%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO533^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:29 AM UTC 2026
% Result : Theorem 1.66s 1.64s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 10
% Syntax : Number of formulae : 97 ( 16 unt; 0 typ; 9 def)
% Number of atoms : 1108 ( 193 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 4104 ( 199 ~; 174 |; 0 &;3585 @)
% ( 3 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1436 (1436 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 9 con; 0-4 aty)
% ( 5 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 2084 (1949 ^; 123 !; 12 ?;2084 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_11,type,
sF0: ( ( ( $i > $i > $o ) > $i ) > $o ) > $o ).
thf(func_def_12,type,
sF1: ( ( $i > $i > $o ) > $o ) > $o ).
thf(func_def_13,type,
sF2: ( $i > $o ) > $o ).
thf(func_def_14,type,
sF3: ( ( $i > $i > $o ) > $i ) > $o ).
thf(func_def_18,type,
ph7:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_20,type,
sK9: ( ( $i > $i > $o ) > $o ) > $i > $i > $o ).
thf(func_def_21,type,
sK10: ( ( ( $i > $i > $o ) > $i ) > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_23,type,
sK11: ( ( $i > $i > $o ) > $i > $i ) > ( ( $i > $i > $o ) > $i > $i ) > $i ).
thf(func_def_24,type,
sK12: ( ( $i > $i > $o ) > $i > $i ) > ( ( $i > $i > $o ) > $i > $i ) > $i > $i > $o ).
thf(func_def_27,type,
sK13: ( ( $i > $i > $o ) > $i > $i > $i > $i ) > $i ).
thf(func_def_28,type,
sK14: ( ( $i > $i > $o ) > $i > $i > $i > $i ) > $i ).
thf(f223,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f36,f39,f222]) ).
thf(f222,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f221]) ).
thf(f221,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i,Y3: $i] : ( Y0 @ Y3 @ Y2 ) )
!= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i,Y3: $i] : ( Y0 @ Y3 @ Y2 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f219]) ).
thf(f219,plain,
( ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] :
( Y1
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] :
( Y3
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] :
( Y3
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] :
( Y1
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] :
( Y3
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i,Y3: $i] :
( Y0
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i,Y7: $i] : Y7
@ Y0
@ Y1
@ Y2
@ Y3 )
@ Y2 ) )
!= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i,Y3: $i] : ( Y0 @ Y3 @ Y2 ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6 ) )
| ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i,Y3: $i] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) )
!= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i,Y3: $i] : ( Y0 @ Y3 @ Y2 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f217]) ).
thf(f217,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6 ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i > $i > $o,Y2: $i,Y3: $i,Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 )
@ ( sK14 @ X0 ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o,Y2: $i,Y3: $i,Y4: $i] : ( Y1 @ Y4 @ Y3 )
@ ( sK14 @ X0 ) ) ) )
| ~ spl6_1 ),
inference(negative_extensionality,[status(thm)],[f216]) ).
thf(f216,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i > $i > $o,Y2: $i,Y3: $i,Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o,Y2: $i,Y3: $i,Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6 ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f215]) ).
thf(f215,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i] :
( ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ Y5 @ Y4 )
@ ( sK13 @ X0 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 )
@ ( sK13 @ X0 ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6 ) ) )
| ~ spl6_1 ),
inference(negative_extensionality,[status(thm)],[f214]) ).
thf(f214,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ Y5 @ Y4 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6 ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f213]) ).
thf(f213,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i] :
( ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i,Y7: $i] :
( Y4 @ ( X0 @ Y4 @ Y5 @ Y6 @ Y7 )
@ ( ^ [Y8: $i > $i > $o,Y9: $i,Y10: $i,Y11: $i] : Y10
@ Y4
@ Y5
@ Y6
@ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] :
( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] : Y8
@ Y2
@ Y3
@ Y4
@ Y5 ) )
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] :
( Y5 @ ( X0 @ Y5 @ Y6 @ Y7 @ Y8 )
@ ( ^ [Y9: $i > $i > $o,Y10: $i,Y11: $i,Y12: $i] : Y11
@ Y5
@ Y6
@ Y7
@ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y2 @ Y5 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i,Y7: $i] :
( Y4 @ ( X0 @ Y4 @ Y5 @ Y6 @ Y7 )
@ ( ^ [Y8: $i > $i > $o,Y9: $i,Y10: $i,Y11: $i] : Y10
@ Y4
@ Y5
@ Y6
@ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] :
( Y6 @ ( X0 @ Y6 @ Y7 @ Y8 @ Y9 )
@ ( ^ [Y10: $i > $i > $o,Y11: $i,Y12: $i,Y13: $i] : Y12
@ Y6
@ Y7
@ Y8
@ Y9 ) )
@ Y3
@ Y4
@ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] :
( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] : Y8
@ Y2
@ Y3
@ Y4
@ Y5 ) ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ Y5 @ Y4 ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6 ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : ( Y3 @ Y6 @ Y5 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 ) )
| ( ( ^ [Y0: $i,Y1: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ Y5 @ Y4 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] : ( sF2 @ ( X0 @ Y3 @ Y4 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X0
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y2 @ Y5 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] :
( Y2
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] : Y9
@ Y2
@ Y3
@ Y4
@ Y5 )
@ Y4 ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] :
( Y3
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] :
( Y1
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] : ( sF2 @ ( X0 @ Y3 @ Y4 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] :
( Y3
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : Y6
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] : ( sF2 @ ( X0 @ Y3 @ Y4 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] :
( Y3
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] :
( Y1
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X0
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] :
( Y2
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] : Y9
@ Y2
@ Y3
@ Y4
@ Y5 )
@ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f210]) ).
thf(f210,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i,X1: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] :
( Y0 @ Y1
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : Y2 ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : X1 ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X1
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) ) )
@ ^ [Y3: $i > $i > $o,Y4: $i] :
( sK8
@ ^ [Y5: $i] :
( sF2
@ ^ [Y6: $i] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f209]) ).
thf(f209,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $i,X1: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] :
( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] : Y8
@ Y2
@ Y3
@ Y4
@ Y5 ) ) )
!= ( ^ [Y0: $i,Y1: $i] : X1 ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i,Y6: $i] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i,Y10: $i] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( X1 @ Y3 @ Y4 @ Y5 ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( X0
@ ( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] :
( Y3 @ Y4
@ ( sK8
@ ^ [Y5: $i] :
( sF2
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] :
( Y6 @ ( X0 @ Y6 @ Y7 @ Y8 @ Y9 )
@ ( ^ [Y10: $i > $i > $o,Y11: $i,Y12: $i,Y13: $i] : Y12
@ Y6
@ Y7
@ Y8
@ Y9 ) )
@ Y3
@ Y4
@ Y5 ) ) ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : Y2 ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i,Y7: $i] :
( Y4 @ ( X0 @ Y4 @ Y5 @ Y6 @ Y7 )
@ ( ^ [Y8: $i > $i > $o,Y9: $i,Y10: $i,Y11: $i] : Y10
@ Y4
@ Y5
@ Y6
@ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X1
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] :
( Y5 @ ( X0 @ Y5 @ Y6 @ Y7 @ Y8 )
@ ( ^ [Y9: $i > $i > $o,Y10: $i,Y11: $i,Y12: $i] : Y11
@ Y5
@ Y6
@ Y7
@ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] :
( sF2
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i,Y7: $i] :
( Y4 @ ( X0 @ Y4 @ Y5 @ Y6 @ Y7 )
@ ( ^ [Y8: $i > $i > $o,Y9: $i,Y10: $i,Y11: $i] : Y10
@ Y4
@ Y5
@ Y6
@ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i,Y5: $i] :
( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i,Y9: $i] : Y8
@ Y2
@ Y3
@ Y4
@ Y5 ) )
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] :
( sF2
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i,Y8: $i] :
( Y5 @ ( X0 @ Y5 @ Y6 @ Y7 @ Y8 )
@ ( ^ [Y9: $i > $i > $o,Y10: $i,Y11: $i,Y12: $i] : Y11
@ Y5
@ Y6
@ Y7
@ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f208]) ).
thf(f208,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $o,X1: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] :
( Y3 @ Y4
@ ( sK8
@ ^ [Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) ) ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] :
( Y0 @ Y1
@ ( sK8
@ ^ [Y2: $i] : ( sF2 @ ( X0 @ Y0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X1
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X0
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i] : X1 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f207]) ).
thf(f207,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i > $i > $o,X1: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i] : ( X0 @ Y2 @ Y3 @ Y4 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i,Y4: $i] : ( X1 @ Y2 @ Y3 @ Y4 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X0
@ ( sK12
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i] : ( sF2 @ ( X1 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) )
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] :
( Y0 @ Y1
@ ( sK8
@ ^ [Y2: $i] : ( sF2 @ ( X0 @ Y0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] :
( Y3 @ Y4
@ ( ^ [Y5: $i > $i > $o,Y6: $i] :
( sK8
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i] : ( sF2 @ ( X1 @ Y7 @ Y8 @ Y9 ) )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f206]) ).
thf(f206,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( X1
@ ( sK12 @ X0
@ ^ [Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( X0
@ ( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) )
!= ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] :
( Y0 @ Y1
@ ( sK8
@ ^ [Y2: $i] : ( sF2 @ ( X1 @ Y0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f205]) ).
thf(f205,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i > $i > $o] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) )
!= ( ^ [Y0: $i,Y1: $i] :
( X1
@ ( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2
@ ( sK8
@ ^ [Y3: $i] :
( Y2 @ Y3
@ ( ^ [Y4: $i > $i > $o,Y5: $i] :
( sK8
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i] : ( sF2 @ ( X1 @ Y6 @ Y7 @ Y8 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) ) )
@ ( sK8
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0
@ Y1 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0
@ ( X0
@ ( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) ) )
@ Y0 ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0
@ ( ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ( sK12 @ X0
@ ^ [Y1: $i > $i > $o,Y2: $i] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : ( sF2 @ ( X1 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) ) )
@ Y0 ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] :
( sK8
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i] : ( sF2 @ ( X1 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) ) ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f204]) ).
thf(f204,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( sK8
@ ^ [Y0: $i] : ( sK12 @ X1 @ X0 @ Y0 @ ( X0 @ ( sK12 @ X1 @ X0 ) @ Y0 ) ) )
!= ( sK8
@ ^ [Y0: $i] : ( sK12 @ X1 @ X0 @ Y0 @ ( X1 @ ( sK12 @ X1 @ X0 ) @ Y0 ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f203]) ).
thf(f203,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK12 @ X1 @ X0 ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK12 @ X1 @ X0 ) ) ) )
| ~ spl6_1 ),
inference(negative_extensionality,[status(thm)],[f202]) ).
thf(f202,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(duplicate_literal_removal,[status(thm)],[f201]) ).
thf(f201,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f200]) ).
thf(f200,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK11 @ X1 @ X0 ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) )
@ ( sK11 @ X1 @ X0 ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl6_1 ),
inference(negative_extensionality,[status(thm)],[f199]) ).
thf(f199,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f198]) ).
thf(f198,plain,
( ! [X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] :
( Y1
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : Y4
@ Y1
@ Y2 )
@ ( X1 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] :
( Y3
@ ( ^ [Y5: $i > $i > $o,Y6: $i] : Y6
@ Y3
@ Y4 )
@ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f197]) ).
thf(f197,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i,X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i] : X2 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] : Y3 ) )
| ( ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK8
@ ^ [Y4: $i] : ( Y3 @ ( X2 @ Y3 @ Y4 ) @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ ( X2 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ ( X2 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f196]) ).
thf(f196,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i,X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] : ( X2 @ Y2 @ Y3 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] : Y3 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ( ^ [Y1: $i > $i > $o,Y2: $i] : ( Y1 @ ( X2 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) )
@ Y0 ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( ^ [Y4: $i > $i > $o] :
( sK8
@ ( ^ [Y5: $i > $i > $o,Y6: $i] : ( Y5 @ ( X2 @ Y5 @ Y6 ) @ ( X1 @ Y5 @ Y6 ) )
@ Y4 ) )
@ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] : ( X0 @ Y2 @ Y3 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o,Y3: $i] : ( X1 @ Y2 @ Y3 ) ) )
| ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : ( Y2 @ ( X2 @ Y2 @ Y3 ) @ ( X1 @ Y2 @ Y3 ) )
@ Y1 ) ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f195]) ).
thf(f195,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( sK8
@ ^ [Y3: $i] : ( Y2 @ Y3 @ ( X1 @ Y2 @ Y3 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) ) ) )
| ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= X0 ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f194]) ).
thf(f194,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] :
( Y1
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : Y4
@ Y1
@ Y2 )
@ ( X1 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( sK8
@ ^ [Y3: $i] :
( Y2
@ ( ^ [Y4: $i > $i > $o,Y5: $i] : Y5
@ Y2
@ Y3 )
@ ( X1 @ Y2 @ Y3 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] :
( Y0
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : Y3
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
!= X0 ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f193]) ).
thf(f193,plain,
( ! [X2: ( $i > $i > $o ) > $i,X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ ( X1 @ Y0 @ Y1 ) @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i] : Y0 ) )
| ( ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK8
@ ^ [Y1: $i] : ( Y0 @ ( X1 @ Y0 @ Y1 ) @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ^ [Y1: $i] : ( Y0 @ ( X1 @ Y0 @ Y1 ) @ ( X0 @ Y0 @ Y1 ) ) ) )
!= X2 )
| ( ( ^ [Y0: $i,Y1: $i] : X2 )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( sK8
@ ^ [Y3: $i] : ( Y2 @ ( X1 @ Y2 @ Y3 ) @ ( X0 @ Y2 @ Y3 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ^ [Y2: $i] : ( Y1 @ ( X1 @ Y1 @ Y2 ) @ ( X0 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: $i] : X2 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f192]) ).
thf(f192,plain,
( ! [X2: ( $i > $i > $o ) > $i,X0: ( $i > $i > $o ) > $i > $i,X1: ( $i > $i > $o ) > $i > $i] :
( ( ( ^ [Y0: $i,Y1: $i > $i > $o] :
( sK8
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : ( Y2 @ ( X1 @ Y2 @ Y3 ) @ ( X0 @ Y2 @ Y3 ) )
@ Y1 ) ) )
!= ( ^ [Y0: $i,Y1: $i > $i > $o] : ( X2 @ Y1 ) ) )
| ( ( ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] :
( X1
@ ( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1
@ ( ^ [Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( Y3 @ ( X1 @ Y3 @ Y4 ) @ ( X0 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 )
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 ) ) )
| ( ( ^ [Y0: $i] :
( X0
@ ( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1
@ ( ^ [Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( Y3 @ ( X1 @ Y3 @ Y4 ) @ ( X0 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 )
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 ) )
!= ( ^ [Y0: $i] :
( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( sK8
@ ( ^ [Y1: $i > $i > $o,Y2: $i] : ( Y1 @ ( X1 @ Y1 @ Y2 ) @ ( X0 @ Y1 @ Y2 ) )
@ Y0 ) ) )
!= X2 )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( Y3 @ ( X1 @ Y3 @ Y4 ) @ ( X0 @ Y3 @ Y4 ) )
@ Y2 ) ) )
!= ( ^ [Y0: $i,Y1: $i] : X2 ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f191]) ).
thf(f191,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( X0 != X1 )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f190]) ).
thf(f190,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( Y0
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] : Y5
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] :
( Y1
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i] : Y6
@ Y1
@ Y2
@ Y3 )
@ Y2 ) ) ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] :
( Y3
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i] : Y8
@ Y3
@ Y4
@ Y5 )
@ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( X0 != X1 )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f183]) ).
thf(f183,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i > $i,X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( ^ [Y0: $i,Y1: $i] : Y1 )
!= ( X2
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ ( X2 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X1 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : X1 )
!= ( ^ [Y0: $i,Y1: $i] : X0 ) )
| ( X0 != X1 ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i > $i,X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( X0 != X1 )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] : ( X1 @ Y2 ) )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] : ( X0 @ Y2 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( sK8
@ ^ [Y2: $i] :
( sF2
@ ( ^ [Y3: $i > $i > $o,Y4: $i,Y5: $i] :
( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: $i > $i > $o,Y7: $i,Y8: $i] : Y7
@ Y3
@ Y4
@ Y5 ) )
@ Y1
@ Y2 ) ) ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X1 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] :
( sF2
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i] :
( Y5 @ ( X2 @ Y5 @ Y6 @ Y7 )
@ ( ^ [Y8: $i > $i > $o,Y9: $i,Y10: $i] : Y9
@ Y5
@ Y6
@ Y7 ) )
@ Y3
@ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ( ^ [Y2: $i > $i > $o,Y3: $i,Y4: $i] :
( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: $i > $i > $o,Y6: $i,Y7: $i] : Y6
@ Y2
@ Y3
@ Y4 ) )
@ Y0
@ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : Y1 )
!= ( ^ [Y0: $i,Y1: $i] :
( X2
@ ( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 )
@ ( sK8
@ ^ [Y3: $i] :
( sF2
@ ( ^ [Y4: $i > $i > $o,Y5: $i,Y6: $i] :
( Y4 @ ( X2 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: $i > $i > $o,Y8: $i,Y9: $i] : Y8
@ Y4
@ Y5
@ Y6 ) )
@ Y2
@ Y3 ) ) ) ) ) )
@ Y0
@ Y1 ) ) ) )
| ~ spl6_1 ),
inference(equality_resolution,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i > $o,X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( X2
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] : ( sF2 @ ( X2 @ Y0 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 )
@ ( sK8
@ ^ [Y3: $i] : ( sF2 @ ( X2 @ Y2 @ Y3 ) ) ) ) )
@ Y1
@ Y0 ) ) )
| ( ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( sK8
@ ^ [Y2: $i] : ( sF2 @ ( X2 @ Y1 @ Y2 ) ) ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK8
@ ^ [Y4: $i] : ( sF2 @ ( X2 @ Y3 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK8
@ ^ [Y1: $i] : ( sF2 @ ( X2 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( X0 != X1 ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i > $o,X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( ^ [Y0: $i,Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 )
@ ( ^ [Y3: $i > $i > $o] :
( sK8
@ ( ^ [Y4: $i > $i > $o,Y5: $i] : ( sF2 @ ( X2 @ Y4 @ Y5 ) )
@ Y3 ) )
@ Y2 ) ) )
@ Y1
@ Y0 ) )
!= ( ^ [Y0: $i] :
( X2
@ ( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( ^ [Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( sF2 @ ( X2 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 ) ) ) )
@ Y0 ) ) )
| ( ( ^ [Y0: $i > $i > $o] : ( X1 @ Y0 ) )
!= ( ^ [Y0: $i > $i > $o] : ( X0 @ Y0 ) ) )
| ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( ^ [Y1: $i > $i > $o] :
( sK8
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : ( sF2 @ ( X2 @ Y2 @ Y3 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( ^ [Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( sF2 @ ( X2 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( ^ [Y4: $i > $i > $o] :
( sK8
@ ( ^ [Y5: $i > $i > $o,Y6: $i] : ( sF2 @ ( X2 @ Y5 @ Y6 ) )
@ Y4 ) )
@ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ! [X2: ( $i > $i > $o ) > $i > $i > $o,X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( ^ [Y0: $i > $i > $o] : ( X1 @ Y0 ) )
!= ( ^ [Y0: $i > $i > $o] : ( X0 @ Y0 ) ) )
| ( $true = $false )
| ( ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( ^ [Y1: $i > $i > $o] :
( sK8
@ ( ^ [Y2: $i > $i > $o,Y3: $i] : ( sF2 @ ( X2 @ Y2 @ Y3 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
!= ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( ^ [Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( sF2 @ ( X2 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( ^ [Y4: $i > $i > $o] :
( sK8
@ ( ^ [Y5: $i > $i > $o,Y6: $i] : ( sF2 @ ( X2 @ Y5 @ Y6 ) )
@ Y4 ) )
@ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 )
@ ( ^ [Y3: $i > $i > $o] :
( sK8
@ ( ^ [Y4: $i > $i > $o,Y5: $i] : ( sF2 @ ( X2 @ Y4 @ Y5 ) )
@ Y3 ) )
@ Y2 ) ) )
@ Y1
@ Y0 ) )
!= ( ^ [Y0: $i] :
( X2
@ ( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( ^ [Y2: $i > $i > $o] :
( sK8
@ ( ^ [Y3: $i > $i > $o,Y4: $i] : ( sF2 @ ( X2 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 ) ) ) )
@ Y0 ) ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[status(thm)],[f143,f173]) ).
thf(f173,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( $true
= ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) )
@ ( sK8
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f172]) ).
thf(f172,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( $true
= ( ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) )
@ ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) )
@ ( sK8
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f66,f167]) ).
thf(f167,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( $true
= ( sF2
@ ^ [Y0: $i] :
( sK9
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK8
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] :
( sK9
@ ^ [Y3: $i > $i > $o] :
( ( sF2
@ ^ [Y4: $i] :
( sF2
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f166]) ).
thf(f166,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) )
@ ( sK8
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) )
= $true )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( $true = $false )
| ( ( ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) )
@ ( sK8
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) )
= $true ) )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f66,f145]) ).
thf(f145,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( sF2
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
= $true )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( $true = $false )
| ( ( sF2
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
= $true ) )
| ~ spl6_1 ),
inference(boolean_simplification,[status(thm)],[f133]) ).
thf(f133,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( sF2
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
= $true )
| ( $false
= ( $false
=> ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(cases_simplifying,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( sF2
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
=> ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f130]) ).
thf(f130,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ( $true = $false ) )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f84,f119]) ).
thf(f119,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( $false
= ( sF1
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
| ~ spl6_1 ),
inference(beta_eta_normalization,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( $false
= ( ^ [Y0: ( $i > $i > $o ) > $i] :
( sF1
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( $false
= ( ^ [Y0: ( $i > $i > $o ) > $i] :
( sF1
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $true = $false ) )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f115,f98]) ).
thf(f98,plain,
! [X2: ( $i > $i > $o ) > $i,X1: ( ( $i > $i > $o ) > $i ) > $o] :
( ( $true
= ( sF0 @ X1 ) )
| ( ( X1 @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: ( ( $i > $i > $o ) > $i ) > $o] :
( ( ( ?? @ ( ( $i > $i > $o ) > $i ) @ X1 )
= $false )
| ( $true
= ( sF0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: ( ( $i > $i > $o ) > $i ) > $o] :
( ( ?? @ ( ( $i > $i > $o ) > $i ) @ X1 )
= ( sF0 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f7]) ).
thf(f7,definition,
( sF0 = ?? ) @ ( ( $i > $i > $o ) > $i ),
introduced(definition,[],[function_definition]) ).
thf(f115,plain,
( ! [X1: ( $i > $i > $o ) > $i] :
( $false
= ( sF0
@ ^ [Y0: ( $i > $i > $o ) > $i] :
( sF1
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 ) @ ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl6_1 ),
inference(backward_demodulation,[status(thm)],[f50,f113]) ).
thf(f113,plain,
( ! [X0: ( $i > $i > $o ) > $i] :
( ( sF3 @ X0 )
= $false )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ! [X0: ( $i > $i > $o ) > $i] :
( ( $true = $false )
| ( ( sF3 @ X0 )
= $false ) )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f46,f98]) ).
thf(f46,plain,
( ( $false
= ( sF0 @ sF3 ) )
| ~ spl6_1 ),
inference(forward_demodulation,[status(thm)],[f11,f21]) ).
thf(f21,plain,
( ( sF4 = $false )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl6_1
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f11,definition,
( sF4
= ( sF0 @ sF3 ) ),
introduced(definition,[],[function_definition]) ).
thf(f50,plain,
! [X1: ( $i > $i > $o ) > $i] :
( ( sF3 @ X1 )
= ( sF0
@ ^ [Y0: ( $i > $i > $o ) > $i] :
( sF1
@ ^ [Y1: $i > $i > $o] :
( ( sF2
@ ^ [Y2: $i] :
( sF2
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 ) @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: ( $i > $i > $o ) > $i] :
( ( sF3 @ X1 )
= ( ^ [Y0: ( $i > $i > $o ) > $i] :
( sF0
@ ^ [Y1: ( $i > $i > $o ) > $i] :
( sF1
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f10]) ).
thf(f10,definition,
( sF3
= ( ^ [Y0: ( $i > $i > $o ) > $i] :
( sF0
@ ^ [Y1: ( $i > $i > $o ) > $i] :
( sF1
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ),
introduced(definition,[],[function_definition]) ).
thf(f84,plain,
! [X1: ( $i > $i > $o ) > $o] :
( ( $true
= ( sF1 @ X1 ) )
| ( ( X1 @ ( sK9 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: ( $i > $i > $o ) > $o] :
( ( ( !! @ ( $i > $i > $o ) @ X1 )
= $false )
| ( $true
= ( sF1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: ( $i > $i > $o ) > $o] :
( ( !! @ ( $i > $i > $o ) @ X1 )
= ( sF1 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f8]) ).
thf(f8,definition,
( !!
@ ( ( $i > $i > $o )
= sF1 ) ),
introduced(definition,[],[function_definition]) ).
thf(f66,plain,
! [X1: $i > $o] :
( ( ( sF2 @ X1 )
= $false )
| ( ( X1 @ ( sK8 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i > $o] :
( ( $true
= ( ?? @ $i @ X1 ) )
| ( ( sF2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i > $o] :
( ( sF2 @ X1 )
= ( ?? @ $i @ X1 ) ),
inference(argument_congruence,[status(thm)],[f9]) ).
thf(f9,definition,
( sF2 = ?? ) @ $i,
introduced(definition,[],[function_definition]) ).
thf(f143,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( $false
= ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f142]) ).
thf(f142,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( $true = $false )
| ( $false
= ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(boolean_simplification,[status(thm)],[f134]) ).
thf(f134,plain,
( ! [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
( ( ( ( sF2
@ ^ [Y0: $i] :
( sF2
@ ^ [Y1: $i] :
( sK9
@ ^ [Y2: $i > $i > $o] :
( ( sF2
@ ^ [Y3: $i] :
( sF2
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
=> $true )
= $false )
| ( $false
= ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK9
@ ^ [Y0: $i > $i > $o] :
( ( sF2
@ ^ [Y1: $i] :
( sF2
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl6_1 ),
inference(cases_simplifying,[status(thm)],[f131]) ).
thf(f39,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl6_2
| ~ spl6_4 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_4 ),
inference(forward_demodulation,[status(thm)],[f34,f25]) ).
thf(f25,plain,
( ( sF5 = $false )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl6_2
<=> ( sF5 = $false ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f34,plain,
( ( $true = sF5 )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl6_4
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f36,plain,
spl6_4,
inference(avatar_split_clause,[status(thm)],[f13,f32]) ).
thf(f13,plain,
$true = sF5,
inference(definition_folding,[status(thm)],[f6,f12,f11,f10,f9,f9,f8,f7,f7]) ).
thf(f12,definition,
( sF5 = ( ~ sF4 ) ),
introduced(definition,[],[function_definition]) ).
thf(f6,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $i > $o ) > $i )
@ ^ [Y0: ( $i > $i > $o ) > $i] :
( ?? @ ( ( $i > $i > $o ) > $i )
@ ^ [Y1: ( $i > $i > $o ) > $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( ( $i > $i > $o ) > $i )
@ ^ [Y0: ( $i > $i > $o ) > $i] :
( ?? @ ( ( $i > $i > $o ) > $i )
@ ^ [Y1: ( $i > $i > $o ) > $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $i > $o ) > $i,X1: ( $i > $i > $o ) > $i] :
! [X2: $i > $i > $o] :
( ? [X3: $i,X4: $i] : ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X2 ) @ ( X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: ( $i > $i > $o ) > $i,X0: ( $i > $i > $o ) > $i] :
! [X2: $i > $i > $o] :
( ? [X3: $i,X4: $i] : ( X2 @ X3 @ X4 )
=> ( X2 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: ( $i > $i > $o ) > $i,X0: ( $i > $i > $o ) > $i] :
! [X2: $i > $i > $o] :
( ? [X3: $i,X4: $i] : ( X2 @ X3 @ X4 )
=> ( X2 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fKG68WVYH8/DTF2THF_17396.p',conj) ).
thf(f26,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f23,f19]) ).
thf(f17,plain,
( ( sF5 = $false )
| ( sF4 = $false ) ),
inference(boolean_simplification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sF5 = ( ~ $true ) )
| ( sF4 = $false ) ),
inference(cases_simplifying,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO533^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:33:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SYO533^1 : TPTP v9.2.1. Released v5.2.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : Binary choice on individuals 4
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English : There is an Epsa such that Epsa and (epsb Epsa) work together to
% 0.19/0.47 % give an a and b such that R a b holds, if such an a and b exist
% 0.19/0.47 % for a binary relation R on $i. A choice operator on i can be used
% 0.19/0.47 % to define a choice operator on i*i (Curried). In this version the
% 0.19/0.47 % prover must synthesize both parts of the solution.
% 0.19/0.47
% 0.19/0.47 % Refs : [Bac10] Backes (2010), Tableaux for Higher-Order Logic with If
% 0.19/0.47 % : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro11]
% 0.19/0.47 % Names : CHOICE10 [Bro11]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.83 v9.1.0, 0.88 v9.0.0, 0.92 v8.2.0, 0.91 v8.1.0, 0.92 v7.4.0, 0.89 v7.3.0, 0.90 v7.2.0, 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 1.00 v5.2.0
% 0.19/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.19/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.47 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% 0.19/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.47 % Number of variables : 5 ( 0 ^; 1 !; 4 ?; 5 :)
% 0.19/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.47
% 0.19/0.47 % Comments :
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(conj,conjecture,
% 0.19/0.47 ? [Epsa: ( $i > $i > $o ) > $i,Epsb: ( $i > $i > $o ) > $i] :
% 0.19/0.47 ! [R: $i > $i > $o] :
% 0.19/0.47 ( ? [X: $i,Y: $i] : ( R @ X @ Y )
% 0.19/0.47 => ( R @ ( Epsa @ R ) @ ( Epsb @ R ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 14:33:41 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fKG68WVYH8/DTF2DTF17396.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.29 thf(conj,conjecture,
% 1.49/1.29 ? [Epsa: ( $i > $i > $o ) > $i,Epsb: ( $i > $i > $o ) > $i] :
% 1.49/1.29 ! [R: $i > $i > $o] :
% 1.49/1.29 ( ? [X: $i,Y: $i] : ( R @ X @ Y )
% 1.49/1.29 => ( R @ ( Epsa @ R ) @ ( Epsb @ R ) ) ) ).
% 1.49/1.29 ------------------------
% 1.66/1.30 % (17588)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/27Mi)
% 1.66/1.30 % (17591)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/275Mi)
% 1.66/1.30 % (17586)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/183Mi)
% 1.66/1.30 % (17591)Refutation not found, incomplete strategy
% 1.66/1.30 % (17591)------------------------------
% 1.66/1.30 % (17591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (17591)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.30
% 1.66/1.30
% 1.66/1.30 % (17591)Memory used [KB]: 5500
% 1.66/1.30 % (17591)Time elapsed: 0.001 s
% 1.66/1.30 % (17591)------------------------------
% 1.66/1.30 % (17591)------------------------------
% 1.66/1.30 % (17588)Refutation not found, incomplete strategy
% 1.66/1.30 % (17588)------------------------------
% 1.66/1.30 % (17588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (17588)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.30
% 1.66/1.30
% 1.66/1.30 % (17588)Memory used [KB]: 5500
% 1.66/1.30 % (17588)Time elapsed: 0.002 s
% 1.66/1.30 % (17588)Instructions burned: 2 (million)
% 1.66/1.30 % (17588)------------------------------
% 1.66/1.30 % (17588)------------------------------
% 1.66/1.31 % (17587)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/4Mi)
% 1.66/1.31 % (17587)Instruction limit reached!
% 1.66/1.31 % (17587)------------------------------
% 1.66/1.31 % (17587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (17587)Termination reason: Unknown
% 1.66/1.31 % (17587)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (17587)Memory used [KB]: 5500
% 1.66/1.31 % (17587)Time elapsed: 0.004 s
% 1.66/1.31 % (17587)Instructions burned: 4 (million)
% 1.66/1.31 % (17587)------------------------------
% 1.66/1.31 % (17587)------------------------------
% 1.66/1.31 % (17589)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/2Mi)
% 1.66/1.31 % (17592)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/18Mi)
% 1.66/1.31 % (17589)Refutation not found, incomplete strategy
% 1.66/1.31 % (17589)------------------------------
% 1.66/1.31 % (17589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (17589)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.31
% 1.66/1.31
% 1.66/1.31 % (17589)Memory used [KB]: 5500
% 1.66/1.31 % (17589)Time elapsed: 0.004 s
% 1.66/1.31 % (17589)Instructions burned: 1 (million)
% 1.66/1.31 % (17589)------------------------------
% 1.66/1.31 % (17589)------------------------------
% 1.66/1.31 % (17593)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.31 % (17594)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/37Mi)
% 1.66/1.31 % (17593)Instruction limit reached!
% 1.66/1.31 % (17593)------------------------------
% 1.66/1.31 % (17593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.31 % (17593)Termination reason: Unknown
% 1.66/1.31 % (17593)Termination phase: Saturation
% 1.66/1.31
% 1.66/1.31 % (17593)Memory used [KB]: 5500
% 1.66/1.31 % (17593)Time elapsed: 0.002 s
% 1.66/1.31 % (17593)Instructions burned: 3 (million)
% 1.66/1.31 % (17593)------------------------------
% 1.66/1.31 % (17593)------------------------------
% 1.66/1.32 % (17590)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/2Mi)
% 1.66/1.32 % (17590)Instruction limit reached!
% 1.66/1.32 % (17590)------------------------------
% 1.66/1.32 % (17590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (17590)Termination reason: Unknown
% 1.66/1.32 % (17590)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (17590)Memory used [KB]: 5500
% 1.66/1.32 % (17590)Time elapsed: 0.005 s
% 1.66/1.32 % (17590)Instructions burned: 2 (million)
% 1.66/1.32 % (17594)Refutation not found, incomplete strategy
% 1.66/1.32 % (17594)------------------------------
% 1.66/1.32 % (17594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (17590)------------------------------
% 1.66/1.32 % (17590)------------------------------
% 1.66/1.32 % (17594)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.32
% 1.66/1.32
% 1.66/1.32 % (17594)Memory used [KB]: 5628
% 1.66/1.32 % (17594)Time elapsed: 0.004 s
% 1.66/1.32 % (17594)Instructions burned: 10 (million)
% 1.66/1.32 % (17594)------------------------------
% 1.66/1.32 % (17594)------------------------------
% 1.66/1.32 % (17592)Instruction limit reached!
% 1.66/1.32 % (17592)------------------------------
% 1.66/1.32 % (17592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (17592)Termination reason: Unknown
% 1.66/1.32 % (17592)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (17592)Memory used [KB]: 5628
% 1.66/1.32 % (17592)Time elapsed: 0.013 s
% 1.66/1.32 % (17592)Instructions burned: 20 (million)
% 1.66/1.32 % (17592)------------------------------
% 1.66/1.32 % (17592)------------------------------
% 1.66/1.32 % (17597)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/1041Mi)
% 1.66/1.33 % (17595)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/15Mi)
% 1.66/1.33 % (17597)Refutation not found, incomplete strategy
% 1.66/1.33 % (17597)------------------------------
% 1.66/1.33 % (17597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (17597)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.33
% 1.66/1.33
% 1.66/1.33 % (17597)Memory used [KB]: 5500
% 1.66/1.33 % (17597)Time elapsed: 0.003 s
% 1.66/1.33 % (17597)Instructions burned: 6 (million)
% 1.66/1.33 % (17597)------------------------------
% 1.66/1.33 % (17597)------------------------------
% 1.66/1.33 % (17598)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/7Mi)
% 1.66/1.33 % (17595)Refutation not found, incomplete strategy
% 1.66/1.33 % (17595)------------------------------
% 1.66/1.33 % (17595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (17595)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.33
% 1.66/1.33
% 1.66/1.33 % (17595)Memory used [KB]: 5500
% 1.66/1.33 % (17595)Time elapsed: 0.003 s
% 1.66/1.33 % (17595)Instructions burned: 2 (million)
% 1.66/1.33 % (17595)------------------------------
% 1.66/1.33 % (17595)------------------------------
% 1.66/1.33 % (17598)Instruction limit reached!
% 1.66/1.33 % (17598)------------------------------
% 1.66/1.33 % (17598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (17598)Termination reason: Unknown
% 1.66/1.33 % (17598)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (17598)Memory used [KB]: 1023
% 1.66/1.33 % (17598)Time elapsed: 0.003 s
% 1.66/1.33 % (17598)Instructions burned: 7 (million)
% 1.66/1.33 % (17598)------------------------------
% 1.66/1.33 % (17598)------------------------------
% 1.66/1.33 % (17596)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.33 % (17596)Instruction limit reached!
% 1.66/1.33 % (17596)------------------------------
% 1.66/1.33 % (17596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (17596)Termination reason: Unknown
% 1.66/1.33 % (17596)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (17596)Memory used [KB]: 5500
% 1.66/1.33 % (17596)Time elapsed: 0.004 s
% 1.66/1.33 % (17596)Instructions burned: 3 (million)
% 1.66/1.33 % (17596)------------------------------
% 1.66/1.33 % (17596)------------------------------
% 1.66/1.34 % (17601)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.34 % (17601)Instruction limit reached!
% 1.66/1.34 % (17601)------------------------------
% 1.66/1.34 % (17601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (17601)Termination reason: Unknown
% 1.66/1.34 % (17601)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (17601)Memory used [KB]: 5500
% 1.66/1.34 % (17601)Time elapsed: 0.002 s
% 1.66/1.34 % (17601)Instructions burned: 3 (million)
% 1.66/1.34 % (17601)------------------------------
% 1.66/1.34 % (17601)------------------------------
% 1.66/1.34 % (17603)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.34 % (17600)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.34 % (17603)Instruction limit reached!
% 1.66/1.34 % (17603)------------------------------
% 1.66/1.34 % (17603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (17603)Termination reason: Unknown
% 1.66/1.34 % (17603)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (17603)Memory used [KB]: 5500
% 1.66/1.34 % (17603)Time elapsed: 0.002 s
% 1.66/1.34 % (17603)Instructions burned: 3 (million)
% 1.66/1.34 % (17603)------------------------------
% 1.66/1.34 % (17603)------------------------------
% 1.66/1.34 % (17600)Instruction limit reached!
% 1.66/1.34 % (17600)------------------------------
% 1.66/1.34 % (17600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (17600)Termination reason: Unknown
% 1.66/1.34 % (17600)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (17600)Memory used [KB]: 895
% 1.66/1.34 % (17600)Time elapsed: 0.003 s
% 1.66/1.34 % (17600)Instructions burned: 3 (million)
% 1.66/1.34 % (17600)------------------------------
% 1.66/1.34 % (17600)------------------------------
% 1.66/1.34 % (17599)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/16Mi)
% 1.66/1.34 % (17602)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/7Mi)
% 1.66/1.34 % (17602)Refutation not found, incomplete strategy
% 1.66/1.34 % (17602)------------------------------
% 1.66/1.34 % (17602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (17602)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.34
% 1.66/1.34
% 1.66/1.34 % (17602)Memory used [KB]: 5500
% 1.66/1.34 % (17602)Time elapsed: 0.024 s
% 1.66/1.34 % (17602)Instructions burned: 1 (million)
% 1.66/1.34 % (17602)------------------------------
% 1.66/1.34 % (17602)------------------------------
% 1.66/1.35 % (17605)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/18Mi)
% 1.66/1.35 % (17605)Refutation not found, incomplete strategy
% 1.66/1.35 % (17605)------------------------------
% 1.66/1.35 % (17605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (17605)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.35
% 1.66/1.35
% 1.66/1.35 % (17605)Memory used [KB]: 5500
% 1.66/1.35 % (17605)Time elapsed: 0.001 s
% 1.66/1.35 % (17605)Instructions burned: 1 (million)
% 1.66/1.35 % (17605)------------------------------
% 1.66/1.35 % (17605)------------------------------
% 1.66/1.35 % (17606)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/710Mi)
% 1.66/1.35 % (17604)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/4Mi)
% 1.66/1.35 % (17607)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/6Mi)
% 1.66/1.35 % (17604)Instruction limit reached!
% 1.66/1.35 % (17604)------------------------------
% 1.66/1.35 % (17604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (17604)Termination reason: Unknown
% 1.66/1.35 % (17604)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (17604)Memory used [KB]: 5500
% 1.66/1.35 % (17604)Time elapsed: 0.005 s
% 1.66/1.35 % (17604)Instructions burned: 4 (million)
% 1.66/1.35 % (17604)------------------------------
% 1.66/1.35 % (17604)------------------------------
% 1.66/1.35 % (17607)Refutation not found, incomplete strategy
% 1.66/1.35 % (17607)------------------------------
% 1.66/1.35 % (17607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (17607)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.35
% 1.66/1.35
% 1.66/1.35 % (17607)Memory used [KB]: 5500
% 1.66/1.35 % (17607)Time elapsed: 0.002 s
% 1.66/1.35 % (17607)Instructions burned: 1 (million)
% 1.66/1.35 % (17607)------------------------------
% 1.66/1.35 % (17607)------------------------------
% 1.66/1.35 % (17599)Instruction limit reached!
% 1.66/1.35 % (17599)------------------------------
% 1.66/1.35 % (17599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (17599)Termination reason: Unknown
% 1.66/1.35 % (17599)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (17599)Memory used [KB]: 5628
% 1.66/1.35 % (17599)Time elapsed: 0.035 s
% 1.66/1.35 % (17599)Instructions burned: 17 (million)
% 1.66/1.35 % (17599)------------------------------
% 1.66/1.35 % (17599)------------------------------
% 1.66/1.36 % (17586)Instruction limit reached!
% 1.66/1.36 % (17586)------------------------------
% 1.66/1.36 % (17586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (17586)Termination reason: Unknown
% 1.66/1.36 % (17586)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (17586)Memory used [KB]: 6012
% 1.66/1.36 % (17586)Time elapsed: 0.053 s
% 1.66/1.36 % (17586)Instructions burned: 185 (million)
% 1.66/1.36 % (17586)------------------------------
% 1.66/1.36 % (17586)------------------------------
% 1.66/1.36 % (17608)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/902Mi)
% 1.66/1.36 % (17609)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/21Mi)
% 1.66/1.36 % (17608)Refutation not found, incomplete strategy
% 1.66/1.36 % (17608)------------------------------
% 1.66/1.36 % (17608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (17608)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.36
% 1.66/1.36
% 1.66/1.36 % (17608)Memory used [KB]: 5500
% 1.66/1.36 % (17608)Time elapsed: 0.003 s
% 1.66/1.36 % (17608)Instructions burned: 1 (million)
% 1.66/1.36 % (17608)------------------------------
% 1.66/1.36 % (17608)------------------------------
% 1.66/1.36 % (17611)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/6Mi)
% 1.66/1.36 % (17609)Instruction limit reached!
% 1.66/1.36 % (17609)------------------------------
% 1.66/1.36 % (17609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (17609)Termination reason: Unknown
% 1.66/1.36 % (17609)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (17609)Memory used [KB]: 5628
% 1.66/1.36 % (17609)Time elapsed: 0.009 s
% 1.66/1.36 % (17609)Instructions burned: 23 (million)
% 1.66/1.36 % (17609)------------------------------
% 1.66/1.36 % (17609)------------------------------
% 1.66/1.37 % (17613)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/779Mi)
% 1.66/1.37 % (17611)Instruction limit reached!
% 1.66/1.37 % (17611)------------------------------
% 1.66/1.37 % (17611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (17611)Termination reason: Unknown
% 1.66/1.37 % (17611)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (17611)Memory used [KB]: 5500
% 1.66/1.37 % (17611)Time elapsed: 0.004 s
% 1.66/1.37 % (17611)Instructions burned: 6 (million)
% 1.66/1.37 % (17611)------------------------------
% 1.66/1.37 % (17611)------------------------------
% 1.66/1.37 % (17610)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/5Mi)
% 1.66/1.37 % (17614)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/19Mi)
% 1.66/1.37 % (17614)Refutation not found, incomplete strategy
% 1.66/1.37 % (17614)------------------------------
% 1.66/1.37 % (17614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (17614)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.37
% 1.66/1.37
% 1.66/1.37 % (17614)Memory used [KB]: 5500
% 1.66/1.37 % (17614)Time elapsed: 0.002 s
% 1.66/1.37 % (17614)Instructions burned: 2 (million)
% 1.66/1.37 % (17614)------------------------------
% 1.66/1.37 % (17614)------------------------------
% 1.66/1.37 % (17610)Instruction limit reached!
% 1.66/1.37 % (17610)------------------------------
% 1.66/1.37 % (17610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (17610)Termination reason: Unknown
% 1.66/1.37 % (17610)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (17610)Memory used [KB]: 5500
% 1.66/1.37 % (17610)Time elapsed: 0.005 s
% 1.66/1.37 % (17610)Instructions burned: 5 (million)
% 1.66/1.37 % (17610)------------------------------
% 1.66/1.37 % (17610)------------------------------
% 1.66/1.37 % (17615)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/879Mi)
% 1.66/1.37 % (17615)Refutation not found, incomplete strategy
% 1.66/1.37 % (17615)------------------------------
% 1.66/1.37 % (17615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (17615)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.37
% 1.66/1.37
% 1.66/1.37 % (17615)Memory used [KB]: 5500
% 1.66/1.37 % (17615)Time elapsed: 0.001 s
% 1.66/1.37 % (17615)Instructions burned: 1 (million)
% 1.66/1.37 % (17615)------------------------------
% 1.66/1.37 % (17615)------------------------------
% 1.66/1.38 % (17616)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/17Mi)
% 1.66/1.38 % (17612)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/377Mi)
% 1.66/1.38 % (17612)Refutation not found, incomplete strategy
% 1.66/1.38 % (17612)------------------------------
% 1.66/1.38 % (17612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (17612)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.38
% 1.66/1.38
% 1.66/1.38 % (17612)Memory used [KB]: 5500
% 1.66/1.38 % (17612)Time elapsed: 0.005 s
% 1.66/1.38 % (17612)Instructions burned: 3 (million)
% 1.66/1.38 % (17612)------------------------------
% 1.66/1.38 % (17612)------------------------------
% 1.66/1.38 % (17616)Instruction limit reached!
% 1.66/1.38 % (17616)------------------------------
% 1.66/1.38 % (17616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (17616)Termination reason: Unknown
% 1.66/1.38 % (17616)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (17616)Memory used [KB]: 5500
% 1.66/1.38 % (17616)Time elapsed: 0.008 s
% 1.66/1.38 % (17616)Instructions burned: 19 (million)
% 1.66/1.38 % (17616)------------------------------
% 1.66/1.38 % (17616)------------------------------
% 1.66/1.38 % (17619)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/127Mi)
% 1.66/1.38 % (17617)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.39 % (17617)Instruction limit reached!
% 1.66/1.39 % (17617)------------------------------
% 1.66/1.39 % (17617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (17617)Termination reason: Unknown
% 1.66/1.39 % (17617)Termination phase: Saturation
% 1.66/1.39
% 1.66/1.39 % (17617)Memory used [KB]: 5500
% 1.66/1.39 % (17617)Time elapsed: 0.003 s
% 1.66/1.39 % (17617)Instructions burned: 4 (million)
% 1.66/1.39 % (17617)------------------------------
% 1.66/1.39 % (17617)------------------------------
% 1.66/1.39 % (17618)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/30Mi)
% 1.66/1.39 % (17620)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/100Mi)
% 1.66/1.39 % (17620)Refutation not found, incomplete strategy
% 1.66/1.39 % (17620)------------------------------
% 1.66/1.39 % (17620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (17620)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.39
% 1.66/1.39
% 1.66/1.39 % (17620)Memory used [KB]: 5500
% 1.66/1.39 % (17620)Time elapsed: 0.002 s
% 1.66/1.39 % (17620)Instructions burned: 1 (million)
% 1.66/1.39 % (17620)------------------------------
% 1.66/1.39 % (17620)------------------------------
% 1.66/1.40 % (17622)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/20Mi)
% 1.66/1.40 % (17622)Refutation not found, incomplete strategy
% 1.66/1.40 % (17622)------------------------------
% 1.66/1.40 % (17622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (17622)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.40
% 1.66/1.40
% 1.66/1.40 % (17622)Memory used [KB]: 5500
% 1.66/1.40 % (17622)Time elapsed: 0.002 s
% 1.66/1.40 % (17622)Instructions burned: 1 (million)
% 1.66/1.40 % (17622)------------------------------
% 1.66/1.40 % (17622)------------------------------
% 1.66/1.40 % (17621)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/3Mi)
% 1.66/1.40 % (17621)Instruction limit reached!
% 1.66/1.40 % (17621)------------------------------
% 1.66/1.40 % (17621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.40 % (17621)Termination reason: Unknown
% 1.66/1.40 % (17621)Termination phase: Saturation
% 1.66/1.40
% 1.66/1.40 % (17621)Memory used [KB]: 5500
% 1.66/1.40 % (17621)Time elapsed: 0.004 s
% 1.66/1.40 % (17621)Instructions burned: 3 (million)
% 1.66/1.40 % (17621)------------------------------
% 1.66/1.40 % (17621)------------------------------
% 1.66/1.40 % (17623)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_17396 for (2999ds/86Mi)
% 1.66/1.41 % (17623)Refutation not found, incomplete strategy
% 1.66/1.41 % (17623)------------------------------
% 1.66/1.41 % (17623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (17623)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (17623)Memory used [KB]: 5500
% 1.66/1.41 % (17623)Time elapsed: 0.002 s
% 1.66/1.41 % (17623)Instructions burned: 2 (million)
% 1.66/1.41 % (17623)------------------------------
% 1.66/1.41 % (17623)------------------------------
% 1.66/1.41 % (17624)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/107Mi)
% 1.66/1.41 % (17624)Refutation not found, incomplete strategy
% 1.66/1.41 % (17624)------------------------------
% 1.66/1.41 % (17624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (17624)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.41
% 1.66/1.41
% 1.66/1.41 % (17624)Memory used [KB]: 5500
% 1.66/1.41 % (17624)Time elapsed: 0.002 s
% 1.66/1.41 % (17624)Instructions burned: 1 (million)
% 1.66/1.41 % (17624)------------------------------
% 1.66/1.41 % (17624)------------------------------
% 1.66/1.41 % (17618)Instruction limit reached!
% 1.66/1.41 % (17618)------------------------------
% 1.66/1.41 % (17618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.41 % (17618)Termination reason: Unknown
% 1.66/1.41 % (17618)Termination phase: Saturation
% 1.66/1.41
% 1.66/1.41 % (17618)Memory used [KB]: 5500
% 1.66/1.41 % (17618)Time elapsed: 0.021 s
% 1.66/1.41 % (17618)Instructions burned: 30 (million)
% 1.66/1.41 % (17618)------------------------------
% 1.66/1.41 % (17618)------------------------------
% 1.66/1.42 % (17619)Instruction limit reached!
% 1.66/1.42 % (17619)------------------------------
% 1.66/1.42 % (17619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.42 % (17619)Termination reason: Unknown
% 1.66/1.42 % (17619)Termination phase: Saturation
% 1.66/1.42
% 1.66/1.42 % (17619)Memory used [KB]: 5756
% 1.66/1.42 % (17619)Time elapsed: 0.038 s
% 1.66/1.42 % (17619)Instructions burned: 129 (million)
% 1.66/1.42 % (17619)------------------------------
% 1.66/1.42 % (17619)------------------------------
% 1.66/1.42 % (17632)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/46Mi)
% 1.66/1.42 % (17627)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/39Mi)
% 1.66/1.43 % (17631)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/448Mi)
% 1.66/1.43 % (17633)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/98Mi)
% 1.66/1.43 % (17633)Refutation not found, incomplete strategy
% 1.66/1.43 % (17633)------------------------------
% 1.66/1.43 % (17633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.43 % (17633)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.43
% 1.66/1.43
% 1.66/1.43 % (17633)Memory used [KB]: 1023
% 1.66/1.43 % (17633)Time elapsed: 0.005 s
% 1.66/1.43 % (17633)Instructions burned: 5 (million)
% 1.66/1.43 % (17633)------------------------------
% 1.66/1.43 % (17633)------------------------------
% 1.66/1.44 % (17643)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/507Mi)
% 1.66/1.44 % (17643)Refutation not found, incomplete strategy
% 1.66/1.44 % (17643)------------------------------
% 1.66/1.44 % (17643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (17643)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.44
% 1.66/1.44
% 1.66/1.44 % (17643)Memory used [KB]: 5500
% 1.66/1.44 % (17643)Time elapsed: 0.003 s
% 1.66/1.44 % (17643)Instructions burned: 3 (million)
% 1.66/1.44 % (17643)------------------------------
% 1.66/1.44 % (17643)------------------------------
% 1.66/1.44 % (17627)Instruction limit reached!
% 1.66/1.44 % (17627)------------------------------
% 1.66/1.44 % (17627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (17627)Termination reason: Unknown
% 1.66/1.44 % (17627)Termination phase: Saturation
% 1.66/1.44
% 1.66/1.44 % (17627)Memory used [KB]: 6140
% 1.66/1.44 % (17627)Time elapsed: 0.021 s
% 1.66/1.44 % (17627)Instructions burned: 41 (million)
% 1.66/1.44 % (17627)------------------------------
% 1.66/1.44 % (17627)------------------------------
% 1.66/1.44 % (17632)Instruction limit reached!
% 1.66/1.44 % (17632)------------------------------
% 1.66/1.44 % (17632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (17632)Termination reason: Unknown
% 1.66/1.44 % (17632)Termination phase: Saturation
% 1.66/1.44
% 1.66/1.44 % (17632)Memory used [KB]: 5628
% 1.66/1.44 % (17632)Time elapsed: 0.024 s
% 1.66/1.44 % (17632)Instructions burned: 48 (million)
% 1.66/1.44 % (17632)------------------------------
% 1.66/1.44 % (17632)------------------------------
% 1.66/1.45 % (17645)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/149Mi)
% 1.66/1.45 % (17645)Refutation not found, incomplete strategy
% 1.66/1.45 % (17645)------------------------------
% 1.66/1.45 % (17645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17645)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (17645)Memory used [KB]: 5500
% 1.66/1.45 % (17645)Time elapsed: 0.002 s
% 1.66/1.45 % (17645)Instructions burned: 3 (million)
% 1.66/1.45 % (17645)------------------------------
% 1.66/1.45 % (17645)------------------------------
% 1.66/1.45 % (17648)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/39Mi)
% 1.66/1.45 % (17648)Refutation not found, incomplete strategy
% 1.66/1.45 % (17648)------------------------------
% 1.66/1.45 % (17648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (17648)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.45
% 1.66/1.45
% 1.66/1.45 % (17648)Memory used [KB]: 5500
% 1.66/1.45 % (17648)Time elapsed: 0.002 s
% 1.66/1.45 % (17648)------------------------------
% 1.66/1.45 % (17648)------------------------------
% 1.66/1.45 % (17650)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/6Mi)
% 1.66/1.45 % (17651)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/1087Mi)
% 1.66/1.46 % (17650)Instruction limit reached!
% 1.66/1.46 % (17650)------------------------------
% 1.66/1.46 % (17650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (17650)Termination reason: Unknown
% 1.66/1.46 % (17650)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (17650)Memory used [KB]: 9978
% 1.66/1.46 % (17650)Time elapsed: 0.005 s
% 1.66/1.46 % (17650)Instructions burned: 7 (million)
% 1.66/1.46 % (17650)------------------------------
% 1.66/1.46 % (17650)------------------------------
% 1.66/1.46 % (17651)Refutation not found, incomplete strategy
% 1.66/1.46 % (17651)------------------------------
% 1.66/1.46 % (17651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (17651)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.46
% 1.66/1.46
% 1.66/1.46 % (17651)Memory used [KB]: 5500
% 1.66/1.46 % (17651)Time elapsed: 0.002 s
% 1.66/1.46 % (17651)Instructions burned: 1 (million)
% 1.66/1.46 % (17651)------------------------------
% 1.66/1.46 % (17651)------------------------------
% 1.66/1.46 % (17652)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/47Mi)
% 1.66/1.46 % (17653)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/44Mi)
% 1.66/1.47 % (17654)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/432Mi)
% 1.66/1.47 % (17655)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/62Mi)
% 1.66/1.47 % (17653)Instruction limit reached!
% 1.66/1.47 % (17653)------------------------------
% 1.66/1.47 % (17653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (17653)Termination reason: Unknown
% 1.66/1.47 % (17653)Termination phase: Saturation
% 1.66/1.47
% 1.66/1.47 % (17653)Memory used [KB]: 1151
% 1.66/1.47 % (17653)Time elapsed: 0.014 s
% 1.66/1.47 % (17653)Instructions burned: 46 (million)
% 1.66/1.47 % (17653)------------------------------
% 1.66/1.47 % (17653)------------------------------
% 1.66/1.47 % (17652)Instruction limit reached!
% 1.66/1.47 % (17652)------------------------------
% 1.66/1.47 % (17652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.47 % (17652)Termination reason: Unknown
% 1.66/1.47 % (17652)Termination phase: Saturation
% 1.66/1.47
% 1.66/1.47 % (17652)Memory used [KB]: 5628
% 1.66/1.47 % (17652)Time elapsed: 0.016 s
% 1.66/1.47 % (17652)Instructions burned: 48 (million)
% 1.66/1.47 % (17652)------------------------------
% 1.66/1.47 % (17652)------------------------------
% 1.66/1.48 % (17654)Refutation not found, incomplete strategy
% 1.66/1.48 % (17654)------------------------------
% 1.66/1.48 % (17654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (17654)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.48
% 1.66/1.48
% 1.66/1.48 % (17654)Memory used [KB]: 1407
% 1.66/1.48 % (17654)Time elapsed: 0.011 s
% 1.66/1.48 % (17654)Instructions burned: 30 (million)
% 1.66/1.48 % (17654)------------------------------
% 1.66/1.48 % (17654)------------------------------
% 1.66/1.48 % (17656)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/31Mi)
% 1.66/1.48 % (17657)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/96Mi)
% 1.66/1.49 % (17655)Instruction limit reached!
% 1.66/1.49 % (17655)------------------------------
% 1.66/1.49 % (17655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (17655)Termination reason: Unknown
% 1.66/1.49 % (17655)Termination phase: Saturation
% 1.66/1.49
% 1.66/1.49 % (17655)Memory used [KB]: 5756
% 1.66/1.49 % (17655)Time elapsed: 0.042 s
% 1.66/1.49 % (17655)Instructions burned: 64 (million)
% 1.66/1.49 % (17655)------------------------------
% 1.66/1.49 % (17655)------------------------------
% 1.66/1.49 % (17658)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/453Mi)
% 1.66/1.49 % (17658)Refutation not found, incomplete strategy
% 1.66/1.49 % (17658)------------------------------
% 1.66/1.49 % (17658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (17658)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.49
% 1.66/1.49
% 1.66/1.49 % (17658)Memory used [KB]: 5500
% 1.66/1.49 % (17658)Time elapsed: 0.004 s
% 1.66/1.49 % (17658)Instructions burned: 6 (million)
% 1.66/1.49 % (17658)------------------------------
% 1.66/1.49 % (17658)------------------------------
% 1.66/1.49 % (17656)Instruction limit reached!
% 1.66/1.49 % (17656)------------------------------
% 1.66/1.49 % (17656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.49 % (17656)Termination reason: Unknown
% 1.66/1.49 % (17656)Termination phase: Saturation
% 1.66/1.49
% 1.66/1.49 % (17656)Memory used [KB]: 5628
% 1.66/1.49 % (17656)Time elapsed: 0.010 s
% 1.66/1.49 % (17656)Instructions burned: 33 (million)
% 1.66/1.49 % (17656)------------------------------
% 1.66/1.49 % (17656)------------------------------
% 1.66/1.50 % (17659)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_17396 for (2998ds/71Mi)
% 1.66/1.50 % (17660)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/83Mi)
% 1.66/1.50 % (17661)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/11Mi)
% 1.66/1.50 % (17661)Instruction limit reached!
% 1.66/1.50 % (17661)------------------------------
% 1.66/1.50 % (17661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.50 % (17661)Termination reason: Unknown
% 1.66/1.50 % (17661)Termination phase: Saturation
% 1.66/1.50
% 1.66/1.50 % (17661)Memory used [KB]: 5500
% 1.66/1.50 % (17661)Time elapsed: 0.005 s
% 1.66/1.50 % (17661)Instructions burned: 14 (million)
% 1.66/1.50 % (17661)------------------------------
% 1.66/1.50 % (17661)------------------------------
% 1.66/1.51 % (17657)Instruction limit reached!
% 1.66/1.51 % (17657)------------------------------
% 1.66/1.51 % (17657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.51 % (17657)Termination reason: Unknown
% 1.66/1.51 % (17657)Termination phase: Saturation
% 1.66/1.51
% 1.66/1.51 % (17657)Memory used [KB]: 5628
% 1.66/1.51 % (17657)Time elapsed: 0.052 s
% 1.66/1.51 % (17657)Instructions burned: 97 (million)
% 1.66/1.51 % (17657)------------------------------
% 1.66/1.51 % (17657)------------------------------
% 1.66/1.51 % (17662)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/41Mi)
% 1.66/1.51 % (17662)Refutation not found, incomplete strategy
% 1.66/1.51 % (17662)------------------------------
% 1.66/1.51 % (17662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.51 % (17662)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.51
% 1.66/1.51
% 1.66/1.51 % (17662)Memory used [KB]: 5500
% 1.66/1.51 % (17662)Time elapsed: 0.002 s
% 1.66/1.51 % (17662)Instructions burned: 3 (million)
% 1.66/1.51 % (17662)------------------------------
% 1.66/1.51 % (17662)------------------------------
% 1.66/1.52 % (17659)Instruction limit reached!
% 1.66/1.52 % (17659)------------------------------
% 1.66/1.52 % (17659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.52 % (17659)Termination reason: Unknown
% 1.66/1.52 % (17659)Termination phase: Saturation
% 1.66/1.52
% 1.66/1.52 % (17659)Memory used [KB]: 5756
% 1.66/1.52 % (17659)Time elapsed: 0.026 s
% 1.66/1.52 % (17659)Instructions burned: 71 (million)
% 1.66/1.52 % (17659)------------------------------
% 1.66/1.52 % (17659)------------------------------
% 1.66/1.52 % (17663)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/6Mi)
% 1.66/1.52 % (17663)Refutation not found, incomplete strategy
% 1.66/1.52 % (17663)------------------------------
% 1.66/1.52 % (17663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.52 % (17663)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.52
% 1.66/1.52
% 1.66/1.52 % (17663)Memory used [KB]: 5500
% 1.66/1.52 % (17663)Time elapsed: 0.002 s
% 1.66/1.52 % (17663)Instructions burned: 1 (million)
% 1.66/1.52 % (17663)------------------------------
% 1.66/1.52 % (17663)------------------------------
% 1.66/1.52 % (17660)Instruction limit reached!
% 1.66/1.52 % (17660)------------------------------
% 1.66/1.52 % (17660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.52 % (17660)Termination reason: Unknown
% 1.66/1.52 % (17660)Termination phase: Saturation
% 1.66/1.52
% 1.66/1.52 % (17660)Memory used [KB]: 5628
% 1.66/1.52 % (17660)Time elapsed: 0.026 s
% 1.66/1.52 % (17660)Instructions burned: 84 (million)
% 1.66/1.52 % (17660)------------------------------
% 1.66/1.52 % (17660)------------------------------
% 1.66/1.52 % (17664)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/150Mi)
% 1.66/1.53 % (17665)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/343Mi)
% 1.66/1.53 % (17665)Refutation not found, incomplete strategy
% 1.66/1.53 % (17665)------------------------------
% 1.66/1.53 % (17665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.53 % (17665)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.53
% 1.66/1.53
% 1.66/1.53 % (17665)Memory used [KB]: 5500
% 1.66/1.53 % (17665)Time elapsed: 0.002 s
% 1.66/1.53 % (17665)Instructions burned: 1 (million)
% 1.66/1.53 % (17665)------------------------------
% 1.66/1.53 % (17665)------------------------------
% 1.66/1.53 % (17666)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/109Mi)
% 1.66/1.53 % (17667)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/253Mi)
% 1.66/1.53 % (17667)Refutation not found, incomplete strategy
% 1.66/1.53 % (17667)------------------------------
% 1.66/1.53 % (17667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.53 % (17667)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.53
% 1.66/1.53
% 1.66/1.53 % (17667)Memory used [KB]: 5500
% 1.66/1.53 % (17667)Time elapsed: 0.003 s
% 1.66/1.53 % (17667)Instructions burned: 3 (million)
% 1.66/1.53 % (17667)------------------------------
% 1.66/1.53 % (17667)------------------------------
% 1.66/1.54 % (17606)Instruction limit reached!
% 1.66/1.54 % (17606)------------------------------
% 1.66/1.54 % (17606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.54 % (17606)Termination reason: Unknown
% 1.66/1.54 % (17606)Termination phase: Saturation
% 1.66/1.54
% 1.66/1.54 % (17606)Memory used [KB]: 6524
% 1.66/1.54 % (17606)Time elapsed: 0.188 s
% 1.66/1.54 % (17606)Instructions burned: 713 (million)
% 1.66/1.54 % (17606)------------------------------
% 1.66/1.54 % (17606)------------------------------
% 1.66/1.54 % (17668)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/140Mi)
% 1.66/1.54 % (17668)Refutation not found, incomplete strategy
% 1.66/1.54 % (17668)------------------------------
% 1.66/1.54 % (17668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.54 % (17668)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.54
% 1.66/1.54
% 1.66/1.54 % (17668)Memory used [KB]: 5500
% 1.66/1.54 % (17668)Time elapsed: 0.002 s
% 1.66/1.54 % (17668)Instructions burned: 1 (million)
% 1.66/1.54 % (17668)------------------------------
% 1.66/1.54 % (17668)------------------------------
% 1.66/1.54 % (17671)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/614Mi)
% 1.66/1.55 % (17673)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/202Mi)
% 1.66/1.55 % (17671)Refutation not found, incomplete strategy
% 1.66/1.55 % (17671)------------------------------
% 1.66/1.55 % (17671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.55 % (17671)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.55
% 1.66/1.55
% 1.66/1.55 % (17671)Memory used [KB]: 5500
% 1.66/1.55 % (17671)Time elapsed: 0.002 s
% 1.66/1.55 % (17671)Instructions burned: 1 (million)
% 1.66/1.55 % (17671)------------------------------
% 1.66/1.55 % (17671)------------------------------
% 1.66/1.55 % (17673)Refutation not found, incomplete strategy
% 1.66/1.55 % (17673)------------------------------
% 1.66/1.55 % (17673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.55 % (17673)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.55
% 1.66/1.55
% 1.66/1.55 % (17673)Memory used [KB]: 5500
% 1.66/1.55 % (17673)Time elapsed: 0.002 s
% 1.66/1.55 % (17673)Instructions burned: 3 (million)
% 1.66/1.55 % (17673)------------------------------
% 1.66/1.55 % (17673)------------------------------
% 1.66/1.55 % (17675)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/339Mi)
% 1.66/1.55 % (17675)Refutation not found, incomplete strategy
% 1.66/1.55 % (17675)------------------------------
% 1.66/1.55 % (17675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.55 % (17675)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.55
% 1.66/1.55
% 1.66/1.55 % (17675)Memory used [KB]: 5500
% 1.66/1.55 % (17675)Time elapsed: 0.002 s
% 1.66/1.55 % (17675)Instructions burned: 1 (million)
% 1.66/1.55 % (17675)------------------------------
% 1.66/1.55 % (17675)------------------------------
% 1.66/1.56 % (17678)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/283Mi)
% 1.66/1.56 % (17679)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/134Mi)
% 1.66/1.56 % (17683)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/298Mi)
% 1.66/1.56 % (17666)Instruction limit reached!
% 1.66/1.56 % (17666)------------------------------
% 1.66/1.56 % (17666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.56 % (17666)Termination reason: Unknown
% 1.66/1.56 % (17666)Termination phase: Saturation
% 1.66/1.56
% 1.66/1.56 % (17666)Memory used [KB]: 5756
% 1.66/1.56 % (17666)Time elapsed: 0.034 s
% 1.66/1.56 % (17666)Instructions burned: 112 (million)
% 1.66/1.56 % (17666)------------------------------
% 1.66/1.56 % (17666)------------------------------
% 1.66/1.56 % (17664)Instruction limit reached!
% 1.66/1.56 % (17664)------------------------------
% 1.66/1.56 % (17664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.56 % (17664)Termination reason: Unknown
% 1.66/1.56 % (17664)Termination phase: Saturation
% 1.66/1.56
% 1.66/1.56 % (17664)Memory used [KB]: 5756
% 1.66/1.56 % (17664)Time elapsed: 0.042 s
% 1.66/1.56 % (17664)Instructions burned: 152 (million)
% 1.66/1.56 % (17664)------------------------------
% 1.66/1.56 % (17664)------------------------------
% 1.66/1.57 % (17689)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/258Mi)
% 1.66/1.57 % (17688)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/192Mi)
% 1.66/1.57 % (17689)Refutation not found, incomplete strategy
% 1.66/1.57 % (17689)------------------------------
% 1.66/1.57 % (17689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.57 % (17689)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.57
% 1.66/1.57
% 1.66/1.57 % (17689)Memory used [KB]: 5500
% 1.66/1.57 % (17689)Time elapsed: 0.001 s
% 1.66/1.57 % (17689)Instructions burned: 1 (million)
% 1.66/1.57 % (17689)------------------------------
% 1.66/1.57 % (17689)------------------------------
% 1.66/1.58 % (17695)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/90Mi)
% 1.66/1.59 % (17695)Refutation not found, incomplete strategy
% 1.66/1.59 % (17695)------------------------------
% 1.66/1.59 % (17695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.59 % (17695)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.59
% 1.66/1.59
% 1.66/1.59 % (17695)Memory used [KB]: 5500
% 1.66/1.59 % (17695)Time elapsed: 0.002 s
% 1.66/1.59 % (17695)Instructions burned: 2 (million)
% 1.66/1.59 % (17695)------------------------------
% 1.66/1.59 % (17695)------------------------------
% 1.66/1.60 % (17700)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_17396 for (2997ds/231Mi)
% 1.66/1.60 % (17613)Instruction limit reached!
% 1.66/1.60 % (17613)------------------------------
% 1.66/1.60 % (17613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.60 % (17613)Termination reason: Unknown
% 1.66/1.60 % (17613)Termination phase: Saturation
% 1.66/1.60
% 1.66/1.60 % (17613)Memory used [KB]: 6524
% 1.66/1.60 % (17613)Time elapsed: 0.234 s
% 1.66/1.60 % (17613)Instructions burned: 780 (million)
% 1.66/1.60 % (17613)------------------------------
% 1.66/1.60 % (17613)------------------------------
% 1.66/1.60 % (17679)Instruction limit reached!
% 1.66/1.60 % (17679)------------------------------
% 1.66/1.60 % (17679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.60 % (17679)Termination reason: Unknown
% 1.66/1.60 % (17679)Termination phase: Saturation
% 1.66/1.60
% 1.66/1.60 % (17679)Memory used [KB]: 6140
% 1.66/1.60 % (17679)Time elapsed: 0.043 s
% 1.66/1.60 % (17679)Instructions burned: 134 (million)
% 1.66/1.60 % (17679)------------------------------
% 1.66/1.60 % (17679)------------------------------
% 1.66/1.61 % (17631)Instruction limit reached!
% 1.66/1.61 % (17631)------------------------------
% 1.66/1.61 % (17631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.61 % (17631)Termination reason: Unknown
% 1.66/1.61 % (17631)Termination phase: Saturation
% 1.66/1.61
% 1.66/1.61 % (17631)Memory used [KB]: 6268
% 1.66/1.61 % (17631)Time elapsed: 0.179 s
% 1.66/1.61 % (17631)Instructions burned: 450 (million)
% 1.66/1.61 % (17631)------------------------------
% 1.66/1.61 % (17631)------------------------------
% 1.66/1.61 % (17705)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/458Mi)
% 1.66/1.61 % (17706)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/31Mi)
% 1.66/1.61 % (17705)Refutation not found, incomplete strategy
% 1.66/1.61 % (17705)------------------------------
% 1.66/1.61 % (17705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.61 % (17705)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.61
% 1.66/1.61
% 1.66/1.61 % (17705)Memory used [KB]: 5500
% 1.66/1.61 % (17705)Time elapsed: 0.001 s
% 1.66/1.61 % (17705)Instructions burned: 1 (million)
% 1.66/1.61 % (17705)------------------------------
% 1.66/1.61 % (17705)------------------------------
% 1.66/1.62 % (17706)Instruction limit reached!
% 1.66/1.62 % (17706)------------------------------
% 1.66/1.62 % (17706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.62 % (17706)Termination reason: Unknown
% 1.66/1.62 % (17706)Termination phase: Saturation
% 1.66/1.62
% 1.66/1.62 % (17706)Memory used [KB]: 5628
% 1.66/1.62 % (17706)Time elapsed: 0.010 s
% 1.66/1.62 % (17706)Instructions burned: 33 (million)
% 1.66/1.62 % (17706)------------------------------
% 1.66/1.62 % (17706)------------------------------
% 1.66/1.62 % (17712)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/297Mi)
% 1.66/1.62 % (17713)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/987Mi)
% 1.66/1.62 % (17713)Refutation not found, incomplete strategy
% 1.66/1.62 % (17713)------------------------------
% 1.66/1.62 % (17713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.62 % (17713)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.62
% 1.66/1.62
% 1.66/1.62 % (17713)Memory used [KB]: 5500
% 1.66/1.62 % (17713)Time elapsed: 0.004 s
% 1.66/1.62 % (17713)Instructions burned: 9 (million)
% 1.66/1.62 % (17713)------------------------------
% 1.66/1.62 % (17713)------------------------------
% 1.66/1.63 % (17719)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/182Mi)
% 1.66/1.63 % (17688)Instruction limit reached!
% 1.66/1.63 % (17688)------------------------------
% 1.66/1.63 % (17688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.63 % (17688)Termination reason: Unknown
% 1.66/1.63 % (17688)Termination phase: Saturation
% 1.66/1.63
% 1.66/1.63 % (17688)Memory used [KB]: 5884
% 1.66/1.63 % (17688)Time elapsed: 0.057 s
% 1.66/1.63 % (17688)Instructions burned: 193 (million)
% 1.66/1.63 % (17688)------------------------------
% 1.66/1.63 % (17688)------------------------------
% 1.66/1.63 % (17722)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/182Mi)
% 1.66/1.63 % (17722)Refutation not found, incomplete strategy
% 1.66/1.63 % (17722)------------------------------
% 1.66/1.63 % (17722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.63 % (17722)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.63
% 1.66/1.63
% 1.66/1.63 % (17722)Memory used [KB]: 5500
% 1.66/1.63 % (17722)Time elapsed: 0.002 s
% 1.66/1.63 % (17722)Instructions burned: 2 (million)
% 1.66/1.63 % (17722)------------------------------
% 1.66/1.63 % (17722)------------------------------
% 1.66/1.63 % (17700)First to succeed.
% 1.66/1.64 % (17678)Instruction limit reached!
% 1.66/1.64 % (17678)------------------------------
% 1.66/1.64 % (17678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.64 % (17678)Termination reason: Unknown
% 1.66/1.64 % (17678)Termination phase: Saturation
% 1.66/1.64
% 1.66/1.64 % (17678)Memory used [KB]: 6140
% 1.66/1.64 % (17678)Time elapsed: 0.082 s
% 1.66/1.64 % (17678)Instructions burned: 283 (million)
% 1.66/1.64 % (17678)------------------------------
% 1.66/1.64 % (17678)------------------------------
% 1.66/1.64 % (17725)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/154Mi)
% 1.66/1.64 % (17726)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_17396 for (2996ds/79Mi)
% 1.66/1.64 % (17700)Refutation found. Thanks to Tanya!
% 1.66/1.64 % SZS status Theorem for DTF2THF_17396
% 1.66/1.64 % SZS output start Proof for DTF2THF_17396
% 1.66/1.64 thf(func_def_11, type, sF0: ((($i > $i > $o) > $i) > $o) > $o).
% 1.66/1.64 thf(func_def_12, type, sF1: (($i > $i > $o) > $o) > $o).
% 1.66/1.64 thf(func_def_13, type, sF2: ($i > $o) > $o).
% 1.66/1.64 thf(func_def_14, type, sF3: (($i > $i > $o) > $i) > $o).
% 1.66/1.64 thf(func_def_18, type, ph7: !>[X0: $tType]:(X0)).
% 1.66/1.64 thf(func_def_19, type, sK8: ($i > $o) > $i).
% 1.66/1.64 thf(func_def_20, type, sK9: (($i > $i > $o) > $o) > $i > $i > $o).
% 1.66/1.64 thf(func_def_21, type, sK10: ((($i > $i > $o) > $i) > $o) > ($i > $i > $o) > $i).
% 1.66/1.64 thf(func_def_23, type, sK11: (($i > $i > $o) > $i > $i) > (($i > $i > $o) > $i > $i) > $i).
% 1.66/1.64 thf(func_def_24, type, sK12: (($i > $i > $o) > $i > $i) > (($i > $i > $o) > $i > $i) > $i > $i > $o).
% 1.66/1.64 thf(func_def_27, type, sK13: (($i > $i > $o) > $i > $i > $i > $i) > $i).
% 1.66/1.64 thf(func_def_28, type, sK14: (($i > $i > $o) > $i > $i > $i > $i) > $i).
% 1.66/1.64 thf(f223,plain,(
% 1.66/1.64 $false),
% 1.66/1.64 inference(avatar_sat_refutation,[status(thm)],[f26,f36,f39,f222])).
% 1.66/1.64 thf(f222,plain,(
% 1.66/1.64 ~spl6_1),
% 1.66/1.64 inference(avatar_contradiction_clause,[status(thm)],[f221])).
% 1.66/1.64 thf(f221,plain,(
% 1.66/1.64 $false | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 1.66/1.64 thf(f220,plain,(
% 1.66/1.64 ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y3 @ Y2)))))))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y3 @ Y2))))))))) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f219])).
% 1.66/1.64 thf(f219,plain,(
% 1.66/1.64 ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))))))) @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y7)))))))) @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y3 @ Y2))))))))) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f218])).
% 1.66/1.64 thf(f218,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6))))))))))))))) | ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y0 @ Y3 @ Y2))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (X0 @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f217])).
% 1.66/1.64 thf(f217,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6))))))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (X0 @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1))))))))) | (((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))))) @ (sK14 @ X0)) != ((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))))) @ (sK14 @ X0)))) ) | ~spl6_1),
% 1.66/1.64 inference(negative_extensionality,[status(thm)],[f216])).
% 1.66/1.64 thf(f216,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))))) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y4 @ Y3))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6))))))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (X0 @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f215])).
% 1.66/1.64 thf(f215,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i] : (((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (X0 @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1))))))))) | (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ Y5 @ Y4)))))))))))) @ (sK13 @ X0)) != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4)))))))))))) @ (sK13 @ X0))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))))))))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(negative_extensionality,[status(thm)],[f214])).
% 1.66/1.64 thf(f214,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ Y5 @ Y4)))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6))))))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ (X0 @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f213])).
% 1.66/1.64 thf(f213,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i] : (((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y4 @ (X0 @ Y4 @ Y5 @ Y6 @ Y7) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10)))))))) @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))))))) @ Y2 @ Y3 @ Y4 @ Y5))))))))) @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y5 @ (X0 @ Y5 @ Y6 @ Y7 @ Y8) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11)))))))) @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y2 @ Y5 @ Y4))))))))) @ Y0 @ Y1))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y4 @ (X0 @ Y4 @ Y5 @ Y6 @ Y7) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10)))))))) @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y6 @ (X0 @ Y6 @ Y7 @ Y8 @ Y9) @ ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (Y12)))))))) @ Y6 @ Y7 @ Y8 @ Y9))))))))) @ Y3 @ Y4 @ Y5))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))))))) @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ Y5 @ Y4))))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (X0 @ Y3 @ Y4 @ Y5 @ Y6)))))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))))))))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f212])).
% 1.66/1.64 thf(f212,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X0)))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ Y5 @ Y4))))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X0 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X0 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y2 @ Y5 @ Y4))))))))) @ Y0 @ Y1))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f211])).
% 1.66/1.64 thf(f211,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: (X0)))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y9)))))))) @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))))))) @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X0 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X0 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y2 @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y9)))))))) @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))) @ Y0 @ Y1))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f210])).
% 1.66/1.64 thf(f210,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i,X1 : ($i > $i > $o) > $i > $i > $i > $o] : (((X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (sK8 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y2))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X1))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X1 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))) @ Y0 @ Y1))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK12 @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ (^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sK8 @ (^[Y5 : $i]: (sF2 @ (^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f209])).
% 1.66/1.64 thf(f209,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $i,X1 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))))))) @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X1))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (X1 @ Y3 @ Y4 @ Y5))))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (sK8 @ (^[Y5 : $i]: (sF2 @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y6 @ (X0 @ Y6 @ Y7 @ Y8 @ Y9) @ ((^[Y10 : $i > $i > $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (Y12)))))))) @ Y6 @ Y7 @ Y8 @ Y9))))))))) @ Y3 @ Y4 @ Y5))))))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))))))) @ Y0 @ Y1 @ Y2)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y2))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y4 @ (X0 @ Y4 @ Y5 @ Y6 @ Y7) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10)))))))) @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X1 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y5 @ (X0 @ Y5 @ Y6 @ Y7 @ Y8) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11)))))))) @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y4 @ (X0 @ Y4 @ Y5 @ Y6 @ Y7) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10)))))))) @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))))))) @ Y2 @ Y3 @ Y4 @ Y5))))))))) @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y5 @ (X0 @ Y5 @ Y6 @ Y7 @ Y8) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (Y11)))))))) @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f208])).
% 1.66/1.64 thf(f208,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $o,X1 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (sK8 @ (^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (sK8 @ (^[Y2 : $i]: (sF2 @ (X0 @ Y0 @ Y1 @ Y2))))))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X1 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X0 @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X0 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X0 @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1)))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X0)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X1)))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f207])).
% 1.66/1.64 thf(f207,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i > $i > $o,X1 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (X0 @ Y2 @ Y3 @ Y4)))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (X1 @ Y2 @ Y3 @ Y4))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3)))))))) @ Y0)))) != (sK8 @ (^[Y0 : $i]: (sK12 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X0 @ (sK12 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (sF2 @ (X1 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X0 @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1)))))))) | ((X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (sK8 @ (^[Y2 : $i]: (sF2 @ (X0 @ Y0 @ Y1 @ Y2))))))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: (sK8 @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (sF2 @ (X1 @ Y7 @ Y8 @ Y9))))))) @ Y5 @ Y6))))) @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f206])).
% 1.66/1.64 thf(f206,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4))))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X1 @ (sK12 @ X0 @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ (^[Y4 : $i]: (sF2 @ (X1 @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1))))))) != (sK8 @ (^[Y0 : $i]: (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (X0 @ (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ (^[Y3 : $i]: (sF2 @ (X1 @ Y1 @ Y2 @ Y3)))))))) @ Y0))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (sK8 @ (^[Y2 : $i]: (sF2 @ (X1 @ Y0 @ Y1 @ Y2))))))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f205])).
% 1.66/1.64 thf(f205,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i > $i > $o] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (sK8 @ (^[Y3 : $i]: (Y2 @ Y3 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: (sK8 @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (sF2 @ (X1 @ Y6 @ Y7 @ Y8))))))) @ Y4 @ Y5))))) @ Y2 @ Y3)))) @ (sK8 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))))))) @ Y0 @ Y1))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0 @ (X0 @ (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2)))))) @ Y0)))) != (sK8 @ (^[Y0 : $i]: (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (sK12 @ X0 @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (sF2 @ (X1 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2)))))) @ Y0))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X0)))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sK8 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (sF2 @ (X1 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f204])).
% 1.66/1.64 thf(f204,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK12 @ X1 @ X0 @ Y0 @ (X0 @ (sK12 @ X1 @ X0) @ Y0)))) != (sK8 @ (^[Y0 : $i]: (sK12 @ X1 @ X0 @ Y0 @ (X1 @ (sK12 @ X1 @ X0) @ Y0))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f203])).
% 1.66/1.64 thf(f203,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | (((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) @ (sK12 @ X1 @ X0)) != ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) @ (sK12 @ X1 @ X0)))) ) | ~spl6_1),
% 1.66/1.64 inference(negative_extensionality,[status(thm)],[f202])).
% 1.66/1.64 thf(f202,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))))) | ((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(duplicate_literal_removal,[status(thm)],[f201])).
% 1.66/1.64 thf(f201,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | ((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f200])).
% 1.66/1.64 thf(f200,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | (((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2))))))) @ (sK11 @ X1 @ X0)) != ((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2))))))) @ (sK11 @ X1 @ X0))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))))) ) | ~spl6_1),
% 1.66/1.64 inference(negative_extensionality,[status(thm)],[f199])).
% 1.66/1.64 thf(f199,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2)))))))) | ((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f198])).
% 1.66/1.64 thf(f198,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (Y4)))) @ Y1 @ Y2) @ (X1 @ Y1 @ Y2)))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: (Y6)))) @ Y3 @ Y4) @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f197])).
% 1.66/1.64 thf(f197,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i,X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: (X2)))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y3))))))))) | ((X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK8 @ (^[Y4 : $i]: (Y3 @ (X2 @ Y3 @ Y4) @ (X1 @ Y3 @ Y4)))) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ (X2 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ (X2 @ Y1 @ Y2) @ (X1 @ Y1 @ Y2)))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f196])).
% 1.66/1.64 thf(f196,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i,X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (X2 @ Y2 @ Y3)))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y3))))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (Y1 @ (X2 @ Y1 @ Y2) @ (X1 @ Y1 @ Y2))))) @ Y0))) != (^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ ((^[Y4 : $i > $i > $o]: (sK8 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: (Y5 @ (X2 @ Y5 @ Y6) @ (X1 @ Y5 @ Y6))))) @ Y4))) @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (X0 @ Y2 @ Y3)))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (X1 @ Y2 @ Y3))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y2 @ (X2 @ Y2 @ Y3) @ (X1 @ Y2 @ Y3))))) @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f195])).
% 1.66/1.64 thf(f195,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (sK8 @ (^[Y3 : $i]: (Y2 @ Y3 @ (X1 @ Y2 @ Y3))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2)))))))) | ((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != X0)) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f194])).
% 1.66/1.64 thf(f194,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (Y4)))) @ Y1 @ Y2) @ (X1 @ Y1 @ Y2)))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (sK8 @ (^[Y3 : $i]: (Y2 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3) @ (X1 @ Y2 @ Y3))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | ((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) != X0)) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f193])).
% 1.66/1.64 thf(f193,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i,X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ (X1 @ Y0 @ Y1) @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : $i]: (Y0))) | ((^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK8 @ (^[Y1 : $i]: (Y0 @ (X1 @ Y0 @ Y1) @ (X0 @ Y0 @ Y1)))) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ (^[Y1 : $i]: (Y0 @ (X1 @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) != X2) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X2)))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (sK8 @ (^[Y3 : $i]: (Y2 @ (X1 @ Y2 @ Y3) @ (X0 @ Y2 @ Y3)))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ (^[Y2 : $i]: (Y1 @ (X1 @ Y1 @ Y2) @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : $i]: (X2)))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f192])).
% 1.66/1.64 thf(f192,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i,X0 : ($i > $i > $o) > $i > $i,X1 : ($i > $i > $o) > $i > $i] : (((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (sK8 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (Y2 @ (X1 @ Y2 @ Y3) @ (X0 @ Y2 @ Y3))))) @ Y1))))) != (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (X2 @ Y1))))) | ((^[Y0 : $i]: (Y0)) != (^[Y0 : $i]: (X1 @ (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (Y3 @ (X1 @ Y3 @ Y4) @ (X0 @ Y3 @ Y4))))) @ Y2))) @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))))))) @ Y0))) | ((^[Y0 : $i]: (X0 @ (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (Y3 @ (X1 @ Y3 @ Y4) @ (X0 @ Y3 @ Y4))))) @ Y2))) @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))))))) @ Y0)) != (^[Y0 : $i]: (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : $i > $i > $o]: (sK8 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: (Y1 @ (X1 @ Y1 @ Y2) @ (X0 @ Y1 @ Y2))))) @ Y0))) != X2) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (Y3 @ (X1 @ Y3 @ Y4) @ (X0 @ Y3 @ Y4))))) @ Y2))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X2)))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f191])).
% 1.66/1.64 thf(f191,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))))) != (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))))) | (X0 != X1) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f190])).
% 1.66/1.64 thf(f190,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))))) != (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y6)))))) @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y8)))))) @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1))))))))) | (X0 != X1) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0)))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f183])).
% 1.66/1.64 thf(f183,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i > $i,X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != (X2 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | ((sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ (X2 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X1 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1)))))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (X1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X0))))) | (X0 != X1)) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.66/1.64 thf(f182,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i > $i,X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ((X0 != X1) | ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (X1 @ Y2)))))) != (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (X0 @ Y2))))))) | ((sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y7)))))) @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X1 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y5 @ (X2 @ Y5 @ Y6 @ Y7) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9)))))) @ Y5 @ Y6 @ Y7))))))) @ Y3 @ Y4))))))) @ Y2 @ Y1)))))))) != (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6)))))) @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1)))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (sK8 @ (^[Y3 : $i]: (sF2 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ (X2 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8)))))) @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3)))))))) @ Y0 @ Y1)))))) ) | ~spl6_1),
% 1.66/1.64 inference(equality_resolution,[status(thm)],[f179])).
% 1.66/1.64 thf(f179,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i > $o,X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((X2 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X2 @ Y0 @ Y1))))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (sK8 @ (^[Y3 : $i]: (sF2 @ (X2 @ Y2 @ Y3))))))) @ Y1 @ Y0))))) | ((sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (sK8 @ (^[Y2 : $i]: (sF2 @ (X2 @ Y1 @ Y2))))))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK8 @ (^[Y4 : $i]: (sF2 @ (X2 @ Y3 @ Y4))))))) @ Y2 @ Y1)))))))) != (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK8 @ (^[Y1 : $i]: (sF2 @ (X2 @ Y0 @ Y1)))))))))) | (X0 != X1)) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f178])).
% 1.66/1.64 thf(f178,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i > $o,X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ ((^[Y3 : $i > $i > $o]: (sK8 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: (sF2 @ (X2 @ Y4 @ Y5))))) @ Y3))) @ Y2)))) @ Y1 @ Y0)))) != (^[Y0 : $i]: (X2 @ (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sF2 @ (X2 @ Y3 @ Y4))))) @ Y2))) @ Y1))))) @ Y0))) | ((^[Y0 : $i > $i > $o]: (X1 @ Y0)) != (^[Y0 : $i > $i > $o]: (X0 @ Y0))) | ((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ ((^[Y1 : $i > $i > $o]: (sK8 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sF2 @ (X2 @ Y2 @ Y3))))) @ Y1))) @ Y0)))))) != (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sF2 @ (X2 @ Y3 @ Y4))))) @ Y2))) @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ ((^[Y4 : $i > $i > $o]: (sK8 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: (sF2 @ (X2 @ Y5 @ Y6))))) @ Y4))) @ Y3)))) @ Y2 @ Y1)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.66/1.64 thf(f177,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i > $i > $o,X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((^[Y0 : $i > $i > $o]: (X1 @ Y0)) != (^[Y0 : $i > $i > $o]: (X0 @ Y0))) | ($true = $false) | ((X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ ((^[Y1 : $i > $i > $o]: (sK8 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: (sF2 @ (X2 @ Y2 @ Y3))))) @ Y1))) @ Y0)))))) != (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sF2 @ (X2 @ Y3 @ Y4))))) @ Y2))) @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ ((^[Y4 : $i > $i > $o]: (sK8 @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: (sF2 @ (X2 @ Y5 @ Y6))))) @ Y4))) @ Y3)))) @ Y2 @ Y1))))))))) | ((^[Y0 : $i]: ((^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ ((^[Y3 : $i > $i > $o]: (sK8 @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: (sF2 @ (X2 @ Y4 @ Y5))))) @ Y3))) @ Y2)))) @ Y1 @ Y0)))) != (^[Y0 : $i]: (X2 @ (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ ((^[Y2 : $i > $i > $o]: (sK8 @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (sF2 @ (X2 @ Y3 @ Y4))))) @ Y2))) @ Y1))))) @ Y0)))) ) | ~spl6_1),
% 1.66/1.64 inference(constrained_superposition,[status(thm)],[f143,f173])).
% 1.66/1.64 thf(f173,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1)))))))) @ (sK8 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f172])).
% 1.66/1.64 thf(f172,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = ((^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))) @ (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.66/1.64 thf(f171,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = $false) | ($true = ((^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))) @ (sK8 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(superposition,[status(thm)],[f66,f167])).
% 1.66/1.64 thf(f167,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = (sF2 @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK8 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i > $i > $o]: ((sF2 @ (^[Y4 : $i]: (sF2 @ (^[Y5 : $i]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f166])).
% 1.66/1.64 thf(f166,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ((((^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))) @ (sK8 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))))) = $true)) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.66/1.64 thf(f165,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = $false) | (((^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))) @ (sK8 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))))) = $true)) ) | ~spl6_1),
% 1.66/1.64 inference(superposition,[status(thm)],[f66,f145])).
% 1.66/1.64 thf(f145,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((sF2 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) = $true)) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.66/1.64 thf(f144,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = $false) | ((sF2 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) = $true)) ) | ~spl6_1),
% 1.66/1.64 inference(boolean_simplification,[status(thm)],[f133])).
% 1.66/1.64 thf(f133,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (((sF2 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) = $true) | ($false = ($false => (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(cases_simplifying,[status(thm)],[f131])).
% 1.66/1.64 thf(f131,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ((((sF2 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) => (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))))) = $false)) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f130])).
% 1.66/1.64 thf(f130,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ((((^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) = $false)) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.66/1.64 thf(f129,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ((((^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) = $false) | ($true = $false)) ) | ~spl6_1),
% 1.66/1.64 inference(superposition,[status(thm)],[f84,f119])).
% 1.66/1.64 thf(f119,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($false = (sF1 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))) ) | ~spl6_1),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f118])).
% 1.66/1.64 thf(f118,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($false = ((^[Y0 : ($i > $i > $o) > $i]: (sF1 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (Y0 @ Y1)))))) @ X1))) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.66/1.64 thf(f116,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($false = ((^[Y0 : ($i > $i > $o) > $i]: (sF1 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (Y0 @ Y1)))))) @ X1)) | ($true = $false)) ) | ~spl6_1),
% 1.66/1.64 inference(superposition,[status(thm)],[f115,f98])).
% 1.66/1.64 thf(f98,plain,(
% 1.66/1.64 ( ! [X2 : ($i > $i > $o) > $i,X1 : (($i > $i > $o) > $i) > $o] : (($true = (sF0 @ X1)) | ((X1 @ X2) = $false)) )),
% 1.66/1.64 inference(pi_clausification,[status(thm)],[f56])).
% 1.66/1.64 thf(f56,plain,(
% 1.66/1.64 ( ! [X1 : (($i > $i > $o) > $i) > $o] : (((?? @ (($i > $i > $o) > $i) @ X1) = $false) | ($true = (sF0 @ X1))) )),
% 1.66/1.64 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.66/1.64 thf(f48,plain,(
% 1.66/1.64 ( ! [X1 : (($i > $i > $o) > $i) > $o] : (((?? @ (($i > $i > $o) > $i) @ X1) = (sF0 @ X1))) )),
% 1.66/1.64 inference(argument_congruence,[status(thm)],[f7])).
% 1.66/1.64 thf(f7,definition,(
% 1.66/1.64 (sF0 = ?? @ (($i > $i > $o) > $i))),
% 1.66/1.64 introduced(definition,[],[function_definition])).
% 1.66/1.64 thf(f115,plain,(
% 1.66/1.64 ( ! [X1 : ($i > $i > $o) > $i] : (($false = (sF0 @ (^[Y0 : ($i > $i > $o) > $i]: (sF1 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (Y0 @ Y1))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(backward_demodulation,[status(thm)],[f50,f113])).
% 1.66/1.64 thf(f113,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i] : (((sF3 @ X0) = $false)) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.66/1.64 thf(f107,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i] : (($true = $false) | ((sF3 @ X0) = $false)) ) | ~spl6_1),
% 1.66/1.64 inference(superposition,[status(thm)],[f46,f98])).
% 1.66/1.64 thf(f46,plain,(
% 1.66/1.64 ($false = (sF0 @ sF3)) | ~spl6_1),
% 1.66/1.64 inference(forward_demodulation,[status(thm)],[f11,f21])).
% 1.66/1.64 thf(f21,plain,(
% 1.66/1.64 (sF4 = $false) | ~spl6_1),
% 1.66/1.64 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.66/1.64 thf(f19,definition,(
% 1.66/1.64 spl6_1 <=> (sF4 = $false)),
% 1.66/1.64 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.66/1.64 thf(f11,definition,(
% 1.66/1.64 (sF4 = (sF0 @ sF3))),
% 1.66/1.64 introduced(definition,[],[function_definition])).
% 1.66/1.64 thf(f50,plain,(
% 1.66/1.64 ( ! [X1 : ($i > $i > $o) > $i] : (((sF3 @ X1) = (sF0 @ (^[Y0 : ($i > $i > $o) > $i]: (sF1 @ (^[Y1 : $i > $i > $o]: ((sF2 @ (^[Y2 : $i]: (sF2 @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (Y0 @ Y1))))))))) )),
% 1.66/1.64 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.66/1.64 thf(f49,plain,(
% 1.66/1.64 ( ! [X1 : ($i > $i > $o) > $i] : (((sF3 @ X1) = ((^[Y0 : ($i > $i > $o) > $i]: (sF0 @ (^[Y1 : ($i > $i > $o) > $i]: (sF1 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))) @ X1))) )),
% 1.66/1.64 inference(argument_congruence,[status(thm)],[f10])).
% 1.66/1.64 thf(f10,definition,(
% 1.66/1.64 (sF3 = (^[Y0 : ($i > $i > $o) > $i]: (sF0 @ (^[Y1 : ($i > $i > $o) > $i]: (sF1 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))))),
% 1.66/1.64 introduced(definition,[],[function_definition])).
% 1.66/1.64 thf(f84,plain,(
% 1.66/1.64 ( ! [X1 : ($i > $i > $o) > $o] : (($true = (sF1 @ X1)) | ((X1 @ (sK9 @ X1)) = $false)) )),
% 1.66/1.64 inference(sigma_clausification,[status(thm)],[f54])).
% 1.66/1.64 thf(f54,plain,(
% 1.66/1.64 ( ! [X1 : ($i > $i > $o) > $o] : (((!! @ ($i > $i > $o) @ X1) = $false) | ($true = (sF1 @ X1))) )),
% 1.66/1.64 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.66/1.64 thf(f47,plain,(
% 1.66/1.64 ( ! [X1 : ($i > $i > $o) > $o] : (((!! @ ($i > $i > $o) @ X1) = (sF1 @ X1))) )),
% 1.66/1.64 inference(argument_congruence,[status(thm)],[f8])).
% 1.66/1.64 thf(f8,definition,(
% 1.66/1.64 (!! @ ($i > $i > $o) = sF1)),
% 1.66/1.64 introduced(definition,[],[function_definition])).
% 1.66/1.64 thf(f66,plain,(
% 1.66/1.64 ( ! [X1 : $i > $o] : (((sF2 @ X1) = $false) | ((X1 @ (sK8 @ X1)) = $true)) )),
% 1.66/1.64 inference(sigma_clausification,[status(thm)],[f52])).
% 1.66/1.64 thf(f52,plain,(
% 1.66/1.64 ( ! [X1 : $i > $o] : (($true = (?? @ $i @ X1)) | ((sF2 @ X1) = $false)) )),
% 1.66/1.64 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.66/1.64 thf(f45,plain,(
% 1.66/1.64 ( ! [X1 : $i > $o] : (((sF2 @ X1) = (?? @ $i @ X1))) )),
% 1.66/1.64 inference(argument_congruence,[status(thm)],[f9])).
% 1.66/1.64 thf(f9,definition,(
% 1.66/1.64 (sF2 = ?? @ $i)),
% 1.66/1.64 introduced(definition,[],[function_definition])).
% 1.66/1.64 thf(f143,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($false = (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f142])).
% 1.66/1.64 thf(f142,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : (($true = $false) | ($false = (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(boolean_simplification,[status(thm)],[f134])).
% 1.66/1.64 thf(f134,plain,(
% 1.66/1.64 ( ! [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ((((sF2 @ (^[Y0 : $i]: (sF2 @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i > $i > $o]: ((sF2 @ (^[Y3 : $i]: (sF2 @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) => $true) = $false) | ($false = (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK9 @ (^[Y0 : $i > $i > $o]: ((sF2 @ (^[Y1 : $i]: (sF2 @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))))) ) | ~spl6_1),
% 1.66/1.64 inference(cases_simplifying,[status(thm)],[f131])).
% 1.66/1.64 thf(f39,plain,(
% 1.66/1.64 ~spl6_2 | ~spl6_4),
% 1.66/1.64 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.66/1.64 thf(f38,plain,(
% 1.66/1.64 $false | (~spl6_2 | ~spl6_4)),
% 1.66/1.64 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.66/1.64 thf(f37,plain,(
% 1.66/1.64 ($true = $false) | (~spl6_2 | ~spl6_4)),
% 1.66/1.64 inference(forward_demodulation,[status(thm)],[f34,f25])).
% 1.66/1.64 thf(f25,plain,(
% 1.66/1.64 (sF5 = $false) | ~spl6_2),
% 1.66/1.64 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.66/1.64 thf(f23,definition,(
% 1.66/1.64 spl6_2 <=> (sF5 = $false)),
% 1.66/1.64 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.66/1.64 thf(f34,plain,(
% 1.66/1.64 ($true = sF5) | ~spl6_4),
% 1.66/1.64 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.66/1.64 thf(f32,definition,(
% 1.66/1.64 spl6_4 <=> ($true = sF5)),
% 1.66/1.64 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.66/1.64 thf(f36,plain,(
% 1.66/1.64 spl6_4),
% 1.66/1.64 inference(avatar_split_clause,[status(thm)],[f13,f32])).
% 1.66/1.64 thf(f13,plain,(
% 1.66/1.64 ($true = sF5)),
% 1.66/1.64 inference(definition_folding,[status(thm)],[f6,f12,f11,f10,f9,f9,f8,f7,f7])).
% 1.66/1.64 thf(f12,definition,(
% 1.66/1.64 (sF5 = (~ sF4))),
% 1.66/1.64 introduced(definition,[],[function_definition])).
% 1.66/1.64 thf(f6,plain,(
% 1.66/1.64 ($true = (~ (?? @ (($i > $i > $o) > $i) @ (^[Y0 : ($i > $i > $o) > $i]: (?? @ (($i > $i > $o) > $i) @ (^[Y1 : ($i > $i > $o) > $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))))))),
% 1.66/1.64 inference(cnf_transformation,[status(thm)],[f5])).
% 1.66/1.64 thf(f5,plain,(
% 1.66/1.64 ($true = (~ (?? @ (($i > $i > $o) > $i) @ (^[Y0 : ($i > $i > $o) > $i]: (?? @ (($i > $i > $o) > $i) @ (^[Y1 : ($i > $i > $o) > $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))))))),
% 1.66/1.64 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.64 thf(f4,plain,(
% 1.66/1.64 ~? [X0 : ($i > $i > $o) > $i,X1 : ($i > $i > $o) > $i] : ! [X2 : $i > $i > $o] : (? [X3 : $i,X4 : $i] : (X2 @ X3 @ X4) => (X2 @ (X1 @ X2) @ (X0 @ X2)))),
% 1.66/1.64 inference(rectify,[status(thm)],[f2])).
% 1.66/1.64 thf(f2,negated_conjecture,(
% 1.66/1.64 ~? [X1 : ($i > $i > $o) > $i,X0 : ($i > $i > $o) > $i] : ! [X2 : $i > $i > $o] : (? [X3 : $i,X4 : $i] : (X2 @ X3 @ X4) => (X2 @ (X0 @ X2) @ (X1 @ X2)))),
% 1.66/1.64 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.64 thf(f1,conjecture,(
% 1.66/1.64 ? [X1 : ($i > $i > $o) > $i,X0 : ($i > $i > $o) > $i] : ! [X2 : $i > $i > $o] : (? [X3 : $i,X4 : $i] : (X2 @ X3 @ X4) => (X2 @ (X0 @ X2) @ (X1 @ X2)))),
% 1.66/1.64 file('/export/starexec/sandbox/tmp/tmp.fKG68WVYH8/DTF2THF_17396.p',conj)).
% 1.66/1.64 thf(f26,plain,(
% 1.66/1.64 spl6_1 | spl6_2),
% 1.66/1.64 inference(avatar_split_clause,[status(thm)],[f17,f23,f19])).
% 1.66/1.64 thf(f17,plain,(
% 1.66/1.64 (sF5 = $false) | (sF4 = $false)),
% 1.66/1.64 inference(boolean_simplification,[status(thm)],[f14])).
% 1.66/1.64 thf(f14,plain,(
% 1.66/1.64 (sF5 = (~ $true)) | (sF4 = $false)),
% 1.66/1.64 inference(cases_simplifying,[status(thm)],[f12])).
% 1.66/1.64 % SZS output end Proof for DTF2THF_17396
% 1.66/1.64 % (17700)------------------------------
% 1.66/1.64 % (17700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.64 % (17700)Termination reason: Refutation
% 1.66/1.64
% 1.66/1.64 % (17700)Memory used [KB]: 6524
% 1.66/1.64 % (17700)Time elapsed: 0.046 s
% 1.66/1.64 % (17700)Instructions burned: 125 (million)
% 1.66/1.64 % (17700)------------------------------
% 1.66/1.64 % (17700)------------------------------
% 1.66/1.64 % (17585)Success in time 0.34 s
%------------------------------------------------------------------------------