time elapsed: 0.003 s
% 0.22/0.36 % (1911010)Peak memory usage: 10 MB
% 0.22/0.36 % (1911010)Instructions burned: 7 (million)
% 0.22/0.36 % (1911014)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (1911014)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
% 0.22/0.36 % (1911013)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2354135437:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (1911014)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=2833148450:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (1911009)Instruction limit reached!
% 0.22/0.36 % (1911009)------------------------------
% 0.22/0.36 % (1911009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911009)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911009)Termination reason: Instruction limit
% 0.22/0.36 % (1911009)Termination phase: Saturation
% 0.22/0.36 % (1911009)Time elapsed: 0.009 s
% 0.22/0.36 % (1911009)Peak memory usage: 11 MB
% 0.22/0.36 % (1911009)Instructions burned: 19 (million)
% 0.22/0.36 % (1911012)Instruction limit reached!
% 0.22/0.36 % (1911012)------------------------------
% 0.22/0.36 % (1911012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911012)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911012)Termination reason: Instruction limit
% 0.22/0.36 % (1911012)Termination phase: Saturation
% 0.22/0.36 % (1911012)Time elapsed: 0.012 s
% 0.22/0.36 % (1911012)Peak memory usage: 11 MB
% 0.22/0.36 % (1911012)Instructions burned: 24 (million)
% 0.22/0.36 % (1911023)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3505175995:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.36 % (1911023)Instruction limit reached!
% 0.22/0.36 % (1911023)------------------------------
% 0.22/0.36 % (1911023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911023)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911023)Termination reason: Instruction limit
% 0.22/0.36 % (1911023)Termination phase: Property scanning
% 0.22/0.36 % (1911023)Time elapsed: 0.003 s
% 0.22/0.36 % (1911023)Peak memory usage: 10 MB
% 0.22/0.36 % (1911023)Instructions burned: 6 (million)
% 0.22/0.36 % (1911020)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3629519571:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.36 % (1911020)Instruction limit reached!
% 0.22/0.36 % (1911020)------------------------------
% 0.22/0.36 % (1911020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911020)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911020)Termination reason: Instruction limit
% 0.22/0.36 % (1911020)Termination phase: Property scanning
% 0.22/0.36 % (1911020)Time elapsed: 0.001 s
% 0.22/0.36 % (1911020)Peak memory usage: 10 MB
% 0.22/0.36 % (1911020)Instructions burned: 3 (million)
% 0.22/0.36 % (1911024)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (1911008)Instruction limit reached!
% 0.22/0.36 % (1911008)------------------------------
% 0.22/0.36 % (1911008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911008)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911008)Termination reason: Instruction limit
% 0.22/0.36 % (1911008)Termination phase: Saturation
% 0.22/0.36 % (1911008)Time elapsed: 0.042 s
% 0.22/0.36 % (1911008)Peak memory usage: 12 MB
% 0.22/0.36 % (1911008)Instructions burned: 88 (million)
% 0.22/0.36 % (1911014) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1911003-1911014"...
% 0.22/0.36 % (1911024)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1318667311:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.36 % (1911028)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
% 0.22/0.36 % (1911028)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (1911024)Instruction limit reached!
% 0.22/0.36 % (1911024)------------------------------
% 0.22/0.36 % (1911024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911024)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911024)Termination reason: Instruction limit
% 0.22/0.36 % (1911024)Termination phase: Saturation
% 0.22/0.36 % (1911024)Time elapsed: 0.004 s
% 0.22/0.36 % (1911024)Peak memory usage: 11 MB
% 0.22/0.36 % (1911024)Instructions burned: 9 (million)
% 0.22/0.36 % (1911028)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=942837048:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.36 % (1911026)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1535354506:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.36 % (1911013)Instruction limit reached!
% 0.22/0.36 % (1911013)------------------------------
% 0.22/0.36 % (1911013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1911013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1911013)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1911013)Termination reason: Instruction limit
% 0.22/0.36 % (1911013)Termination phase: Saturation
% 0.22/0.36 % (1911013)Time elapsed: 0.051 s
% 0.22/0.36 % (1911013)Peak memory usage: 12 MB
% 0.22/0.36 % (1911013)Instructions burned: 75 (million)
% 0.22/0.36 % (1911014)...printing done.
% 0.22/0.36 % (1911014)Refutation found. Thanks to Tanya!
% 0.22/0.36 % SZS status Theorem for theBenchmark
% 0.22/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.37 % (1911014)------------------------------
% 0.22/0.37 % (1911014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1911014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1911014)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1911014)Termination reason: Refutation
% 0.22/0.37 % (1911014)Time elapsed: 0.049 s
% 0.22/0.37 % (1911014)Peak memory usage: 14 MB
% 0.22/0.37 % (1911014)Instructions burned: 97 (million)
% 0.22/0.37 % (1911003)Success in time 0.103 s
% 0.22/0.37 % Vampire exiting
%------------------------------------------------------------------------------