%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO509^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 09:54:25 AM UTC 2026
% Result : Theorem 1.56s 1.63s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 12
% Syntax : Number of formulae : 118 ( 18 unt; 0 typ; 11 def)
% Number of atoms : 1600 ( 301 equ; 0 cnn)
% Maximal formula atoms : 9 ( 13 avg)
% Number of connectives : 6611 ( 308 ~; 274 |; 0 &;5824 @)
% ( 3 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 2104 (2104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 22 usr; 9 con; 0-4 aty)
% ( 5 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 3133 (2924 ^; 197 !; 12 ?;3133 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_13,type,
sF0: ( ( ( a > b > $o ) > a ) > $o ) > $o ).
thf(func_def_14,type,
sF1: ( ( ( a > b > $o ) > b ) > $o ) > $o ).
thf(func_def_15,type,
sF2: ( ( a > b > $o ) > $o ) > $o ).
thf(func_def_16,type,
sF3: ( b > $o ) > $o ).
thf(func_def_17,type,
sF4: ( a > $o ) > $o ).
thf(func_def_18,type,
sF5: ( ( a > b > $o ) > a ) > $o ).
thf(func_def_22,type,
ph9:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK10: ( b > $o ) > b ).
thf(func_def_24,type,
sK11: ( a > $o ) > a ).
thf(func_def_25,type,
sK12: ( ( a > b > $o ) > $o ) > a > b > $o ).
thf(func_def_26,type,
sK13: ( ( ( a > b > $o ) > a ) > $o ) > ( a > b > $o ) > a ).
thf(func_def_27,type,
sK14: ( ( ( a > b > $o ) > b ) > $o ) > ( a > b > $o ) > b ).
thf(func_def_29,type,
sK15: ( ( a > b > $o ) > b > a > a ) > ( ( a > b > $o ) > b > a > a ) > a > b > $o ).
thf(func_def_30,type,
sK16: ( ( a > b > $o ) > a > b ) > ( ( a > b > $o ) > a > b ) > a ).
thf(func_def_31,type,
sK17: ( ( a > b > $o ) > a > b ) > ( ( a > b > $o ) > a > b ) > a > b > $o ).
thf(func_def_34,type,
sK18: ( ( a > b > $o ) > a > b > a > a ) > ( ( a > b > $o ) > a > b > a > a ) > b ).
thf(func_def_35,type,
sK19: ( ( a > b > $o ) > a > b > a > a ) > a ).
thf(f272,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f38,f41,f271]) ).
thf(f271,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f270]) ).
thf(f270,plain,
( $false
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f269]) ).
thf(f269,plain,
( ( ( ^ [Y0: a > b > $o,Y1: a,Y2: b,Y3: a] : ( Y0 @ Y3 @ Y2 ) )
!= ( ^ [Y0: a > b > $o,Y1: a,Y2: b,Y3: a] : ( Y0 @ Y3 @ Y2 ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ( ( ^ [Y0: a > b > $o,Y1: a,Y2: b,Y3: a] :
( Y0
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b,Y7: a] : Y7
@ Y0
@ Y1
@ Y2
@ Y3 )
@ Y2 ) )
!= ( ^ [Y0: a > b > $o,Y1: a,Y2: b,Y3: a] : ( Y0 @ Y3 @ Y2 ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y6
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f267]) ).
thf(f267,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: a,Y1: b,Y2: a] : X0 )
!= ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y6 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o,Y1: a,Y2: b,Y3: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) )
!= ( ^ [Y0: a > b > $o,Y1: a,Y2: b,Y3: a] : ( Y0 @ Y3 @ Y2 ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f266]) ).
thf(f266,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: a,Y1: b,Y2: a] : X0 )
!= ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y6 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ Y4 @ Y3 )
@ ( sK19 @ X0 ) )
!= ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 )
@ ( sK19 @ X0 ) ) ) )
| ~ spl8_1 ),
inference(negative_extensionality,[status(thm)],[f265]) ).
thf(f265,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ Y4 @ Y3 ) )
!= ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ Y4 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ Y6 @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X0 )
!= ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y6 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f264]) ).
thf(f264,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a] :
( ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y6
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y10
@ Y3
@ Y4
@ Y5
@ Y6 )
@ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] :
( Y1
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y8
@ Y1
@ Y2
@ Y3
@ Y4 )
@ Y3 ) )
!= ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X0 )
!= ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y6 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f263]) ).
thf(f263,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a,X1: ( a > b > $o ) > a > b > a > a] :
( ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) )
!= ( ^ [Y0: a,Y1: a > b > $o,Y2: a,Y3: b,Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f262]) ).
thf(f262,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a,X1: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 )
@ ( sK18 @ X1 @ X0 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 )
@ ( sK18 @ X1 @ X0 ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) ) )
| ~ spl8_1 ),
inference(negative_extensionality,[status(thm)],[f261]) ).
thf(f261,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a,X1: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f260]) ).
thf(f260,plain,
( ! [X0: ( a > b > $o ) > a > b > a > a,X1: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] :
( Y2 @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: a > b > $o,Y7: a,Y8: b,Y9: a] : Y8
@ Y2
@ Y3
@ Y4
@ Y5 ) ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y7
@ Y1
@ Y2
@ Y3
@ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y7
@ Y1
@ Y2
@ Y3
@ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y5
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f259]) ).
thf(f259,plain,
( ! [X2: ( a > b > $o ) > a > b > a > b,X0: ( a > b > $o ) > a > b > a > a,X1: ( a > b > $o ) > a > b > a > a] :
( ( ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y5 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X2 ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X2 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X2 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ ( X2
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y5 ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X2 @ Y2 @ Y3 @ Y4 @ Y5 ) ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f258]) ).
thf(f258,plain,
( ! [X2: ( a > b > $o ) > a > b > a > b,X0: ( a > b > $o ) > a > b > a > a,X1: ( a > b > $o ) > a > b > a > a] :
( ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y7
@ Y1
@ Y2
@ Y3
@ Y4 ) ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X2 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ ( X2
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] :
( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : Y7
@ Y1
@ Y2
@ Y3
@ Y4 ) ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X2 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y5
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] :
( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b,Y10: a] : Y9
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : Y5 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X2 ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X2 @ Y2 @ Y3 @ Y4 @ Y5 ) ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] :
( Y2 @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: a > b > $o,Y7: a,Y8: b,Y9: a] : Y8
@ Y2
@ Y3
@ Y4
@ Y5 ) ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] :
( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 )
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b,Y7: a] : Y6
@ Y0
@ Y1
@ Y2
@ Y3 ) ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f257]) ).
thf(f257,plain,
( ! [X2: ( a > b > $o ) > a > b > a > a,X3: ( a > b > $o ) > a > b > a > a,X0: ( a > b > $o ) > a > b > a > b,X1: ( a > b > $o ) > a > b > a > b] :
( ( ( ^ [Y0: a,Y1: b,Y2: a] : Y1 )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X3 @ Y0 @ Y1 @ Y2 @ Y3 ) @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X3 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X2 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ( X3
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ ( X1
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X3 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X1 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y1 @ ( X2 @ Y1 @ Y2 @ Y3 @ Y4 ) @ ( X0 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ( X2
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
@ ( X0
@ ( sK17
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
@ ^ [Y3: a > b > $o,Y4: a] :
( sK10
@ ^ [Y5: b] :
( sF4
@ ^ [Y6: a] : ( Y3 @ ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) ) ) ) ) ) )
| ( ( X3
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y0 @ ( X3 @ Y0 @ Y1 @ Y2 @ Y3 ) @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X3 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X1 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X0 ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] : X2 )
!= ( ^ [Y0: a,Y1: b,Y2: a] : X3 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X2: ( a > b > $o ) > a > b > a > a,X3: ( a > b > $o ) > a > b > a > a,X0: ( a > b > $o ) > a > b > a > b,X1: ( a > b > $o ) > a > b > a > b] :
( ( ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : ( X1 @ Y3 @ Y4 @ Y5 @ Y6 ) )
!= ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : ( X0 @ Y3 @ Y4 @ Y5 @ Y6 ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] :
( X3
@ ( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] :
( Y3 @ Y4
@ ( sK10
@ ^ [Y5: b] :
( sF4
@ ( ^ [Y6: a > b > $o,Y7: a,Y8: b,Y9: a] : ( Y6 @ ( X3 @ Y6 @ Y7 @ Y8 @ Y9 ) @ ( X1 @ Y6 @ Y7 @ Y8 @ Y9 ) )
@ Y3
@ Y4
@ Y5 ) ) ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y2 ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X3 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b,Y7: a] : ( Y4 @ ( X3 @ Y4 @ Y5 @ Y6 @ Y7 ) @ ( X1 @ Y4 @ Y5 @ Y6 @ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b,Y7: a] : ( Y4 @ ( X2 @ Y4 @ Y5 @ Y6 @ Y7 ) @ ( X0 @ Y4 @ Y5 @ Y6 @ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( ^ [Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X3 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X1 @ Y2 @ Y3 @ Y4 @ Y5 ) )
@ ( sK17
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] :
( sF4
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : ( Y5 @ ( X3 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X1 @ Y5 @ Y6 @ Y7 @ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) )
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] :
( sF4
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : ( Y5 @ ( X2 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X0 @ Y5 @ Y6 @ Y7 @ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b,Y7: a] : ( Y4 @ ( X3 @ Y4 @ Y5 @ Y6 @ Y7 ) @ ( X1 @ Y4 @ Y5 @ Y6 @ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b,Y7: a] : ( Y4 @ ( X2 @ Y4 @ Y5 @ Y6 @ Y7 ) @ ( X0 @ Y4 @ Y5 @ Y6 @ Y7 ) )
@ Y1
@ Y2
@ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( ^ [Y2: a > b > $o,Y3: a,Y4: b,Y5: a] : ( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 @ Y5 ) @ ( X0 @ Y2 @ Y3 @ Y4 @ Y5 ) )
@ ( sK17
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] :
( sF4
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : ( Y5 @ ( X3 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X1 @ Y5 @ Y6 @ Y7 @ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) )
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] :
( sF4
@ ( ^ [Y5: a > b > $o,Y6: a,Y7: b,Y8: a] : ( Y5 @ ( X2 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X0 @ Y5 @ Y6 @ Y7 @ Y8 ) )
@ Y2
@ Y3
@ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] :
( X1
@ ( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] :
( Y3 @ Y4
@ ( sK10
@ ^ [Y5: b] :
( sF4
@ ( ^ [Y6: a > b > $o,Y7: a,Y8: b,Y9: a] : ( Y6 @ ( X3 @ Y6 @ Y7 @ Y8 @ Y9 ) @ ( X1 @ Y6 @ Y7 @ Y8 @ Y9 ) )
@ Y3
@ Y4
@ Y5 ) ) ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
@ Y0
@ Y1
@ Y2 ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] : Y1 ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : ( X2 @ Y3 @ Y4 @ Y5 @ Y6 ) )
!= ( ^ [Y0: a,Y1: b,Y2: a,Y3: a > b > $o,Y4: a,Y5: b,Y6: a] : ( X3 @ Y3 @ Y4 @ Y5 @ Y6 ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f255]) ).
thf(f255,plain,
( ! [X0: ( a > b > $o ) > a > b > a > $o,X1: ( a > b > $o ) > a > b > a > $o] :
( ( ( ^ [Y0: a,Y1: b,Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] :
( Y3 @ Y4
@ ( sK10
@ ^ [Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) ) ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] : ( sF4 @ ( X1 @ Y0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( X0
@ ( sK17
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( X1
@ ( sK17
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f254]) ).
thf(f254,plain,
( ! [X0: ( a > b > $o ) > a > b > a > $o,X1: ( a > b > $o ) > a > b > a > $o] :
( ( ( ^ [Y0: a,Y1: b,Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] :
( Y3 @ Y4
@ ( ^ [Y5: a > b > $o,Y6: a] :
( sK10
@ ( ^ [Y7: a > b > $o,Y8: a,Y9: b] : ( sF4 @ ( X0 @ Y7 @ Y8 @ Y9 ) )
@ Y5
@ Y6 ) )
@ Y3
@ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] : ( sF4 @ ( X1 @ Y0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( X1
@ ( sK17
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X1 @ Y2 @ Y3 @ Y4 ) ) )
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b] : ( sF4 @ ( X0 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0
@ ( ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X1 @ Y1 @ Y2 @ Y3 ) ) )
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) ) )
@ Y0 ) ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b] : ( X0 @ Y2 @ Y3 @ Y4 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a,Y4: b] : ( X1 @ Y2 @ Y3 @ Y4 ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f253]) ).
thf(f253,plain,
( ! [X0: ( a > b > $o ) > a > b > a > $o,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ X1
@ Y0
@ ( X1
@ ( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ X1 )
@ Y0 ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ^ [Y3: b] : ( sF4 @ ( X0 @ Y1 @ Y2 @ Y3 ) ) )
@ X1
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( X0
@ ( sK17
@ ^ [Y2: a > b > $o,Y3: a] :
( sK10
@ ^ [Y4: b] : ( sF4 @ ( X0 @ Y2 @ Y3 @ Y4 ) ) )
@ X1 )
@ Y0
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: b,Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) )
!= ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0 @ Y1
@ ( sK10
@ ^ [Y2: b] : ( sF4 @ ( X0 @ Y0 @ Y1 @ Y2 ) ) ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
( ! [X0: ( a > b > $o ) > a > b > a > $o,X1: ( a > b > $o ) > a > b] :
( ( ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ X1
@ Y0
@ ( X1
@ ( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ X1 )
@ Y0 ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ X1
@ Y0
@ ( ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ ( sK17
@ ^ [Y1: a > b > $o,Y2: a] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: a,Y5: b] : ( sF4 @ ( X0 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ X1 )
@ Y0 ) ) ) )
| ( ( ^ [Y0: a,Y1: b] :
( X0
@ ( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2
@ ( sK11
@ ^ [Y3: a] :
( Y2 @ Y3
@ ( ^ [Y4: a > b > $o,Y5: a] :
( sK10
@ ( ^ [Y6: a > b > $o,Y7: a,Y8: b] : ( sF4 @ ( X0 @ Y6 @ Y7 @ Y8 ) )
@ Y4
@ Y5 ) )
@ Y2
@ Y3 ) ) )
@ ( sK10
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0
@ Y1 ) )
!= ( ^ [Y0: a,Y1: b,Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] :
( sK10
@ ( ^ [Y4: a > b > $o,Y5: a,Y6: b] : ( sF4 @ ( X0 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) ) )
!= ( ^ [Y0: b,Y1: a] : X1 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f251]) ).
thf(f251,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( sK11
@ ^ [Y0: a] : ( sK17 @ X1 @ X0 @ Y0 @ ( X0 @ ( sK17 @ X1 @ X0 ) @ Y0 ) ) )
!= ( sK11
@ ^ [Y0: a] : ( sK17 @ X1 @ X0 @ Y0 @ ( X1 @ ( sK17 @ X1 @ X0 ) @ Y0 ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK17 @ X1 @ X0 ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK17 @ X1 @ X0 ) ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(negative_extensionality,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(duplicate_literal_removal,[status(thm)],[f248]) ).
thf(f248,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f247]) ).
thf(f247,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) )
@ ( sK16 @ X1 @ X0 ) )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) )
@ ( sK16 @ X1 @ X0 ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ~ spl8_1 ),
inference(negative_extensionality,[status(thm)],[f246]) ).
thf(f246,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ Y4 @ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f245]) ).
thf(f245,plain,
( ! [X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] :
( Y1
@ ( ^ [Y3: a > b > $o,Y4: a] : Y4
@ Y1
@ Y2 )
@ ( X0 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] :
( Y3
@ ( ^ [Y5: a > b > $o,Y6: a] : Y6
@ Y3
@ Y4 )
@ ( X0 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] :
( Y0
@ ( ^ [Y2: a > b > $o,Y3: a] : Y3
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f238]) ).
thf(f238,plain,
( ! [X2: ( a > b > $o ) > a > a,X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] : Y3 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ ( X2 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( sK11
@ ^ [Y4: a] : ( Y3 @ ( X2 @ Y3 @ Y4 ) @ ( X1 @ Y3 @ Y4 ) ) )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ ( X2 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f237]) ).
thf(f237,plain,
( ! [X2: ( a > b > $o ) > a > a,X0: ( a > b > $o ) > a > b,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] : ( X0 @ Y2 @ Y3 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] : ( X1 @ Y2 @ Y3 ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ( ^ [Y1: a > b > $o,Y2: a] : ( Y1 @ ( X2 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) )
@ Y0 ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3
@ ( ^ [Y4: a > b > $o] :
( sK11
@ ( ^ [Y5: a > b > $o,Y6: a] : ( Y5 @ ( X2 @ Y5 @ Y6 ) @ ( X1 @ Y5 @ Y6 ) )
@ Y4 ) )
@ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X0 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ( ^ [Y2: a > b > $o,Y3: a] : ( Y2 @ ( X2 @ Y2 @ Y3 ) @ ( X1 @ Y2 @ Y3 ) )
@ Y1 ) ) )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X0 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] : ( X2 @ Y2 @ Y3 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: a] : Y3 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f236]) ).
thf(f236,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o] :
( sK11
@ ^ [Y3: a] : ( Y2 @ Y3 @ ( X1 @ Y2 @ Y3 ) ) ) )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ Y1 @ ( X1 @ Y0 @ Y1 ) ) ) )
!= X0 )
| ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ Y2 @ ( X1 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f235]) ).
thf(f235,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] :
( Y1
@ ( ^ [Y3: a > b > $o,Y4: a] : Y4
@ Y1
@ Y2 )
@ ( X1 @ Y1 @ Y2 ) ) ) )
!= ( ^ [Y0: a] : X0 ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o] :
( sK11
@ ^ [Y3: a] :
( Y2
@ ( ^ [Y4: a > b > $o,Y5: a] : Y5
@ Y2
@ Y3 )
@ ( X1 @ Y2 @ Y3 ) ) ) )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] :
( Y0
@ ( ^ [Y2: a > b > $o,Y3: a] : Y3
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) ) )
!= X0 )
| ( ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] :
( Y0
@ ( ^ [Y2: a > b > $o,Y3: a] : Y3
@ Y0
@ Y1 )
@ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f234]) ).
thf(f234,plain,
( ! [X2: ( a > b > $o ) > a,X0: ( a > b > $o ) > a > a,X1: ( a > b > $o ) > a > b] :
( ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] : Y0 ) )
| ( ( ^ [Y0: a] : X2 )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ^ [Y2: a] : ( Y1 @ ( X0 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o] :
( sK11
@ ^ [Y3: a] : ( Y2 @ ( X0 @ Y2 @ Y3 ) @ ( X1 @ Y2 @ Y3 ) ) ) ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0
@ ( sK11
@ ^ [Y1: a] : ( Y0 @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ^ [Y1: a] : ( Y0 @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) )
!= X2 ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f233]) ).
thf(f233,plain,
( ! [X2: ( a > b > $o ) > a,X0: ( a > b > $o ) > a > a,X1: ( a > b > $o ) > a > b] :
( ( ( ^ [Y0: a] : Y0 )
!= ( ^ [Y0: a] :
( X0
@ ( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1
@ ( ^ [Y2: a > b > $o] :
( sK11
@ ( ^ [Y3: a > b > $o,Y4: a] : ( Y3 @ ( X0 @ Y3 @ Y4 ) @ ( X1 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 ) ) )
| ( ( ^ [Y0: a] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) )
!= ( ^ [Y0: a] :
( X1
@ ( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1
@ ( ^ [Y2: a > b > $o] :
( sK11
@ ( ^ [Y3: a > b > $o,Y4: a] : ( Y3 @ ( X0 @ Y3 @ Y4 ) @ ( X1 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
@ Y0 ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o] :
( sK11
@ ( ^ [Y3: a > b > $o,Y4: a] : ( Y3 @ ( X0 @ Y3 @ Y4 ) @ ( X1 @ Y3 @ Y4 ) )
@ Y2 ) ) )
!= ( ^ [Y0: b,Y1: a] : X2 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK11
@ ( ^ [Y1: a > b > $o,Y2: a] : ( Y1 @ ( X0 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) )
@ Y0 ) ) )
!= X2 )
| ( ( ^ [Y0: a,Y1: a > b > $o] : ( X2 @ Y1 ) )
!= ( ^ [Y0: a,Y1: a > b > $o] :
( sK11
@ ( ^ [Y2: a > b > $o,Y3: a] : ( Y2 @ ( X0 @ Y2 @ Y3 ) @ ( X1 @ Y2 @ Y3 ) )
@ Y1 ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f232]) ).
thf(f232,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a] :
( ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X1 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( X0 != X1 ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f231]) ).
thf(f231,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a] :
( ( ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ Y1
@ Y0 ) ) )
!= ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ Y1
@ Y0 ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X1 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( X0 != X1 ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f230]) ).
thf(f230,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a] :
( ( ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ Y1
@ Y0 ) ) )
!= ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ( ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ( sK15
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4 )
@ Y0
@ Y1 )
@ Y0 ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] :
( Y1
@ ( ^ [Y4: a > b > $o,Y5: b,Y6: a] : Y6
@ Y1
@ Y2
@ Y3 )
@ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X1 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] :
( Y3
@ ( ^ [Y6: a > b > $o,Y7: b,Y8: a] : Y8
@ Y3
@ Y4
@ Y5 )
@ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( X0 != X1 ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f229]) ).
thf(f229,plain,
( ! [X2: ( a > b > $o ) > a,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b > a > a] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : Y4 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X2 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ Y1
@ Y0 ) ) )
!= ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ( X1
@ ( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4 )
@ Y0
@ Y1 )
@ Y0 ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X0 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f228]) ).
thf(f228,plain,
( ! [X2: ( a > b > $o ) > a,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b > a > a] :
( ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X2 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( Y0
@ ( ^ [Y3: a > b > $o,Y4: b,Y5: a] : Y5
@ Y0
@ Y1
@ Y2 )
@ Y1 ) ) ) ) ) ) ) )
| ( X0 != X2 )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ( ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4 )
@ Y0
@ Y1 )
@ Y0 ) ) )
!= ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4
@ ( X1
@ ( sK15 @ X1
@ ^ [Y2: a > b > $o,Y3: b,Y4: a] : Y4 )
@ Y0
@ Y1 )
@ Y0 ) ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : Y4 )
!= ( ^ [Y0: b,Y1: a] : X1 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f227]) ).
thf(f227,plain,
( ! [X2: ( a > b > $o ) > a,X3: ( a > b > $o ) > b > a > a,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > a] :
( ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X2 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X3 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
| ( ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] : ( sK15 @ X3 @ X0 @ ( X0 @ ( sK15 @ X3 @ X0 ) @ Y0 @ Y1 ) @ Y0 ) ) )
!= ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] : ( sK15 @ X3 @ X0 @ ( X3 @ ( sK15 @ X3 @ X0 ) @ Y0 @ Y1 ) @ Y0 ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( ( ^ [Y0: b,Y1: a] : X3 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( X1 != X2 ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f226]) ).
thf(f226,plain,
( ! [X2: ( a > b > $o ) > a,X3: ( a > b > $o ) > b > a > a,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > a] :
( ( X1 != X2 )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( ^ [Y0: b,Y1: a] : X3 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X3 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) )
@ ( sK15 @ X3 @ X0 ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) )
@ ( sK15 @ X3 @ X0 ) ) )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X2 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X3 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(negative_extensionality,[status(thm)],[f225]) ).
thf(f225,plain,
( ! [X2: ( a > b > $o ) > a,X3: ( a > b > $o ) > b > a > a,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > a] :
( ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X3 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X2 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X3 @ Y1 @ Y2 @ Y3 ) @ Y2 ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 ) @ Y4 ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( ( ^ [Y0: b,Y1: a] : X3 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( X1 != X2 ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f224]) ).
thf(f224,plain,
( ! [X2: ( a > b > $o ) > a,X3: ( a > b > $o ) > b > a > a,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > a] :
( ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X2 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] :
( Y1 @ ( X3 @ Y1 @ Y2 @ Y3 )
@ ( ^ [Y4: a > b > $o,Y5: b,Y6: a] : Y5
@ Y1
@ Y2
@ Y3 ) ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X2 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] :
( Y3 @ ( X3 @ Y3 @ Y4 @ Y5 )
@ ( ^ [Y6: a > b > $o,Y7: b,Y8: a] : Y7
@ Y3
@ Y4
@ Y5 ) ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( Y0 @ ( X3 @ Y0 @ Y1 @ Y2 )
@ ( ^ [Y3: a > b > $o,Y4: b,Y5: a] : Y4
@ Y0
@ Y1
@ Y2 ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( ^ [Y0: b,Y1: a] : X3 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( X1 != X2 ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f223]) ).
thf(f223,plain,
( ! [X2: ( a > b > $o ) > b > a > a,X3: ( a > b > $o ) > a,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > b > a > b,X4: ( a > b > $o ) > a] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : Y3 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X3 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X4 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 ) @ ( X1 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X4 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 ) @ ( X1 @ Y3 @ Y4 @ Y5 ) ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X3
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X3 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ Y1 ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X1 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
| ( X3 != X4 )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( ^ [Y0: b,Y1: a] : X4 )
!= ( ^ [Y0: b,Y1: a] : X3 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f222]) ).
thf(f222,plain,
( ! [X2: ( a > b > $o ) > b > a > a,X3: ( a > b > $o ) > a,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > b > a > b,X4: ( a > b > $o ) > a] :
( ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X4 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X0 @ Y1 @ Y2 @ Y3 ) @ ( X1 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X4 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X0 @ Y3 @ Y4 @ Y5 ) @ ( X1 @ Y3 @ Y4 @ Y5 ) ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X3
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X3 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 )
@ ( ^ [Y3: a > b > $o,Y4: b,Y5: a] : Y4
@ Y0
@ Y1
@ Y2 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : Y3 )
!= ( ^ [Y0: b,Y1: a] : X1 ) )
| ( X3 != X4 )
| ( ( ^ [Y0: b,Y1: a] : X4 )
!= ( ^ [Y0: b,Y1: a] : X3 ) )
| ( ( ^ [Y0: b,Y1: a] : X2 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X3 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 )
@ ( ^ [Y3: a > b > $o,Y4: b,Y5: a] : Y4
@ Y0
@ Y1
@ Y2 ) ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 )
@ ( ^ [Y3: a > b > $o,Y4: b,Y5: a] : Y4
@ Y0
@ Y1
@ Y2 ) ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X1 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f221]) ).
thf(f221,plain,
( ! [X2: ( a > b > $o ) > b > a > b,X3: ( a > b > $o ) > b > a > b,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > b > a > a,X4: ( a > b > $o ) > a,X5: ( a > b > $o ) > a] :
( ( ( ^ [Y0: b,Y1: a] : Y0 )
!= ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X4 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X1 @ Y0 @ Y1 @ Y2 ) @ ( X3 @ Y0 @ Y1 @ Y2 ) ) ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X4 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( X4
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X4 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X5 @ Y1 )
@ ( sK10
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ ( X1 @ Y1 @ Y2 @ Y3 ) @ ( X3 @ Y1 @ Y2 @ Y3 ) ) ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X5 @ Y3 )
@ ( sK10
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 ) @ ( X3 @ Y3 @ Y4 @ Y5 ) ) ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( X4 != X5 )
| ( ( ^ [Y0: b,Y1: a] : X3 )
!= ( ^ [Y0: b,Y1: a] : X2 ) )
| ( ( ^ [Y0: b,Y1: a] : X5 )
!= ( ^ [Y0: b,Y1: a] : X4 ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f220]) ).
thf(f220,plain,
( ! [X2: ( a > b > $o ) > b > a > b,X3: ( a > b > $o ) > b > a > b,X0: ( a > b > $o ) > b > a > a,X1: ( a > b > $o ) > b > a > a,X4: ( a > b > $o ) > a,X5: ( a > b > $o ) > a] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : ( X1 @ Y2 @ Y3 @ Y4 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : ( X0 @ Y2 @ Y3 @ Y4 ) ) )
| ( X4 != X5 )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : ( X3 @ Y2 @ Y3 @ Y4 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b,Y4: a] : ( X2 @ Y2 @ Y3 @ Y4 ) ) )
| ( ( ^ [Y0: b,Y1: a] : X5 )
!= ( ^ [Y0: b,Y1: a] : X4 ) )
| ( ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X4 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
!= ( ^ [Y0: b,Y1: a] : Y1 ) )
| ( ( ^ [Y0: b,Y1: a] : Y0 )
!= ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X4 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( X4
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X4 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X5 @ Y1 )
@ ( sK10
@ ( ^ [Y2: a > b > $o,Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: b,Y6: a] : ( Y4 @ ( X1 @ Y4 @ Y5 @ Y6 ) @ ( X3 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) )
@ Y1 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X5 @ Y3 )
@ ( sK10
@ ( ^ [Y4: a > b > $o,Y5: b] :
( sF4
@ ( ^ [Y6: a > b > $o,Y7: b,Y8: a] : ( Y6 @ ( X1 @ Y6 @ Y7 @ Y8 ) @ ( X3 @ Y6 @ Y7 @ Y8 ) )
@ Y4
@ Y5 ) )
@ Y3 ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ( ^ [Y1: a > b > $o,Y2: b] :
( sF4
@ ( ^ [Y3: a > b > $o,Y4: b,Y5: a] : ( Y3 @ ( X1 @ Y3 @ Y4 @ Y5 ) @ ( X3 @ Y3 @ Y4 @ Y5 ) )
@ Y1
@ Y2 ) )
@ Y0 ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) @ ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f219]) ).
thf(f219,plain,
( ! [X2: ( a > b > $o ) > b > a > a,X3: ( a > b > $o ) > b > a > b,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a,X4: ( a > b > $o ) > b > $o] :
( ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 ) @ ( X3 @ Y2 @ Y3 @ Y4 ) ) ) )
!= ( ^ [Y0: b,Y1: a] : X4 ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ ( X3 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( sK10 @ ( X4 @ Y1 ) ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( sK10 @ ( X4 @ Y3 ) ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : Y0 )
!= ( X3
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ ( X3 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] : ( sK10 @ ( X4 @ Y0 ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ ( X3 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : Y1 )
!= ( X2
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ ( X2 @ Y0 @ Y1 @ Y2 ) @ ( X3 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a] : X1 )
!= ( ^ [Y0: b,Y1: a] : X0 ) )
| ( X0 != X1 ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X2: ( a > b > $o ) > b > a > a,X3: ( a > b > $o ) > b > a > b,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a,X4: ( a > b > $o ) > b > $o] :
( ( ( ^ [Y0: b,Y1: a] : Y0 )
!= ( ^ [Y0: b,Y1: a] :
( X3
@ ( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X1 @ Y2 )
@ ( sK10
@ ^ [Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: b,Y6: a] : ( Y4 @ ( X2 @ Y4 @ Y5 @ Y6 ) @ ( X3 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) ) ) ) ) )
@ Y0
@ Y1 ) ) )
| ( X0 != X1 )
| ( ( ^ [Y0: b,Y1: a] : Y1 )
!= ( ^ [Y0: b,Y1: a] :
( X2
@ ( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X1 @ Y2 )
@ ( sK10
@ ^ [Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: b,Y6: a] : ( Y4 @ ( X2 @ Y4 @ Y5 @ Y6 ) @ ( X3 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) ) ) ) ) )
@ Y0
@ Y1 ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o,Y3: b] :
( sF4
@ ( ^ [Y4: a > b > $o,Y5: b,Y6: a] : ( Y4 @ ( X2 @ Y4 @ Y5 @ Y6 ) @ ( X3 @ Y4 @ Y5 @ Y6 ) )
@ Y2
@ Y3 ) ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o] : ( X4 @ Y2 ) ) )
| ( ( ^ [Y0: a > b > $o] : ( sK10 @ ( X4 @ Y0 ) ) )
!= ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] :
( sF4
@ ( ^ [Y2: a > b > $o,Y3: b,Y4: a] : ( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 ) @ ( X3 @ Y2 @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ) )
| ( ( ^ [Y0: b,Y1: a,Y2: a > b > $o] : ( X1 @ Y2 ) )
!= ( ^ [Y0: b,Y1: a,Y2: a > b > $o] : ( X0 @ Y2 ) ) )
| ( ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 )
@ ( ^ [Y2: a > b > $o] : ( sK10 @ ( X4 @ Y2 ) )
@ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 )
@ ( ^ [Y4: a > b > $o] : ( sK10 @ ( X4 @ Y4 ) )
@ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) )
!= ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ( ^ [Y2: a > b > $o,Y3: b,Y4: a] : ( Y2 @ ( X2 @ Y2 @ Y3 @ Y4 ) @ ( X3 @ Y2 @ Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f215]) ).
thf(f215,plain,
( ! [X2: ( a > b > $o ) > b,X3: ( a > b > $o ) > b > a > $o,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a] :
( ( ( ^ [Y0: b,Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X2 @ Y2 ) ) )
@ Y1
@ Y0 ) )
!= ( X3
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] : ( sF4 @ ( X3 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( sK10
@ ^ [Y1: b] : ( sF4 @ ( X3 @ Y0 @ Y1 ) ) ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X2 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X2 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ^ [Y1: b] : ( sF4 @ ( X3 @ Y0 @ Y1 ) ) ) )
!= X2 )
| ( X0 != X1 ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f214]) ).
thf(f214,plain,
( ! [X2: ( a > b > $o ) > b,X3: ( a > b > $o ) > b > a > $o,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a] :
( ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( ^ [Y1: a > b > $o] :
( sK10
@ ( ^ [Y2: a > b > $o,Y3: b] : ( sF4 @ ( X3 @ Y2 @ Y3 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X2 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X2 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] : ( X1 @ Y0 ) )
!= ( ^ [Y0: a > b > $o] : ( X0 @ Y0 ) ) )
| ( ( ^ [Y0: b] :
( X3
@ ( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( ^ [Y2: a > b > $o] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: b] : ( sF4 @ ( X3 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 ) ) ) )
@ Y0 ) )
!= ( ^ [Y0: b,Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X2 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ( ^ [Y1: a > b > $o,Y2: b] : ( sF4 @ ( X3 @ Y1 @ Y2 ) )
@ Y0 ) ) )
!= ( ^ [Y0: a > b > $o] : ( X2 @ Y0 ) ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X2: ( a > b > $o ) > b,X3: ( a > b > $o ) > b > a > $o,X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > a] :
( ( ( ^ [Y0: a > b > $o] : ( X1 @ Y0 ) )
!= ( ^ [Y0: a > b > $o] : ( X0 @ Y0 ) ) )
| ( ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X1 @ Y0 )
@ ( ^ [Y1: a > b > $o] :
( sK10
@ ( ^ [Y2: a > b > $o,Y3: b] : ( sF4 @ ( X3 @ Y2 @ Y3 ) )
@ Y1 ) )
@ Y0 ) ) ) ) )
!= ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X2 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X2 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: a > b > $o] :
( sK10
@ ( ^ [Y1: a > b > $o,Y2: b] : ( sF4 @ ( X3 @ Y1 @ Y2 ) )
@ Y0 ) ) )
!= ( ^ [Y0: a > b > $o] : ( X2 @ Y0 ) ) )
| ( ( ^ [Y0: b] :
( X3
@ ( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 )
@ ( ^ [Y2: a > b > $o] :
( sK10
@ ( ^ [Y3: a > b > $o,Y4: b] : ( sF4 @ ( X3 @ Y3 @ Y4 ) )
@ Y2 ) )
@ Y1 ) ) ) )
@ Y0 ) )
!= ( ^ [Y0: b,Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X2 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
| ( $true = $false ) )
| ~ spl8_1 ),
inference(constrained_superposition,[status(thm)],[f209,f170]) ).
thf(f170,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f169]) ).
thf(f169,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) )
= $false )
| ( $true = $false ) )
| ~ spl8_1 ),
inference(boolean_simplification,[status(thm)],[f161]) ).
thf(f161,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( ( ( sF3
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
=> $true )
= $false )
| ( ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) )
= $false ) )
| ~ spl8_1 ),
inference(cases_simplifying,[status(thm)],[f158]) ).
thf(f158,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $false
= ( ( sF3
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) )
=> ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f157]) ).
thf(f157,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( ( ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ( $true = $false ) )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f105,f141]) ).
thf(f141,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $false
= ( sF2
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $false
= ( ^ [Y0: ( a > b > $o ) > b] :
( sF2
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( Y0 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( $true = $false )
| ( $false
= ( ^ [Y0: ( a > b > $o ) > b] :
( sF2
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( Y0 @ Y1 ) ) ) )
@ X1 ) ) )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f134,f133]) ).
thf(f133,plain,
( ! [X1: ( a > b > $o ) > a] :
( ( sF1
@ ^ [Y0: ( a > b > $o ) > b] :
( sF2
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 ) @ ( Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl8_1 ),
inference(backward_demodulation,[status(thm)],[f50,f124]) ).
thf(f124,plain,
( ! [X0: ( a > b > $o ) > a] :
( ( sF5 @ X0 )
= $false )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ! [X0: ( a > b > $o ) > a] :
( ( $true = $false )
| ( ( sF5 @ X0 )
= $false ) )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f45,f117]) ).
thf(f117,plain,
! [X2: ( a > b > $o ) > a,X1: ( ( a > b > $o ) > a ) > $o] :
( ( $true
= ( sF0 @ X1 ) )
| ( $false
= ( X1 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: ( ( a > b > $o ) > a ) > $o] :
( ( $false
= ( ?? @ ( ( a > b > $o ) > a ) @ X1 ) )
| ( $true
= ( sF0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: ( ( a > b > $o ) > a ) > $o] :
( ( sF0 @ X1 )
= ( ?? @ ( ( a > b > $o ) > a ) @ X1 ) ),
inference(argument_congruence,[status(thm)],[f7]) ).
thf(f7,definition,
( ??
@ ( ( ( a > b > $o ) > a )
= sF0 ) ),
introduced(definition,[],[function_definition]) ).
thf(f45,plain,
( ( $false
= ( sF0 @ sF5 ) )
| ~ spl8_1 ),
inference(forward_demodulation,[status(thm)],[f13,f23]) ).
thf(f23,plain,
( ( sF6 = $false )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl8_1
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f13,definition,
( sF6
= ( sF0 @ sF5 ) ),
introduced(definition,[],[function_definition]) ).
thf(f50,plain,
! [X1: ( a > b > $o ) > a] :
( ( sF1
@ ^ [Y0: ( a > b > $o ) > b] :
( sF2
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X1 @ Y1 ) @ ( Y0 @ Y1 ) ) ) ) )
= ( sF5 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: ( a > b > $o ) > a] :
( ( sF5 @ X1 )
= ( ^ [Y0: ( a > b > $o ) > a] :
( sF1
@ ^ [Y1: ( a > b > $o ) > b] :
( sF2
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,definition,
( ( ^ [Y0: ( a > b > $o ) > a] :
( sF1
@ ^ [Y1: ( a > b > $o ) > b] :
( sF2
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= sF5 ),
introduced(definition,[],[function_definition]) ).
thf(f134,plain,
! [X2: ( a > b > $o ) > b,X1: ( ( a > b > $o ) > b ) > $o] :
( ( $true
= ( sF1 @ X1 ) )
| ( $false
= ( X1 @ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: ( ( a > b > $o ) > b ) > $o] :
( ( $false
= ( ?? @ ( ( a > b > $o ) > b ) @ X1 ) )
| ( $true
= ( sF1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: ( ( a > b > $o ) > b ) > $o] :
( ( sF1 @ X1 )
= ( ?? @ ( ( a > b > $o ) > b ) @ X1 ) ),
inference(argument_congruence,[status(thm)],[f8]) ).
thf(f8,definition,
( ??
@ ( ( ( a > b > $o ) > b )
= sF1 ) ),
introduced(definition,[],[function_definition]) ).
thf(f105,plain,
! [X1: ( a > b > $o ) > $o] :
( ( ( sF2 @ X1 )
= $true )
| ( ( X1 @ ( sK12 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: ( a > b > $o ) > $o] :
( ( $false
= ( !! @ ( a > b > $o ) @ X1 ) )
| ( ( sF2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: ( a > b > $o ) > $o] :
( ( sF2 @ X1 )
= ( !! @ ( a > b > $o ) @ X1 ) ),
inference(argument_congruence,[status(thm)],[f9]) ).
thf(f9,definition,
( sF2 = !! ) @ ( a > b > $o ),
introduced(definition,[],[function_definition]) ).
thf(f209,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $true
= ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) )
@ ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f208]) ).
thf(f208,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $true
= ( ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) )
@ ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f206]) ).
thf(f206,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( $true
= ( ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) )
@ ( sK11
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) ) )
| ( $true = $false ) )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f197,f77]) ).
thf(f77,plain,
! [X1: a > $o] :
( ( $false
= ( sF4 @ X1 ) )
| ( ( X1 @ ( sK11 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: a > $o] :
( ( ( ?? @ a @ X1 )
= $true )
| ( $false
= ( sF4 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: a > $o] :
( ( ?? @ a @ X1 )
= ( sF4 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f11]) ).
thf(f11,definition,
?? @ ( a = sF4 ),
introduced(definition,[],[function_definition]) ).
thf(f197,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $true
= ( sF4
@ ^ [Y0: a] :
( sK12
@ ^ [Y1: a > b > $o] :
( ( sF3
@ ^ [Y2: b] :
( sF4
@ ^ [Y3: a] : ( Y1 @ Y3 @ Y2 ) ) )
=> ( Y1 @ ( X0 @ Y1 ) @ ( X1 @ Y1 ) ) )
@ Y0
@ ( sK10
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] :
( sK12
@ ^ [Y3: a > b > $o] :
( ( sF3
@ ^ [Y4: b] :
( sF4
@ ^ [Y5: a] : ( Y3 @ Y5 @ Y4 ) ) )
=> ( Y3 @ ( X0 @ Y3 ) @ ( X1 @ Y3 ) ) )
@ Y2
@ Y1 ) ) ) ) ) )
| ~ spl8_1 ),
inference(beta_eta_normalization,[status(thm)],[f196]) ).
thf(f196,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $true
= ( ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) )
@ ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f194]) ).
thf(f194,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( $true
= ( ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) )
@ ( sK10
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) ) )
| ( $true = $false ) )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f172,f65]) ).
thf(f65,plain,
! [X1: b > $o] :
( ( $false
= ( sF3 @ X1 ) )
| ( ( X1 @ ( sK10 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: b > $o] :
( ( $true
= ( ?? @ b @ X1 ) )
| ( $false
= ( sF3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: b > $o] :
( ( ?? @ b @ X1 )
= ( sF3 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f10]) ).
thf(f10,definition,
( sF3 = ?? ) @ b,
introduced(definition,[],[function_definition]) ).
thf(f172,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( $true
= ( sF3
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( $true = $false )
| ( $true
= ( sF3
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) ) )
| ~ spl8_1 ),
inference(boolean_simplification,[status(thm)],[f160]) ).
thf(f160,plain,
( ! [X0: ( a > b > $o ) > a,X1: ( a > b > $o ) > b] :
( ( $false
= ( $false
=> ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) )
@ ( X0
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
@ ( X1
@ ( sK12
@ ^ [Y0: a > b > $o] :
( ( sF3
@ ^ [Y1: b] :
( sF4
@ ^ [Y2: a] : ( Y0 @ Y2 @ Y1 ) ) )
=> ( Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( sF3
@ ^ [Y0: b] :
( sF4
@ ^ [Y1: a] :
( sK12
@ ^ [Y2: a > b > $o] :
( ( sF3
@ ^ [Y3: b] :
( sF4
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( X0 @ Y2 ) @ ( X1 @ Y2 ) ) )
@ Y1
@ Y0 ) ) ) ) )
| ~ spl8_1 ),
inference(cases_simplifying,[status(thm)],[f158]) ).
thf(f41,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
| ~ spl8_2
| ~ spl8_4 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_4 ),
inference(forward_demodulation,[status(thm)],[f36,f27]) ).
thf(f27,plain,
( ( sF7 = $false )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl8_2
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f36,plain,
( ( sF7 = $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl8_4
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f38,plain,
spl8_4,
inference(avatar_split_clause,[status(thm)],[f15,f34]) ).
thf(f15,plain,
sF7 = $true,
inference(definition_folding,[status(thm)],[f6,f14,f13,f12,f11,f10,f9,f8,f7]) ).
thf(f14,definition,
( ( ~ sF6 ) = sF7 ),
introduced(definition,[],[function_definition]) ).
thf(f6,plain,
( $true
= ( ~ ( ?? @ ( ( a > b > $o ) > a )
@ ^ [Y0: ( a > b > $o ) > a] :
( ?? @ ( ( a > b > $o ) > b )
@ ^ [Y1: ( a > b > $o ) > b] :
( !! @ ( a > b > $o )
@ ^ [Y2: a > b > $o] :
( ( ?? @ b
@ ^ [Y3: b] :
( ?? @ a
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( ?? @ ( ( a > b > $o ) > a )
@ ^ [Y0: ( a > b > $o ) > a] :
( ?? @ ( ( a > b > $o ) > b )
@ ^ [Y1: ( a > b > $o ) > b] :
( !! @ ( a > b > $o )
@ ^ [Y2: a > b > $o] :
( ( ?? @ b
@ ^ [Y3: b] :
( ?? @ a
@ ^ [Y4: a] : ( Y2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( a > b > $o ) > b,X1: ( a > b > $o ) > a] :
! [X2: a > b > $o] :
( ? [X3: a,X4: b] : ( X2 @ X3 @ X4 )
=> ( X2 @ ( X1 @ X2 ) @ ( X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X1: ( a > b > $o ) > b,X0: ( a > b > $o ) > a] :
! [X2: a > b > $o] :
( ? [X3: a,X4: b] : ( X2 @ X3 @ X4 )
=> ( X2 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X1: ( a > b > $o ) > b,X0: ( a > b > $o ) > a] :
! [X2: a > b > $o] :
( ? [X3: a,X4: b] : ( X2 @ X3 @ X4 )
=> ( X2 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eE209qcMJe/DTF2THF_26135.p',claim) ).
thf(f28,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f25,f21]) ).
thf(f19,plain,
( ( sF7 = $false )
| ( sF6 = $false ) ),
inference(boolean_simplification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( sF6 = $false )
| ( ( ~ $true ) = sF7 ) ),
inference(cases_simplifying,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO509^1 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:33:12 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO509^1 : TPTP v9.2.1. Released v4.1.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : Existence of choice functions for binary relations
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : choice4 [Bro09]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % 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 v4.1.0
% 0.18/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.45 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.18/0.45 % Number of types : 3 ( 2 usr)
% 0.18/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.18/0.45 % Number of variables : 5 ( 0 ^; 1 !; 4 ?; 5 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments :
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(a,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(b,type,
% 0.18/0.45 b: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(claim,conjecture,
% 0.18/0.45 ? [C1: ( a > b > $o ) > a,C2: ( a > b > $o ) > b] :
% 0.18/0.45 ! [R: a > b > $o] :
% 0.18/0.45 ( ? [X: a,Y: b] : ( R @ X @ Y )
% 0.18/0.45 => ( R @ ( C1 @ R ) @ ( C2 @ R ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 14:33:13 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eE209qcMJe/DTF2DTF26135.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(a,type,
% 1.45/1.27 a: $tType ).
% 1.45/1.27
% 1.45/1.27 thf(b,type,
% 1.45/1.27 b: $tType ).
% 1.45/1.27
% 1.45/1.27 thf(claim,conjecture,
% 1.45/1.27 ? [C1: ( a > b > $o ) > a,C2: ( a > b > $o ) > b] :
% 1.45/1.27 ! [R: a > b > $o] :
% 1.45/1.27 ( ? [X: a,Y: b] : ( R @ X @ Y )
% 1.45/1.27 => ( R @ ( C1 @ R ) @ ( C2 @ R ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.29 % (26245)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/2Mi)
% 1.45/1.29 % (26245)Instruction limit reached!
% 1.45/1.29 % (26245)------------------------------
% 1.45/1.29 % (26245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (26245)Termination reason: Unknown
% 1.45/1.29 % (26245)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (26245)Memory used [KB]: 5373
% 1.45/1.29 % (26245)Time elapsed: 0.002 s
% 1.45/1.29 % (26245)Instructions burned: 2 (million)
% 1.45/1.29 % (26245)------------------------------
% 1.45/1.29 % (26245)------------------------------
% 1.45/1.30 % (26244)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_26135 for (2999ds/27Mi)
% 1.45/1.30 % (26242)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/183Mi)
% 1.45/1.30 % (26243)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_26135 for (2999ds/4Mi)
% 1.45/1.30 % (26247)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_26135 for (2999ds/275Mi)
% 1.45/1.30 % (26246)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_26135 for (2999ds/2Mi)
% 1.45/1.30 % (26248)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/18Mi)
% 1.56/1.30 % (26244)Refutation not found, incomplete strategy
% 1.56/1.30 % (26244)------------------------------
% 1.56/1.30 % (26244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (26244)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.30
% 1.56/1.30
% 1.56/1.30 % (26244)Memory used [KB]: 5500
% 1.56/1.30 % (26244)Time elapsed: 0.003 s
% 1.56/1.30 % (26244)Instructions burned: 2 (million)
% 1.56/1.30 % (26244)------------------------------
% 1.56/1.30 % (26244)------------------------------
% 1.56/1.30 % (26246)Instruction limit reached!
% 1.56/1.30 % (26246)------------------------------
% 1.56/1.30 % (26246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (26246)Termination reason: Unknown
% 1.56/1.30 % (26246)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (26246)Memory used [KB]: 5500
% 1.56/1.30 % (26246)Time elapsed: 0.004 s
% 1.56/1.30 % (26246)Instructions burned: 3 (million)
% 1.56/1.30 % (26246)------------------------------
% 1.56/1.30 % (26246)------------------------------
% 1.56/1.30 % (26247)Refutation not found, incomplete strategy
% 1.56/1.30 % (26247)------------------------------
% 1.56/1.30 % (26247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (26247)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.30
% 1.56/1.30
% 1.56/1.30 % (26247)Memory used [KB]: 5500
% 1.56/1.30 % (26247)Time elapsed: 0.004 s
% 1.56/1.30 % (26249)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/3Mi)
% 1.56/1.30 % (26247)Instructions burned: 2 (million)
% 1.56/1.30 % (26247)------------------------------
% 1.56/1.30 % (26247)------------------------------
% 1.56/1.30 % (26243)Instruction limit reached!
% 1.56/1.30 % (26243)------------------------------
% 1.56/1.30 % (26243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (26243)Termination reason: Unknown
% 1.56/1.30 % (26243)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (26243)Memory used [KB]: 5500
% 1.56/1.30 % (26243)Time elapsed: 0.005 s
% 1.56/1.30 % (26243)Instructions burned: 5 (million)
% 1.56/1.30 % (26243)------------------------------
% 1.56/1.30 % (26243)------------------------------
% 1.56/1.30 % (26249)Instruction limit reached!
% 1.56/1.30 % (26249)------------------------------
% 1.56/1.30 % (26249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.30 % (26249)Termination reason: Unknown
% 1.56/1.30 % (26249)Termination phase: Saturation
% 1.56/1.30
% 1.56/1.30 % (26249)Memory used [KB]: 5500
% 1.56/1.30 % (26249)Time elapsed: 0.002 s
% 1.56/1.30 % (26249)Instructions burned: 3 (million)
% 1.56/1.30 % (26249)------------------------------
% 1.56/1.30 % (26249)------------------------------
% 1.56/1.31 % (26248)Instruction limit reached!
% 1.56/1.31 % (26248)------------------------------
% 1.56/1.31 % (26248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (26248)Termination reason: Unknown
% 1.56/1.31 % (26248)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (26248)Memory used [KB]: 5500
% 1.56/1.31 % (26248)Time elapsed: 0.012 s
% 1.56/1.31 % (26248)Instructions burned: 18 (million)
% 1.56/1.31 % (26248)------------------------------
% 1.56/1.31 % (26248)------------------------------
% 1.56/1.31 % (26254)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/7Mi)
% 1.56/1.31 % (26254)Instruction limit reached!
% 1.56/1.31 % (26254)------------------------------
% 1.56/1.31 % (26254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (26254)Termination reason: Unknown
% 1.56/1.31 % (26254)Termination phase: Saturation
% 1.56/1.31
% 1.56/1.31 % (26254)Memory used [KB]: 1023
% 1.56/1.31 % (26254)Time elapsed: 0.004 s
% 1.56/1.31 % (26254)Instructions burned: 10 (million)
% 1.56/1.31 % (26254)------------------------------
% 1.56/1.31 % (26254)------------------------------
% 1.56/1.31 % (26251)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_26135 for (2999ds/15Mi)
% 1.56/1.31 % (26250)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_26135 for (2999ds/37Mi)
% 1.56/1.31 % (26251)Refutation not found, incomplete strategy
% 1.56/1.31 % (26251)------------------------------
% 1.56/1.31 % (26251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.31 % (26251)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.31
% 1.56/1.31
% 1.56/1.31 % (26251)Memory used [KB]: 5500
% 1.56/1.31 % (26251)Time elapsed: 0.002 s
% 1.56/1.31 % (26251)Instructions burned: 1 (million)
% 1.56/1.31 % (26251)------------------------------
% 1.56/1.31 % (26251)------------------------------
% 1.56/1.32 % (26252)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_26135 for (2999ds/3Mi)
% 1.56/1.32 % (26253)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_26135 for (2999ds/1041Mi)
% 1.56/1.32 % (26252)Instruction limit reached!
% 1.56/1.32 % (26252)------------------------------
% 1.56/1.32 % (26252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (26252)Termination reason: Unknown
% 1.56/1.32 % (26252)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (26252)Memory used [KB]: 5500
% 1.56/1.32 % (26252)Time elapsed: 0.004 s
% 1.56/1.32 % (26252)Instructions burned: 3 (million)
% 1.56/1.32 % (26252)------------------------------
% 1.56/1.32 % (26252)------------------------------
% 1.56/1.32 % (26250)Refutation not found, incomplete strategy
% 1.56/1.32 % (26250)------------------------------
% 1.56/1.32 % (26250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (26250)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.32
% 1.56/1.32
% 1.56/1.32 % (26250)Memory used [KB]: 5756
% 1.56/1.32 % (26250)Time elapsed: 0.008 s
% 1.56/1.32 % (26250)Instructions burned: 21 (million)
% 1.56/1.32 % (26250)------------------------------
% 1.56/1.32 % (26250)------------------------------
% 1.56/1.32 % (26256)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_26135 for (2999ds/3Mi)
% 1.56/1.32 % (26253)Refutation not found, incomplete strategy
% 1.56/1.32 % (26253)------------------------------
% 1.56/1.32 % (26253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (26253)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.32
% 1.56/1.32
% 1.56/1.32 % (26253)Memory used [KB]: 5500
% 1.56/1.32 % (26253)Time elapsed: 0.007 s
% 1.56/1.32 % (26253)Instructions burned: 8 (million)
% 1.56/1.32 % (26253)------------------------------
% 1.56/1.32 % (26253)------------------------------
% 1.56/1.32 % (26256)Instruction limit reached!
% 1.56/1.32 % (26256)------------------------------
% 1.56/1.32 % (26256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (26256)Termination reason: Unknown
% 1.56/1.32 % (26256)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (26256)Memory used [KB]: 5500
% 1.56/1.32 % (26256)Time elapsed: 0.002 s
% 1.56/1.32 % (26256)Instructions burned: 3 (million)
% 1.56/1.32 % (26256)------------------------------
% 1.56/1.32 % (26256)------------------------------
% 1.56/1.32 % (26257)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_26135 for (2999ds/3Mi)
% 1.56/1.32 % (26255)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/16Mi)
% 1.56/1.32 % (26257)Instruction limit reached!
% 1.56/1.32 % (26257)------------------------------
% 1.56/1.32 % (26257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.32 % (26257)Termination reason: Unknown
% 1.56/1.32 % (26257)Termination phase: Saturation
% 1.56/1.32
% 1.56/1.32 % (26257)Memory used [KB]: 5500
% 1.56/1.32 % (26257)Time elapsed: 0.003 s
% 1.56/1.32 % (26257)Instructions burned: 3 (million)
% 1.56/1.32 % (26257)------------------------------
% 1.56/1.32 % (26257)------------------------------
% 1.56/1.33 % (26259)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/3Mi)
% 1.56/1.33 % (26260)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/4Mi)
% 1.56/1.33 % (26259)Instruction limit reached!
% 1.56/1.33 % (26259)------------------------------
% 1.56/1.33 % (26259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (26259)Termination reason: Unknown
% 1.56/1.33 % (26259)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (26259)Memory used [KB]: 5500
% 1.56/1.33 % (26259)Time elapsed: 0.003 s
% 1.56/1.33 % (26259)Instructions burned: 3 (million)
% 1.56/1.33 % (26259)------------------------------
% 1.56/1.33 % (26259)------------------------------
% 1.56/1.33 % (26260)Instruction limit reached!
% 1.56/1.33 % (26260)------------------------------
% 1.56/1.33 % (26260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (26260)Termination reason: Unknown
% 1.56/1.33 % (26260)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (26260)Memory used [KB]: 5500
% 1.56/1.33 % (26260)Time elapsed: 0.003 s
% 1.56/1.33 % (26260)Instructions burned: 6 (million)
% 1.56/1.33 % (26260)------------------------------
% 1.56/1.33 % (26260)------------------------------
% 1.56/1.33 % (26255)Instruction limit reached!
% 1.56/1.33 % (26255)------------------------------
% 1.56/1.33 % (26255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.33 % (26255)Termination reason: Unknown
% 1.56/1.33 % (26255)Termination phase: Saturation
% 1.56/1.33
% 1.56/1.33 % (26255)Memory used [KB]: 5628
% 1.56/1.33 % (26255)Time elapsed: 0.012 s
% 1.56/1.33 % (26255)Instructions burned: 16 (million)
% 1.56/1.33 % (26255)------------------------------
% 1.56/1.33 % (26255)------------------------------
% 1.56/1.33 % (26262)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/710Mi)
% 1.56/1.34 % (26258)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/7Mi)
% 1.56/1.34 % (26258)Refutation not found, incomplete strategy
% 1.56/1.34 % (26258)------------------------------
% 1.56/1.34 % (26258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (26258)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.34
% 1.56/1.34
% 1.56/1.34 % (26258)Memory used [KB]: 5500
% 1.56/1.34 % (26258)Time elapsed: 0.003 s
% 1.56/1.34 % (26258)Instructions burned: 2 (million)
% 1.56/1.34 % (26258)------------------------------
% 1.56/1.34 % (26258)------------------------------
% 1.56/1.34 % (26261)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/18Mi)
% 1.56/1.34 % (26263)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/6Mi)
% 1.56/1.34 % (26261)Refutation not found, incomplete strategy
% 1.56/1.34 % (26261)------------------------------
% 1.56/1.34 % (26261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (26261)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.34
% 1.56/1.34
% 1.56/1.34 % (26261)Memory used [KB]: 5500
% 1.56/1.34 % (26261)Time elapsed: 0.004 s
% 1.56/1.34 % (26261)Instructions burned: 1 (million)
% 1.56/1.34 % (26261)------------------------------
% 1.56/1.34 % (26261)------------------------------
% 1.56/1.34 % (26264)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_26135 for (2999ds/902Mi)
% 1.56/1.34 % (26263)Refutation not found, incomplete strategy
% 1.56/1.34 % (26263)------------------------------
% 1.56/1.34 % (26263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (26263)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.34
% 1.56/1.34
% 1.56/1.34 % (26263)Memory used [KB]: 5500
% 1.56/1.34 % (26263)Time elapsed: 0.002 s
% 1.56/1.34 % (26263)Instructions burned: 1 (million)
% 1.56/1.34 % (26263)------------------------------
% 1.56/1.34 % (26263)------------------------------
% 1.56/1.34 % (26264)Refutation not found, incomplete strategy
% 1.56/1.34 % (26264)------------------------------
% 1.56/1.34 % (26264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.34 % (26264)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.34
% 1.56/1.34
% 1.56/1.34 % (26264)Memory used [KB]: 5500
% 1.56/1.34 % (26264)Time elapsed: 0.001 s
% 1.56/1.34 % (26264)Instructions burned: 1 (million)
% 1.56/1.34 % (26264)------------------------------
% 1.56/1.34 % (26264)------------------------------
% 1.56/1.35 % (26265)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_26135 for (2999ds/21Mi)
% 1.56/1.35 % (26269)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_26135 for (2999ds/779Mi)
% 1.56/1.35 % (26268)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/377Mi)
% 1.56/1.35 % (26268)Refutation not found, incomplete strategy
% 1.56/1.35 % (26268)------------------------------
% 1.56/1.35 % (26268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.35 % (26268)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.35
% 1.56/1.35
% 1.56/1.35 % (26268)Memory used [KB]: 5500
% 1.56/1.35 % (26268)Time elapsed: 0.003 s
% 1.56/1.35 % (26268)Instructions burned: 3 (million)
% 1.56/1.35 % (26268)------------------------------
% 1.56/1.35 % (26268)------------------------------
% 1.56/1.35 % (26266)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/5Mi)
% 1.56/1.36 % (26266)Instruction limit reached!
% 1.56/1.36 % (26266)------------------------------
% 1.56/1.36 % (26266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (26266)Termination reason: Unknown
% 1.56/1.36 % (26266)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (26266)Memory used [KB]: 5500
% 1.56/1.36 % (26266)Time elapsed: 0.026 s
% 1.56/1.36 % (26266)Instructions burned: 5 (million)
% 1.56/1.36 % (26266)------------------------------
% 1.56/1.36 % (26266)------------------------------
% 1.56/1.36 % (26267)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_26135 for (2999ds/6Mi)
% 1.56/1.36 % (26267)Instruction limit reached!
% 1.56/1.36 % (26267)------------------------------
% 1.56/1.36 % (26267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (26267)Termination reason: Unknown
% 1.56/1.36 % (26267)Termination phase: Saturation
% 1.56/1.36
% 1.56/1.36 % (26267)Memory used [KB]: 5500
% 1.56/1.36 % (26267)Time elapsed: 0.006 s
% 1.56/1.36 % (26267)Instructions burned: 6 (million)
% 1.56/1.36 % (26267)------------------------------
% 1.56/1.36 % (26267)------------------------------
% 1.56/1.36 % (26270)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_26135 for (2999ds/19Mi)
% 1.56/1.36 % (26265)Instruction limit reached!
% 1.56/1.36 % (26265)------------------------------
% 1.56/1.36 % (26265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.36 % (26265)Termination reason: Unknown
% 1.56/1.36 % (26265)Termination phase: Saturation
% 1.56/1.37
% 1.56/1.37 % (26265)Memory used [KB]: 5628
% 1.56/1.37 % (26265)Time elapsed: 0.037 s
% 1.56/1.37 % (26265)Instructions burned: 21 (million)
% 1.56/1.37 % (26265)------------------------------
% 1.56/1.37 % (26265)------------------------------
% 1.56/1.37 % (26270)Refutation not found, incomplete strategy
% 1.56/1.37 % (26270)------------------------------
% 1.56/1.37 % (26270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (26270)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.37
% 1.56/1.37
% 1.56/1.37 % (26270)Memory used [KB]: 5500
% 1.56/1.37 % (26270)Time elapsed: 0.027 s
% 1.56/1.37 % (26270)Instructions burned: 3 (million)
% 1.56/1.37 % (26270)------------------------------
% 1.56/1.37 % (26270)------------------------------
% 1.56/1.37 % (26271)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/879Mi)
% 1.56/1.37 % (26271)Refutation not found, incomplete strategy
% 1.56/1.37 % (26271)------------------------------
% 1.56/1.37 % (26271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.37 % (26271)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.37
% 1.56/1.37
% 1.56/1.37 % (26271)Memory used [KB]: 5500
% 1.56/1.37 % (26271)Time elapsed: 0.002 s
% 1.56/1.37 % (26271)Instructions burned: 1 (million)
% 1.56/1.37 % (26271)------------------------------
% 1.56/1.37 % (26271)------------------------------
% 1.56/1.38 % (26274)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/30Mi)
% 1.56/1.38 % (26272)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/17Mi)
% 1.56/1.38 % (26273)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/3Mi)
% 1.56/1.38 % (26273)Instruction limit reached!
% 1.56/1.38 % (26273)------------------------------
% 1.56/1.38 % (26273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (26273)Termination reason: Unknown
% 1.56/1.38 % (26273)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (26273)Memory used [KB]: 1023
% 1.56/1.38 % (26273)Time elapsed: 0.004 s
% 1.56/1.38 % (26273)Instructions burned: 3 (million)
% 1.56/1.38 % (26273)------------------------------
% 1.56/1.38 % (26273)------------------------------
% 1.56/1.38 % (26242)Instruction limit reached!
% 1.56/1.38 % (26242)------------------------------
% 1.56/1.38 % (26242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.38 % (26242)Termination reason: Unknown
% 1.56/1.38 % (26242)Termination phase: Saturation
% 1.56/1.38
% 1.56/1.38 % (26242)Memory used [KB]: 6140
% 1.56/1.38 % (26242)Time elapsed: 0.091 s
% 1.56/1.38 % (26242)Instructions burned: 184 (million)
% 1.56/1.38 % (26242)------------------------------
% 1.56/1.38 % (26242)------------------------------
% 1.56/1.39 % (26275)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26135 for (2999ds/127Mi)
% 1.56/1.39 % (26272)Instruction limit reached!
% 1.56/1.39 % (26272)------------------------------
% 1.56/1.39 % (26272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (26272)Termination reason: Unknown
% 1.56/1.39 % (26272)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (26272)Memory used [KB]: 5500
% 1.56/1.39 % (26272)Time elapsed: 0.010 s
% 1.56/1.39 % (26272)Instructions burned: 17 (million)
% 1.56/1.39 % (26272)------------------------------
% 1.56/1.39 % (26272)------------------------------
% 1.56/1.39 % (26274)Instruction limit reached!
% 1.56/1.39 % (26274)------------------------------
% 1.56/1.39 % (26274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.39 % (26274)Termination reason: Unknown
% 1.56/1.39 % (26274)Termination phase: Saturation
% 1.56/1.39
% 1.56/1.39 % (26274)Memory used [KB]: 5628
% 1.56/1.39 % (26274)Time elapsed: 0.014 s
% 1.56/1.39 % (26274)Instructions burned: 32 (million)
% 1.56/1.39 % (26274)------------------------------
% 1.56/1.39 % (26274)------------------------------
% 1.56/1.40 % (26279)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/100Mi)
% 1.56/1.40 % (26279)Refutation not found, incomplete strategy
% 1.56/1.40 % (26279)------------------------------
% 1.56/1.40 % (26279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (26279)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.40
% 1.56/1.40
% 1.56/1.40 % (26279)Memory used [KB]: 5500
% 1.56/1.40 % (26279)Time elapsed: 0.002 s
% 1.56/1.40 % (26279)Instructions burned: 2 (million)
% 1.56/1.40 % (26279)------------------------------
% 1.56/1.40 % (26279)------------------------------
% 1.56/1.40 % (26280)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_26135 for (2998ds/3Mi)
% 1.56/1.40 % (26281)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_26135 for (2998ds/20Mi)
% 1.56/1.40 % (26281)Refutation not found, incomplete strategy
% 1.56/1.40 % (26281)------------------------------
% 1.56/1.40 % (26281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (26281)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.40
% 1.56/1.40
% 1.56/1.40 % (26281)Memory used [KB]: 5500
% 1.56/1.40 % (26281)Time elapsed: 0.002 s
% 1.56/1.40 % (26281)Instructions burned: 1 (million)
% 1.56/1.40 % (26281)------------------------------
% 1.56/1.40 % (26281)------------------------------
% 1.56/1.40 % (26280)Instruction limit reached!
% 1.56/1.40 % (26280)------------------------------
% 1.56/1.40 % (26280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.40 % (26280)Termination reason: Unknown
% 1.56/1.40 % (26280)Termination phase: Saturation
% 1.56/1.40
% 1.56/1.40 % (26280)Memory used [KB]: 5500
% 1.56/1.40 % (26280)Time elapsed: 0.004 s
% 1.56/1.40 % (26280)Instructions burned: 4 (million)
% 1.56/1.40 % (26280)------------------------------
% 1.56/1.40 % (26280)------------------------------
% 1.56/1.40 % (26282)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_26135 for (2998ds/86Mi)
% 1.56/1.41 % (26282)Refutation not found, incomplete strategy
% 1.56/1.41 % (26282)------------------------------
% 1.56/1.41 % (26282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.41 % (26282)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.41
% 1.56/1.41
% 1.56/1.41 % (26282)Memory used [KB]: 5500
% 1.56/1.41 % (26282)Time elapsed: 0.002 s
% 1.56/1.41 % (26282)Instructions burned: 1 (million)
% 1.56/1.41 % (26282)------------------------------
% 1.56/1.41 % (26282)------------------------------
% 1.56/1.41 % (26283)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_26135 for (2998ds/107Mi)
% 1.56/1.41 % (26283)Refutation not found, incomplete strategy
% 1.56/1.41 % (26283)------------------------------
% 1.56/1.41 % (26283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.41 % (26283)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.41
% 1.56/1.41
% 1.56/1.41 % (26283)Memory used [KB]: 5500
% 1.56/1.41 % (26283)Time elapsed: 0.002 s
% 1.56/1.41 % (26283)Instructions burned: 1 (million)
% 1.56/1.41 % (26283)------------------------------
% 1.56/1.41 % (26283)------------------------------
% 1.56/1.41 % (26284)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_26135 for (2998ds/39Mi)
% 1.56/1.41 % (26285)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_26135 for (2998ds/448Mi)
% 1.56/1.42 % (26291)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_26135 for (2998ds/46Mi)
% 1.56/1.42 % (26296)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_26135 for (2998ds/98Mi)
% 1.56/1.42 % (26275)Instruction limit reached!
% 1.56/1.42 % (26275)------------------------------
% 1.56/1.42 % (26275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (26275)Termination reason: Unknown
% 1.56/1.42 % (26275)Termination phase: Saturation
% 1.56/1.42
% 1.56/1.42 % (26275)Memory used [KB]: 5756
% 1.56/1.42 % (26275)Time elapsed: 0.039 s
% 1.56/1.42 % (26275)Instructions burned: 129 (million)
% 1.56/1.42 % (26275)------------------------------
% 1.56/1.42 % (26275)------------------------------
% 1.56/1.42 % (26296)Refutation not found, incomplete strategy
% 1.56/1.42 % (26296)------------------------------
% 1.56/1.42 % (26296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (26296)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.42
% 1.56/1.42
% 1.56/1.42 % (26296)Memory used [KB]: 1023
% 1.56/1.42 % (26296)Time elapsed: 0.003 s
% 1.56/1.42 % (26296)Instructions burned: 4 (million)
% 1.56/1.42 % (26296)------------------------------
% 1.56/1.42 % (26296)------------------------------
% 1.56/1.42 % (26284)Instruction limit reached!
% 1.56/1.42 % (26284)------------------------------
% 1.56/1.42 % (26284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.42 % (26284)Termination reason: Unknown
% 1.56/1.42 % (26284)Termination phase: Saturation
% 1.56/1.42
% 1.56/1.42 % (26284)Memory used [KB]: 5628
% 1.56/1.42 % (26284)Time elapsed: 0.014 s
% 1.56/1.42 % (26284)Instructions burned: 41 (million)
% 1.56/1.42 % (26284)------------------------------
% 1.56/1.42 % (26284)------------------------------
% 1.56/1.43 % (26291)Refutation not found, incomplete strategy
% 1.56/1.43 % (26291)------------------------------
% 1.56/1.43 % (26291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (26291)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (26291)Memory used [KB]: 5628
% 1.56/1.43 % (26291)Time elapsed: 0.010 s
% 1.56/1.43 % (26291)Instructions burned: 24 (million)
% 1.56/1.43 % (26291)------------------------------
% 1.56/1.43 % (26291)------------------------------
% 1.56/1.43 % (26302)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_26135 for (2998ds/507Mi)
% 1.56/1.43 % (26303)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_26135 for (2998ds/149Mi)
% 1.56/1.43 % (26304)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/39Mi)
% 1.56/1.43 % (26302)Refutation not found, incomplete strategy
% 1.56/1.43 % (26302)------------------------------
% 1.56/1.43 % (26302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (26302)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (26302)Memory used [KB]: 5500
% 1.56/1.43 % (26302)Time elapsed: 0.003 s
% 1.56/1.43 % (26302)Instructions burned: 3 (million)
% 1.56/1.43 % (26302)------------------------------
% 1.56/1.43 % (26302)------------------------------
% 1.56/1.43 % (26303)Refutation not found, incomplete strategy
% 1.56/1.43 % (26303)------------------------------
% 1.56/1.43 % (26303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (26304)Refutation not found, incomplete strategy
% 1.56/1.43 % (26304)------------------------------
% 1.56/1.43 % (26304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.43 % (26304)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (26304)Memory used [KB]: 5500
% 1.56/1.43 % (26304)Time elapsed: 0.002 s
% 1.56/1.43 % (26304)Instructions burned: 1 (million)
% 1.56/1.43 % (26304)------------------------------
% 1.56/1.43 % (26304)------------------------------
% 1.56/1.43 % (26303)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.43
% 1.56/1.43
% 1.56/1.43 % (26303)Memory used [KB]: 5500
% 1.56/1.44 % (26303)Time elapsed: 0.003 s
% 1.56/1.44 % (26303)Instructions burned: 1 (million)
% 1.56/1.44 % (26303)------------------------------
% 1.56/1.44 % (26303)------------------------------
% 1.56/1.44 % (26305)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_26135 for (2998ds/6Mi)
% 1.56/1.44 % (26305)Instruction limit reached!
% 1.56/1.44 % (26305)------------------------------
% 1.56/1.44 % (26305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.44 % (26305)Termination reason: Unknown
% 1.56/1.44 % (26305)Termination phase: Saturation
% 1.56/1.44
% 1.56/1.44 % (26305)Memory used [KB]: 9978
% 1.56/1.44 % (26305)Time elapsed: 0.005 s
% 1.56/1.44 % (26305)Instructions burned: 7 (million)
% 1.56/1.44 % (26305)------------------------------
% 1.56/1.44 % (26305)------------------------------
% 1.56/1.44 % (26306)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_26135 for (2998ds/1087Mi)
% 1.56/1.45 % (26308)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_26135 for (2998ds/44Mi)
% 1.56/1.45 % (26307)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/47Mi)
% 1.56/1.45 % (26306)Refutation not found, incomplete strategy
% 1.56/1.45 % (26306)------------------------------
% 1.56/1.45 % (26306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.45 % (26306)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.45
% 1.56/1.45
% 1.56/1.45 % (26306)Memory used [KB]: 5500
% 1.56/1.45 % (26306)Time elapsed: 0.002 s
% 1.56/1.45 % (26306)Instructions burned: 1 (million)
% 1.56/1.45 % (26306)------------------------------
% 1.56/1.45 % (26306)------------------------------
% 1.56/1.45 % (26309)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_26135 for (2998ds/432Mi)
% 1.56/1.46 % (26309)Refutation not found, incomplete strategy
% 1.56/1.46 % (26309)------------------------------
% 1.56/1.46 % (26309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.46 % (26310)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/62Mi)
% 1.56/1.46 % (26309)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.46
% 1.56/1.46
% 1.56/1.46 % (26309)Memory used [KB]: 1151
% 1.56/1.46 % (26309)Time elapsed: 0.008 s
% 1.56/1.46 % (26309)Instructions burned: 19 (million)
% 1.56/1.46 % (26309)------------------------------
% 1.56/1.46 % (26309)------------------------------
% 1.56/1.46 % (26308)Instruction limit reached!
% 1.56/1.46 % (26308)------------------------------
% 1.56/1.46 % (26308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.46 % (26308)Termination reason: Unknown
% 1.56/1.46 % (26308)Termination phase: Saturation
% 1.56/1.46
% 1.56/1.46 % (26308)Memory used [KB]: 1151
% 1.56/1.46 % (26308)Time elapsed: 0.015 s
% 1.56/1.46 % (26308)Instructions burned: 45 (million)
% 1.56/1.46 % (26308)------------------------------
% 1.56/1.46 % (26308)------------------------------
% 1.56/1.46 % (26307)Instruction limit reached!
% 1.56/1.46 % (26307)------------------------------
% 1.56/1.46 % (26307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.46 % (26307)Termination reason: Unknown
% 1.56/1.46 % (26307)Termination phase: Saturation
% 1.56/1.46
% 1.56/1.46 % (26307)Memory used [KB]: 5628
% 1.56/1.46 % (26307)Time elapsed: 0.015 s
% 1.56/1.46 % (26307)Instructions burned: 47 (million)
% 1.56/1.46 % (26307)------------------------------
% 1.56/1.46 % (26307)------------------------------
% 1.56/1.47 % (26311)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_26135 for (2998ds/31Mi)
% 1.56/1.47 % (26312)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/96Mi)
% 1.56/1.47 % (26313)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_26135 for (2998ds/453Mi)
% 1.56/1.47 % (26313)Refutation not found, incomplete strategy
% 1.56/1.47 % (26313)------------------------------
% 1.56/1.47 % (26313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.47 % (26313)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.47
% 1.56/1.47
% 1.56/1.47 % (26313)Memory used [KB]: 5500
% 1.56/1.47 % (26313)Time elapsed: 0.004 s
% 1.56/1.47 % (26313)Instructions burned: 6 (million)
% 1.56/1.47 % (26313)------------------------------
% 1.56/1.47 % (26313)------------------------------
% 1.56/1.48 % (26310)Instruction limit reached!
% 1.56/1.48 % (26310)------------------------------
% 1.56/1.48 % (26310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.48 % (26310)Termination reason: Unknown
% 1.56/1.48 % (26310)Termination phase: Saturation
% 1.56/1.48
% 1.56/1.48 % (26310)Memory used [KB]: 5756
% 1.56/1.48 % (26310)Time elapsed: 0.021 s
% 1.56/1.48 % (26310)Instructions burned: 64 (million)
% 1.56/1.48 % (26310)------------------------------
% 1.56/1.48 % (26310)------------------------------
% 1.56/1.48 % (26311)Instruction limit reached!
% 1.56/1.48 % (26311)------------------------------
% 1.56/1.48 % (26311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.48 % (26311)Termination reason: Unknown
% 1.56/1.48 % (26311)Termination phase: Saturation
% 1.56/1.48
% 1.56/1.48 % (26311)Memory used [KB]: 5628
% 1.56/1.48 % (26311)Time elapsed: 0.011 s
% 1.56/1.48 % (26311)Instructions burned: 31 (million)
% 1.56/1.48 % (26311)------------------------------
% 1.56/1.48 % (26311)------------------------------
% 1.56/1.48 % (26314)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_26135 for (2998ds/71Mi)
% 1.56/1.49 % (26315)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/83Mi)
% 1.56/1.49 % (26316)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26135 for (2998ds/11Mi)
% 1.56/1.49 % (26316)Instruction limit reached!
% 1.56/1.49 % (26316)------------------------------
% 1.56/1.49 % (26316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.49 % (26316)Termination reason: Unknown
% 1.56/1.49 % (26316)Termination phase: Saturation
% 1.56/1.49
% 1.56/1.49 % (26316)Memory used [KB]: 5500
% 1.56/1.49 % (26316)Time elapsed: 0.006 s
% 1.56/1.49 % (26316)Instructions burned: 12 (million)
% 1.56/1.49 % (26316)------------------------------
% 1.56/1.49 % (26316)------------------------------
% 1.56/1.50 % (26312)Instruction limit reached!
% 1.56/1.50 % (26312)------------------------------
% 1.56/1.50 % (26312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.50 % (26312)Termination reason: Unknown
% 1.56/1.50 % (26312)Termination phase: Saturation
% 1.56/1.50
% 1.56/1.50 % (26312)Memory used [KB]: 5628
% 1.56/1.50 % (26312)Time elapsed: 0.030 s
% 1.56/1.50 % (26312)Instructions burned: 96 (million)
% 1.56/1.50 % (26312)------------------------------
% 1.56/1.50 % (26312)------------------------------
% 1.56/1.50 % (26317)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_26135 for (2998ds/41Mi)
% 1.56/1.50 % (26317)Refutation not found, incomplete strategy
% 1.56/1.50 % (26317)------------------------------
% 1.56/1.50 % (26317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.50 % (26317)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.50
% 1.56/1.50
% 1.56/1.50 % (26317)Memory used [KB]: 5500
% 1.56/1.50 % (26317)Time elapsed: 0.003 s
% 1.56/1.50 % (26317)Instructions burned: 3 (million)
% 1.56/1.50 % (26317)------------------------------
% 1.56/1.50 % (26317)------------------------------
% 1.56/1.51 % (26318)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/6Mi)
% 1.56/1.51 % (26314)Instruction limit reached!
% 1.56/1.51 % (26314)------------------------------
% 1.56/1.51 % (26314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.51 % (26314)Termination reason: Unknown
% 1.56/1.51 % (26314)Termination phase: Saturation
% 1.56/1.51
% 1.56/1.51 % (26314)Memory used [KB]: 5756
% 1.56/1.51 % (26314)Time elapsed: 0.027 s
% 1.56/1.51 % (26314)Instructions burned: 73 (million)
% 1.56/1.51 % (26314)------------------------------
% 1.56/1.51 % (26314)------------------------------
% 1.56/1.51 % (26318)Refutation not found, incomplete strategy
% 1.56/1.51 % (26318)------------------------------
% 1.56/1.51 % (26318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.51 % (26318)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.51
% 1.56/1.51
% 1.56/1.51 % (26318)Memory used [KB]: 5500
% 1.56/1.51 % (26318)Time elapsed: 0.002 s
% 1.56/1.51 % (26318)Instructions burned: 1 (million)
% 1.56/1.51 % (26318)------------------------------
% 1.56/1.51 % (26318)------------------------------
% 1.56/1.51 % (26315)Instruction limit reached!
% 1.56/1.51 % (26315)------------------------------
% 1.56/1.51 % (26315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.51 % (26315)Termination reason: Unknown
% 1.56/1.51 % (26315)Termination phase: Saturation
% 1.56/1.51
% 1.56/1.51 % (26315)Memory used [KB]: 5628
% 1.56/1.51 % (26315)Time elapsed: 0.026 s
% 1.56/1.51 % (26315)Instructions burned: 84 (million)
% 1.56/1.51 % (26315)------------------------------
% 1.56/1.51 % (26315)------------------------------
% 1.56/1.51 % (26319)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/150Mi)
% 1.56/1.52 % (26320)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/343Mi)
% 1.56/1.52 % (26321)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_26135 for (2997ds/109Mi)
% 1.56/1.52 % (26320)Refutation not found, incomplete strategy
% 1.56/1.52 % (26320)------------------------------
% 1.56/1.52 % (26320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.52 % (26320)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.52
% 1.56/1.52
% 1.56/1.52 % (26320)Memory used [KB]: 5500
% 1.56/1.52 % (26320)Time elapsed: 0.002 s
% 1.56/1.52 % (26320)Instructions burned: 1 (million)
% 1.56/1.52 % (26320)------------------------------
% 1.56/1.52 % (26320)------------------------------
% 1.56/1.52 % (26322)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_26135 for (2997ds/253Mi)
% 1.56/1.52 % (26322)Refutation not found, incomplete strategy
% 1.56/1.52 % (26322)------------------------------
% 1.56/1.52 % (26322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.52 % (26322)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.52
% 1.56/1.52
% 1.56/1.52 % (26322)Memory used [KB]: 5500
% 1.56/1.52 % (26322)Time elapsed: 0.003 s
% 1.56/1.52 % (26322)Instructions burned: 3 (million)
% 1.56/1.52 % (26322)------------------------------
% 1.56/1.52 % (26322)------------------------------
% 1.56/1.53 % (26323)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/140Mi)
% 1.56/1.53 % (26323)Refutation not found, incomplete strategy
% 1.56/1.53 % (26323)------------------------------
% 1.56/1.53 % (26323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.53 % (26323)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.53
% 1.56/1.53
% 1.56/1.53 % (26323)Memory used [KB]: 5500
% 1.56/1.53 % (26323)Time elapsed: 0.002 s
% 1.56/1.53 % (26323)Instructions burned: 1 (million)
% 1.56/1.53 % (26323)------------------------------
% 1.56/1.53 % (26323)------------------------------
% 1.56/1.53 % (26324)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_26135 for (2997ds/614Mi)
% 1.56/1.53 % (26324)Refutation not found, incomplete strategy
% 1.56/1.53 % (26324)------------------------------
% 1.56/1.53 % (26324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.53 % (26324)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.53
% 1.56/1.53
% 1.56/1.53 % (26324)Memory used [KB]: 5500
% 1.56/1.53 % (26324)Time elapsed: 0.002 s
% 1.56/1.53 % (26324)Instructions burned: 1 (million)
% 1.56/1.53 % (26324)------------------------------
% 1.56/1.53 % (26324)------------------------------
% 1.56/1.54 % (26262)Instruction limit reached!
% 1.56/1.54 % (26262)------------------------------
% 1.56/1.54 % (26262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.54 % (26262)Termination reason: Unknown
% 1.56/1.54 % (26262)Termination phase: Saturation
% 1.56/1.54
% 1.56/1.54 % (26262)Memory used [KB]: 6524
% 1.56/1.54 % (26262)Time elapsed: 0.204 s
% 1.56/1.54 % (26262)Instructions burned: 711 (million)
% 1.56/1.54 % (26262)------------------------------
% 1.56/1.54 % (26262)------------------------------
% 1.56/1.54 % (26285)Instruction limit reached!
% 1.56/1.54 % (26285)------------------------------
% 1.56/1.54 % (26285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.54 % (26285)Termination reason: Unknown
% 1.56/1.54 % (26285)Termination phase: Saturation
% 1.56/1.54
% 1.56/1.54 % (26285)Memory used [KB]: 6268
% 1.56/1.54 % (26285)Time elapsed: 0.128 s
% 1.56/1.54 % (26285)Instructions burned: 449 (million)
% 1.56/1.54 % (26285)------------------------------
% 1.56/1.54 % (26285)------------------------------
% 1.56/1.54 % (26325)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_26135 for (2997ds/202Mi)
% 1.56/1.54 % (26325)Refutation not found, incomplete strategy
% 1.56/1.54 % (26325)------------------------------
% 1.56/1.54 % (26325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.54 % (26325)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.54
% 1.56/1.54
% 1.56/1.54 % (26325)Memory used [KB]: 5500
% 1.56/1.54 % (26325)Time elapsed: 0.002 s
% 1.56/1.54 % (26325)Instructions burned: 3 (million)
% 1.56/1.54 % (26325)------------------------------
% 1.56/1.54 % (26325)------------------------------
% 1.56/1.54 % (26326)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_26135 for (2997ds/339Mi)
% 1.56/1.54 % (26326)Refutation not found, incomplete strategy
% 1.56/1.54 % (26326)------------------------------
% 1.56/1.54 % (26326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.54 % (26326)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.54
% 1.56/1.54
% 1.56/1.54 % (26326)Memory used [KB]: 5500
% 1.56/1.54 % (26326)Time elapsed: 0.002 s
% 1.56/1.54 % (26326)Instructions burned: 1 (million)
% 1.56/1.54 % (26326)------------------------------
% 1.56/1.54 % (26326)------------------------------
% 1.56/1.55 % (26327)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_26135 for (2997ds/283Mi)
% 1.56/1.55 % (26328)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/134Mi)
% 1.56/1.55 % (26321)Instruction limit reached!
% 1.56/1.55 % (26321)------------------------------
% 1.56/1.55 % (26321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.55 % (26321)Termination reason: Unknown
% 1.56/1.55 % (26321)Termination phase: Saturation
% 1.56/1.55
% 1.56/1.55 % (26321)Memory used [KB]: 5756
% 1.56/1.55 % (26321)Time elapsed: 0.033 s
% 1.56/1.55 % (26321)Instructions burned: 109 (million)
% 1.56/1.55 % (26321)------------------------------
% 1.56/1.55 % (26321)------------------------------
% 1.56/1.55 % (26329)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/298Mi)
% 1.56/1.55 % (26330)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26135 for (2997ds/192Mi)
% 1.56/1.56 % (26319)Instruction limit reached!
% 1.56/1.56 % (26319)------------------------------
% 1.56/1.56 % (26319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.56 % (26319)Termination reason: Unknown
% 1.56/1.56 % (26319)Termination phase: Saturation
% 1.56/1.56
% 1.56/1.56 % (26319)Memory used [KB]: 5756
% 1.56/1.56 % (26319)Time elapsed: 0.045 s
% 1.56/1.56 % (26319)Instructions burned: 150 (million)
% 1.56/1.56 % (26319)------------------------------
% 1.56/1.56 % (26319)------------------------------
% 1.56/1.56 % (26269)Instruction limit reached!
% 1.56/1.56 % (26269)------------------------------
% 1.56/1.56 % (26269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.56 % (26269)Termination reason: Unknown
% 1.56/1.56 % (26269)Termination phase: Saturation
% 1.56/1.56
% 1.56/1.56 % (26269)Memory used [KB]: 6524
% 1.56/1.56 % (26269)Time elapsed: 0.228 s
% 1.56/1.56 % (26269)Instructions burned: 782 (million)
% 1.56/1.56 % (26269)------------------------------
% 1.56/1.56 % (26269)------------------------------
% 1.56/1.56 % (26331)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_26135 for (2997ds/258Mi)
% 1.56/1.56 % (26331)Refutation not found, incomplete strategy
% 1.56/1.56 % (26331)------------------------------
% 1.56/1.56 % (26331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.56 % (26331)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.56
% 1.56/1.56
% 1.56/1.56 % (26331)Memory used [KB]: 5500
% 1.56/1.56 % (26331)Time elapsed: 0.002 s
% 1.56/1.56 % (26331)Instructions burned: 1 (million)
% 1.56/1.56 % (26331)------------------------------
% 1.56/1.56 % (26331)------------------------------
% 1.56/1.57 % (26332)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_26135 for (2997ds/90Mi)
% 1.56/1.57 % (26333)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_26135 for (2997ds/231Mi)
% 1.56/1.57 % (26332)Refutation not found, incomplete strategy
% 1.56/1.57 % (26332)------------------------------
% 1.56/1.57 % (26332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.57 % (26332)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.57
% 1.56/1.57
% 1.56/1.57 % (26332)Memory used [KB]: 5500
% 1.56/1.57 % (26332)Time elapsed: 0.002 s
% 1.56/1.57 % (26332)Instructions burned: 1 (million)
% 1.56/1.57 % (26332)------------------------------
% 1.56/1.57 % (26332)------------------------------
% 1.56/1.57 % (26334)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_26135 for (2997ds/458Mi)
% 1.56/1.57 % (26334)Refutation not found, incomplete strategy
% 1.56/1.57 % (26334)------------------------------
% 1.56/1.57 % (26334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.57 % (26334)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.57
% 1.56/1.57
% 1.56/1.57 % (26334)Memory used [KB]: 5500
% 1.56/1.57 % (26334)Time elapsed: 0.002 s
% 1.56/1.57 % (26334)Instructions burned: 1 (million)
% 1.56/1.57 % (26334)------------------------------
% 1.56/1.57 % (26334)------------------------------
% 1.56/1.58 % (26335)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_26135 for (2997ds/31Mi)
% 1.56/1.58 % (26336)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_26135 for (2997ds/297Mi)
% 1.56/1.59 % (26335)Instruction limit reached!
% 1.56/1.59 % (26335)------------------------------
% 1.56/1.59 % (26335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.59 % (26335)Termination reason: Unknown
% 1.56/1.59 % (26335)Termination phase: Saturation
% 1.56/1.59
% 1.56/1.59 % (26335)Memory used [KB]: 5628
% 1.56/1.59 % (26335)Time elapsed: 0.011 s
% 1.56/1.59 % (26335)Instructions burned: 31 (million)
% 1.56/1.59 % (26335)------------------------------
% 1.56/1.59 % (26335)------------------------------
% 1.56/1.59 % (26328)Instruction limit reached!
% 1.56/1.59 % (26328)------------------------------
% 1.56/1.59 % (26328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.59 % (26328)Termination reason: Unknown
% 1.56/1.59 % (26328)Termination phase: Saturation
% 1.56/1.59
% 1.56/1.59 % (26328)Memory used [KB]: 6268
% 1.56/1.59 % (26328)Time elapsed: 0.046 s
% 1.56/1.59 % (26328)Instructions burned: 135 (million)
% 1.56/1.59 % (26328)------------------------------
% 1.56/1.59 % (26328)------------------------------
% 1.56/1.60 % (26337)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_26135 for (2996ds/987Mi)
% 1.56/1.60 % (26337)Refutation not found, incomplete strategy
% 1.56/1.60 % (26337)------------------------------
% 1.56/1.60 % (26337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.60 % (26337)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.60
% 1.56/1.60
% 1.56/1.60 % (26337)Memory used [KB]: 5500
% 1.56/1.60 % (26337)Time elapsed: 0.005 s
% 1.56/1.60 % (26337)Instructions burned: 9 (million)
% 1.56/1.60 % (26337)------------------------------
% 1.56/1.60 % (26337)------------------------------
% 1.56/1.60 % (26338)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_26135 for (2996ds/182Mi)
% 1.56/1.61 % (26330)Instruction limit reached!
% 1.56/1.61 % (26330)------------------------------
% 1.56/1.61 % (26330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.61 % (26330)Termination reason: Unknown
% 1.56/1.61 % (26330)Termination phase: Saturation
% 1.56/1.61
% 1.56/1.61 % (26330)Memory used [KB]: 5884
% 1.56/1.61 % (26330)Time elapsed: 0.057 s
% 1.56/1.61 % (26330)Instructions burned: 193 (million)
% 1.56/1.61 % (26330)------------------------------
% 1.56/1.61 % (26330)------------------------------
% 1.56/1.61 % (26339)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_26135 for (2996ds/182Mi)
% 1.56/1.61 % (26339)Refutation not found, incomplete strategy
% 1.56/1.61 % (26339)------------------------------
% 1.56/1.61 % (26339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.61 % (26339)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.61
% 1.56/1.61
% 1.56/1.61 % (26339)Memory used [KB]: 5500
% 1.56/1.61 % (26339)Time elapsed: 0.002 s
% 1.56/1.61 % (26339)Instructions burned: 1 (million)
% 1.56/1.61 % (26339)------------------------------
% 1.56/1.61 % (26339)------------------------------
% 1.56/1.62 % (26333)First to succeed.
% 1.56/1.62 % (26340)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_26135 for (2996ds/154Mi)
% 1.56/1.62 % (26341)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_26135 for (2996ds/79Mi)
% 1.56/1.62 % (26341)Refutation not found, incomplete strategy
% 1.56/1.62 % (26341)------------------------------
% 1.56/1.62 % (26341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.62 % (26341)Termination reason: Refutation not found, incomplete strategy
% 1.56/1.62
% 1.56/1.62
% 1.56/1.62 % (26341)Memory used [KB]: 5500
% 1.56/1.62 % (26341)Time elapsed: 0.002 s
% 1.56/1.62 % (26341)Instructions burned: 1 (million)
% 1.56/1.62 % (26341)------------------------------
% 1.56/1.62 % (26341)------------------------------
% 1.56/1.63 % (26327)Instruction limit reached!
% 1.56/1.63 % (26327)------------------------------
% 1.56/1.63 % (26327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.63 % (26327)Termination reason: Unknown
% 1.56/1.63 % (26327)Termination phase: Saturation
% 1.56/1.63
% 1.56/1.63 % (26327)Memory used [KB]: 6140
% 1.56/1.63 % (26327)Time elapsed: 0.082 s
% 1.56/1.63 % (26327)Instructions burned: 283 (million)
% 1.56/1.63 % (26327)------------------------------
% 1.56/1.63 % (26327)------------------------------
% 1.56/1.63 % (26333)Refutation found. Thanks to Tanya!
% 1.56/1.63 % SZS status Theorem for DTF2THF_26135
% 1.56/1.63 % SZS output start Proof for DTF2THF_26135
% 1.56/1.63 thf(type_def_5, type, a: $tType).
% 1.56/1.63 thf(type_def_6, type, b: $tType).
% 1.56/1.63 thf(func_def_0, type, a: $tType).
% 1.56/1.63 thf(func_def_1, type, b: $tType).
% 1.56/1.63 thf(func_def_13, type, sF0: (((a > b > $o) > a) > $o) > $o).
% 1.56/1.63 thf(func_def_14, type, sF1: (((a > b > $o) > b) > $o) > $o).
% 1.56/1.63 thf(func_def_15, type, sF2: ((a > b > $o) > $o) > $o).
% 1.56/1.63 thf(func_def_16, type, sF3: (b > $o) > $o).
% 1.56/1.63 thf(func_def_17, type, sF4: (a > $o) > $o).
% 1.56/1.63 thf(func_def_18, type, sF5: ((a > b > $o) > a) > $o).
% 1.56/1.63 thf(func_def_22, type, ph9: !>[X0: $tType]:(X0)).
% 1.56/1.63 thf(func_def_23, type, sK10: (b > $o) > b).
% 1.56/1.63 thf(func_def_24, type, sK11: (a > $o) > a).
% 1.56/1.63 thf(func_def_25, type, sK12: ((a > b > $o) > $o) > a > b > $o).
% 1.56/1.63 thf(func_def_26, type, sK13: (((a > b > $o) > a) > $o) > (a > b > $o) > a).
% 1.56/1.63 thf(func_def_27, type, sK14: (((a > b > $o) > b) > $o) > (a > b > $o) > b).
% 1.56/1.63 thf(func_def_29, type, sK15: ((a > b > $o) > b > a > a) > ((a > b > $o) > b > a > a) > a > b > $o).
% 1.56/1.63 thf(func_def_30, type, sK16: ((a > b > $o) > a > b) > ((a > b > $o) > a > b) > a).
% 1.56/1.63 thf(func_def_31, type, sK17: ((a > b > $o) > a > b) > ((a > b > $o) > a > b) > a > b > $o).
% 1.56/1.63 thf(func_def_34, type, sK18: ((a > b > $o) > a > b > a > a) > ((a > b > $o) > a > b > a > a) > b).
% 1.56/1.63 thf(func_def_35, type, sK19: ((a > b > $o) > a > b > a > a) > a).
% 1.56/1.63 thf(f272,plain,(
% 1.56/1.63 $false),
% 1.56/1.63 inference(avatar_sat_refutation,[status(thm)],[f28,f38,f41,f271])).
% 1.56/1.63 thf(f271,plain,(
% 1.56/1.63 ~spl8_1),
% 1.56/1.63 inference(avatar_contradiction_clause,[status(thm)],[f270])).
% 1.56/1.63 thf(f270,plain,(
% 1.56/1.63 $false | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f269])).
% 1.56/1.63 thf(f269,plain,(
% 1.56/1.63 ((^[Y0 : a > b > $o]: ((^[Y1 : a]: ((^[Y2 : b]: ((^[Y3 : a]: (Y0 @ Y3 @ Y2)))))))) != (^[Y0 : a > b > $o]: ((^[Y1 : a]: ((^[Y2 : b]: ((^[Y3 : a]: (Y0 @ Y3 @ Y2))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ Y2 @ Y1))))))))) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f268])).
% 1.56/1.63 thf(f268,plain,(
% 1.56/1.63 ((^[Y0 : a > b > $o]: ((^[Y1 : a]: ((^[Y2 : b]: ((^[Y3 : a]: (Y0 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: ((^[Y7 : a]: (Y7)))))))) @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) != (^[Y0 : a > b > $o]: ((^[Y1 : a]: ((^[Y2 : b]: ((^[Y3 : a]: (Y0 @ Y3 @ Y2))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ Y2 @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6)))))))) @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1))))))))) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f267])).
% 1.56/1.63 thf(f267,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6))))))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : a > b > $o]: ((^[Y1 : a]: ((^[Y2 : b]: ((^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) != (^[Y0 : a > b > $o]: ((^[Y1 : a]: ((^[Y2 : b]: ((^[Y3 : a]: (Y0 @ Y3 @ Y2)))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f266])).
% 1.56/1.63 thf(f266,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6))))))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ Y2 @ Y1))))))))) | (((^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))))) @ (sK19 @ X0)) != ((^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))))) @ (sK19 @ X0)))) ) | ~spl8_1),
% 1.56/1.63 inference(negative_extensionality,[status(thm)],[f265])).
% 1.56/1.63 thf(f265,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a] : (((^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ Y4 @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ Y6 @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6)))))))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f264])).
% 1.56/1.63 thf(f264,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a] : (((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6)))))))) @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y10)))))))) @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1))))))))) | ((^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y8)))))))) @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3))))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6)))))))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f263])).
% 1.56/1.63 thf(f263,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a,X1 : (a > b > $o) > a > b > a > a] : (((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1))))))))) | ((^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: ((^[Y2 : a]: ((^[Y3 : b]: ((^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3))))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f262])).
% 1.56/1.63 thf(f262,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a,X1 : (a > b > $o) > a > b > a > a] : ((((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X1 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4)))))))))))) @ (sK18 @ X1 @ X0)) != ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4)))))))))))) @ (sK18 @ X1 @ X0))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1))))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(negative_extensionality,[status(thm)],[f261])).
% 1.56/1.63 thf(f261,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a,X1 : (a > b > $o) > a > b > a > a] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X1 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4)))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5))))))))) @ Y0 @ Y1 @ Y2) @ Y1))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f260])).
% 1.56/1.63 thf(f260,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > a,X1 : (a > b > $o) > a > b > a > a] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X1 @ Y2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : a > b > $o]: ((^[Y7 : a]: ((^[Y8 : b]: ((^[Y9 : a]: (Y8)))))))) @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y7)))))))) @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y7)))))))) @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y5)))))))) @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2)))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f259])).
% 1.56/1.63 thf(f259,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a > b > a > b,X0 : (a > b > $o) > a > b > a > a,X1 : (a > b > $o) > a > b > a > a] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y5)))))))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X2))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ (X2 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ Y1)))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ Y3)))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ (X2 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ (X2 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ Y5)))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2)))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X1 @ Y2 @ Y3 @ Y4 @ Y5) @ (X2 @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ Y4))))))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f258])).
% 1.56/1.63 thf(f258,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a > b > a > b,X0 : (a > b > $o) > a > b > a > a,X1 : (a > b > $o) > a > b > a > a] : (((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y7)))))))) @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ (X2 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ (X2 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2))))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3 @ Y4) @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y7)))))))) @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3 @ Y4) @ (X2 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y5)))))))) @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5 @ Y6) @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: ((^[Y10 : a]: (Y9)))))))) @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5 @ Y6) @ (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2)))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (Y5)))))))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X2))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X1 @ Y2 @ Y3 @ Y4 @ Y5) @ (X2 @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X0 @ Y2 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : a > b > $o]: ((^[Y7 : a]: ((^[Y8 : b]: ((^[Y9 : a]: (Y8)))))))) @ Y2 @ Y3 @ Y4 @ Y5)))))))))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2 @ Y3) @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: ((^[Y7 : a]: (Y6)))))))) @ Y0 @ Y1 @ Y2 @ Y3))))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f257])).
% 1.56/1.63 thf(f257,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a > b > a > a,X3 : (a > b > $o) > a > b > a > a,X0 : (a > b > $o) > a > b > a > b,X1 : (a > b > $o) > a > b > a > b] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y1)))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X3 @ Y0 @ Y1 @ Y2 @ Y3) @ (X1 @ Y0 @ Y1 @ Y2 @ Y3))))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X3 @ Y1 @ Y2 @ Y3 @ Y4) @ (X1 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X2 @ Y1 @ Y2 @ Y3 @ Y4) @ (X0 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5 @ Y6) @ (X1 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5 @ Y6) @ (X0 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X3 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5 @ Y6) @ (X1 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5 @ Y6) @ (X0 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ (X1 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5 @ Y6) @ (X1 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5 @ Y6) @ (X0 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2))))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X3 @ Y1 @ Y2 @ Y3 @ Y4) @ (X1 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y1 @ (X2 @ Y1 @ Y2 @ Y3 @ Y4) @ (X0 @ Y1 @ Y2 @ Y3 @ Y4))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5 @ Y6) @ (X1 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5 @ Y6) @ (X0 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (X2 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5 @ Y6) @ (X1 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5 @ Y6) @ (X0 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2) @ (X0 @ (sK17 @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5 @ Y6) @ (X1 @ Y3 @ Y4 @ Y5 @ Y6))))))))) @ (^[Y3 : a > b > $o]: ((^[Y4 : a]: (sK10 @ (^[Y5 : b]: (sF4 @ (^[Y6 : a]: (Y3 @ (X2 @ Y3 @ Y4 @ Y5 @ Y6) @ (X0 @ Y3 @ Y4 @ Y5 @ Y6)))))))))) @ Y0 @ Y1 @ Y2)))))))))) | ((X3 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y0 @ (X3 @ Y0 @ Y1 @ Y2 @ Y3) @ (X1 @ Y0 @ Y1 @ Y2 @ Y3))))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X3 @ Y2 @ Y3 @ Y4 @ Y5) @ (X1 @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4 @ Y5) @ (X0 @ Y2 @ Y3 @ Y4 @ Y5)))))))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X0))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X2)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X3)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f256])).
% 1.56/1.63 thf(f256,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a > b > a > a,X3 : (a > b > $o) > a > b > a > a,X0 : (a > b > $o) > a > b > a > b,X1 : (a > b > $o) > a > b > a > b] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (X1 @ Y3 @ Y4 @ Y5 @ Y6)))))))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (X0 @ Y3 @ Y4 @ Y5 @ Y6))))))))))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X3 @ (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (sK10 @ (^[Y5 : b]: (sF4 @ ((^[Y6 : a > b > $o]: ((^[Y7 : a]: ((^[Y8 : b]: ((^[Y9 : a]: (Y6 @ (X3 @ Y6 @ Y7 @ Y8 @ Y9) @ (X1 @ Y6 @ Y7 @ Y8 @ Y9))))))))) @ Y3 @ Y4 @ Y5))))))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))))))) @ Y0 @ Y1 @ Y2)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y2))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X3 @ Y2 @ Y3 @ Y4 @ Y5) @ (X1 @ Y2 @ Y3 @ Y4 @ Y5))))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4 @ Y5) @ (X0 @ Y2 @ Y3 @ Y4 @ Y5)))))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: ((^[Y7 : a]: (Y4 @ (X3 @ Y4 @ Y5 @ Y6 @ Y7) @ (X1 @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: ((^[Y7 : a]: (Y4 @ (X2 @ Y4 @ Y5 @ Y6 @ Y7) @ (X0 @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X3 @ Y2 @ Y3 @ Y4 @ Y5) @ (X1 @ Y2 @ Y3 @ Y4 @ Y5))))))))) @ (sK17 @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y5 @ (X3 @ Y5 @ Y6 @ Y7 @ Y8) @ (X1 @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y5 @ (X2 @ Y5 @ Y6 @ Y7 @ Y8) @ (X0 @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: ((^[Y7 : a]: (Y4 @ (X3 @ Y4 @ Y5 @ Y6 @ Y7) @ (X1 @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: ((^[Y7 : a]: (Y4 @ (X2 @ Y4 @ Y5 @ Y6 @ Y7) @ (X0 @ Y4 @ Y5 @ Y6 @ Y7))))))))) @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: ((^[Y5 : a]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4 @ Y5) @ (X0 @ Y2 @ Y3 @ Y4 @ Y5))))))))) @ (sK17 @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y5 @ (X3 @ Y5 @ Y6 @ Y7 @ Y8) @ (X1 @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: ((^[Y7 : b]: ((^[Y8 : a]: (Y5 @ (X2 @ Y5 @ Y6 @ Y7 @ Y8) @ (X0 @ Y5 @ Y6 @ Y7 @ Y8))))))))) @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1)))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (X1 @ (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (sK10 @ (^[Y5 : b]: (sF4 @ ((^[Y6 : a > b > $o]: ((^[Y7 : a]: ((^[Y8 : b]: ((^[Y9 : a]: (Y6 @ (X3 @ Y6 @ Y7 @ Y8 @ Y9) @ (X1 @ Y6 @ Y7 @ Y8 @ Y9))))))))) @ Y3 @ Y4 @ Y5))))))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))))))) @ Y0 @ Y1 @ Y2)))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (Y1))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (X2 @ Y3 @ Y4 @ Y5 @ Y6)))))))))))))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: ((^[Y6 : a]: (X3 @ Y3 @ Y4 @ Y5 @ Y6)))))))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f255])).
% 1.56/1.63 thf(f255,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > $o,X1 : (a > b > $o) > a > b > a > $o] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (sK10 @ (^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (X1 @ Y0 @ Y1 @ Y2))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (X0 @ (sK17 @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X0 @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (X1 @ (sK17 @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X0 @ Y2 @ Y3 @ Y4)))))))) @ Y0 @ Y1)))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f254])).
% 1.56/1.63 thf(f254,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > $o,X1 : (a > b > $o) > a > b > a > $o] : (((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: (sK10 @ ((^[Y7 : a > b > $o]: ((^[Y8 : a]: ((^[Y9 : b]: (sF4 @ (X0 @ Y7 @ Y8 @ Y9))))))) @ Y5 @ Y6))))) @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (X1 @ Y0 @ Y1 @ Y2))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (X1 @ (sK17 @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: (sF4 @ (X0 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3)))))) @ Y0 @ Y1))))))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0 @ ((^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X1 @ Y1 @ Y2 @ Y3))))))) @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2)))))) @ Y0))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: (X0 @ Y2 @ Y3 @ Y4)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: ((^[Y4 : b]: (X1 @ Y2 @ Y3 @ Y4)))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f253])).
% 1.56/1.63 thf(f253,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > $o,X1 : (a > b > $o) > a > b] : (((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X0 @ Y2 @ Y3 @ Y4)))))))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ X1 @ Y0 @ (X1 @ (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ X1) @ Y0)))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ (^[Y3 : b]: (sF4 @ (X0 @ Y1 @ Y2 @ Y3))))))) @ X1 @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (X0 @ (sK17 @ (^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ (^[Y4 : b]: (sF4 @ (X0 @ Y2 @ Y3 @ Y4))))))) @ X1) @ Y0 @ Y1)))))))) | ((^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (sK10 @ (^[Y2 : b]: (sF4 @ (X0 @ Y0 @ Y1 @ Y2))))))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f252])).
% 1.56/1.63 thf(f252,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b > a > $o,X1 : (a > b > $o) > a > b] : (((sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ X1 @ Y0 @ (X1 @ (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ X1) @ Y0)))) != (sK11 @ (^[Y0 : a]: (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ X1 @ Y0 @ ((^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ (sK17 @ (^[Y1 : a > b > $o]: ((^[Y2 : a]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: ((^[Y5 : b]: (sF4 @ (X0 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ X1) @ Y0))))) | ((^[Y0 : a]: ((^[Y1 : b]: (X0 @ (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (sK11 @ (^[Y3 : a]: (Y2 @ Y3 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: (sK10 @ ((^[Y6 : a > b > $o]: ((^[Y7 : a]: ((^[Y8 : b]: (sF4 @ (X0 @ Y6 @ Y7 @ Y8))))))) @ Y4 @ Y5))))) @ Y2 @ Y3)))) @ (sK10 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))))))) @ Y0 @ Y1)))) != (^[Y0 : a]: ((^[Y1 : b]: ((^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X1 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (sK10 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: ((^[Y6 : b]: (sF4 @ (X0 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X1)))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f251])).
% 1.56/1.63 thf(f251,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((sK11 @ (^[Y0 : a]: (sK17 @ X1 @ X0 @ Y0 @ (X0 @ (sK17 @ X1 @ X0) @ Y0)))) != (sK11 @ (^[Y0 : a]: (sK17 @ X1 @ X0 @ Y0 @ (X1 @ (sK17 @ X1 @ X0) @ Y0))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f250])).
% 1.56/1.63 thf(f250,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : ((((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))) @ (sK17 @ X1 @ X0)) != ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) @ (sK17 @ X1 @ X0))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(negative_extensionality,[status(thm)],[f249])).
% 1.56/1.63 thf(f249,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(duplicate_literal_removal,[status(thm)],[f248])).
% 1.56/1.63 thf(f248,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f247])).
% 1.56/1.63 thf(f247,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | (((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2))))))) @ (sK16 @ X1 @ X0)) != ((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2))))))) @ (sK16 @ X1 @ X0))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(negative_extensionality,[status(thm)],[f246])).
% 1.56/1.63 thf(f246,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2))))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ Y4 @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f245])).
% 1.56/1.63 thf(f245,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2))))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: (Y4)))) @ Y1 @ Y2) @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: (Y6)))) @ Y3 @ Y4) @ (X0 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y3)))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f238])).
% 1.56/1.63 thf(f238,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a > a,X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y3))))))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ (X2 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (sK11 @ (^[Y4 : a]: (Y3 @ (X2 @ Y3 @ Y4) @ (X1 @ Y3 @ Y4)))) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ (X2 @ Y1 @ Y2) @ (X1 @ Y1 @ Y2))))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f237])).
% 1.56/1.63 thf(f237,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a > a,X0 : (a > b > $o) > a > b,X1 : (a > b > $o) > a > b] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (X0 @ Y2 @ Y3)))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (X1 @ Y2 @ Y3))))))))) | ((^[Y0 : a > b > $o]: (sK11 @ ((^[Y1 : a > b > $o]: ((^[Y2 : a]: (Y1 @ (X2 @ Y1 @ Y2) @ (X1 @ Y1 @ Y2))))) @ Y0))) != (^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))))) | ((^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ ((^[Y4 : a > b > $o]: (sK11 @ ((^[Y5 : a > b > $o]: ((^[Y6 : a]: (Y5 @ (X2 @ Y5 @ Y6) @ (X1 @ Y5 @ Y6))))) @ Y4))) @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X0 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))))))))) | ((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y2 @ (X2 @ Y2 @ Y3) @ (X1 @ Y2 @ Y3))))) @ Y1))))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (X2 @ Y2 @ Y3)))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y3)))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f236])).
% 1.56/1.63 thf(f236,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > a > b] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (sK11 @ (^[Y3 : a]: (Y2 @ Y3 @ (X1 @ Y2 @ Y3))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ Y1 @ (X1 @ Y0 @ Y1))))) != X0) | ((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ Y2 @ (X1 @ Y1 @ Y2))))))) != (^[Y0 : a]: (X0)))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f235])).
% 1.56/1.63 thf(f235,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > a > b] : (((^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: (Y4)))) @ Y1 @ Y2) @ (X1 @ Y1 @ Y2))))))) != (^[Y0 : a]: (X0))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (sK11 @ (^[Y3 : a]: (Y2 @ ((^[Y4 : a > b > $o]: ((^[Y5 : a]: (Y5)))) @ Y2 @ Y3) @ (X1 @ Y2 @ Y3))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y3)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) != X0) | ((^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y3)))) @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f234])).
% 1.56/1.63 thf(f234,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X0 : (a > b > $o) > a > a,X1 : (a > b > $o) > a > b] : (((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (Y0))) | ((^[Y0 : a]: (X2)) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ (^[Y2 : a]: (Y1 @ (X0 @ Y1 @ Y2) @ (X1 @ Y1 @ Y2)))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (sK11 @ (^[Y3 : a]: (Y2 @ (X0 @ Y2 @ Y3) @ (X1 @ Y2 @ Y3)))))))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (sK11 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1)))) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))) | ((^[Y0 : a > b > $o]: (sK11 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1) @ (X1 @ Y0 @ Y1))))) != X2)) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f233])).
% 1.56/1.63 thf(f233,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X0 : (a > b > $o) > a > a,X1 : (a > b > $o) > a > b] : (((^[Y0 : a]: (Y0)) != (^[Y0 : a]: (X0 @ (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ ((^[Y2 : a > b > $o]: (sK11 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: (Y3 @ (X0 @ Y3 @ Y4) @ (X1 @ Y3 @ Y4))))) @ Y2))) @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))))))) @ Y0))) | ((^[Y0 : a]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1)))))) != (^[Y0 : a]: (X1 @ (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ ((^[Y2 : a > b > $o]: (sK11 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: (Y3 @ (X0 @ Y3 @ Y4) @ (X1 @ Y3 @ Y4))))) @ Y2))) @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))))))) @ Y0))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (sK11 @ ((^[Y3 : a > b > $o]: ((^[Y4 : a]: (Y3 @ (X0 @ Y3 @ Y4) @ (X1 @ Y3 @ Y4))))) @ Y2))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X2))))) | ((^[Y0 : a > b > $o]: (sK11 @ ((^[Y1 : a > b > $o]: ((^[Y2 : a]: (Y1 @ (X0 @ Y1 @ Y2) @ (X1 @ Y1 @ Y2))))) @ Y0))) != X2) | ((^[Y0 : a]: ((^[Y1 : a > b > $o]: (X2 @ Y1)))) != (^[Y0 : a]: ((^[Y1 : a > b > $o]: (sK11 @ ((^[Y2 : a > b > $o]: ((^[Y3 : a]: (Y2 @ (X0 @ Y2 @ Y3) @ (X1 @ Y2 @ Y3))))) @ Y1))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f232])).
% 1.56/1.63 thf(f232,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > a] : (((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X1 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (X0 != X1)) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f231])).
% 1.56/1.63 thf(f231,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > a] : (((sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ Y1 @ Y0))))) != (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ Y1 @ Y0)))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X1 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4)))))))) @ Y2 @ Y1))))))))) | (X0 != X1)) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f230])).
% 1.56/1.63 thf(f230,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > a] : (((sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ Y1 @ Y0))))) != (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (sK15 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4))))))) @ Y0 @ Y1) @ Y0)))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: ((^[Y6 : a]: (Y6)))))) @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X1 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ ((^[Y6 : a > b > $o]: ((^[Y7 : b]: ((^[Y8 : a]: (Y8)))))) @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1)))))))) != (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))))))))) | (X0 != X1)) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f229])).
% 1.56/1.63 thf(f229,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X0 : (a > b > $o) > a,X1 : (a > b > $o) > b > a > a] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | ((X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X2 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1)))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1))))))))) | ((sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ Y1 @ Y0))))) != (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (X1 @ (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4))))))) @ Y0 @ Y1) @ Y0)))))) | (X0 != X2) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f228])).
% 1.56/1.63 thf(f228,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X0 : (a > b > $o) > a,X1 : (a > b > $o) > b > a > a] : (((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1)))))))) != (X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X2 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: ((^[Y5 : a]: (Y5)))))) @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | (X0 != X2) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4))))))) @ Y0 @ Y1) @ Y0))))) != (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))) @ (X1 @ (sK15 @ X1 @ (^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4))))))) @ Y0 @ Y1) @ Y0)))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y4)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X1)))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f227])).
% 1.56/1.63 thf(f227,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X3 : (a > b > $o) > b > a > a,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > a] : (((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X2 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X3 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1)))))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | ((sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ X3 @ X0 @ (X0 @ (sK15 @ X3 @ X0) @ Y0 @ Y1) @ Y0))))) != (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK15 @ X3 @ X0 @ (X3 @ (sK15 @ X3 @ X0) @ Y0 @ Y1) @ Y0)))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X3)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (X1 != X2)) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f226])).
% 1.56/1.63 thf(f226,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X3 : (a > b > $o) > b > a > a,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > a] : ((X1 != X2) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X3)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X3 @ Y0 @ Y1 @ Y2) @ Y1)))))) @ (sK15 @ X3 @ X0)) != ((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))) @ (sK15 @ X3 @ X0))) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | ((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X2 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X3 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1)))))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(negative_extensionality,[status(thm)],[f225])).
% 1.56/1.63 thf(f225,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X3 : (a > b > $o) > b > a > a,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > a] : (((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X3 @ Y0 @ Y1 @ Y2) @ Y1))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X2 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X3 @ Y1 @ Y2 @ Y3) @ Y2)))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5) @ Y4)))))))) @ Y2 @ Y1)))))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X3)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (X1 != X2)) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f224])).
% 1.56/1.63 thf(f224,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X3 : (a > b > $o) > b > a > a,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > a] : (((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X2 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X3 @ Y1 @ Y2 @ Y3) @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: ((^[Y6 : a]: (Y5)))))) @ Y1 @ Y2 @ Y3))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X2 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X3 @ Y3 @ Y4 @ Y5) @ ((^[Y6 : a > b > $o]: ((^[Y7 : b]: ((^[Y8 : a]: (Y7)))))) @ Y3 @ Y4 @ Y5))))))))) @ Y2 @ Y1)))))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X3 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: ((^[Y5 : a]: (Y4)))))) @ Y0 @ Y1 @ Y2)))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ Y1)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X3)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (X1 != X2)) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f223])).
% 1.56/1.63 thf(f223,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b > a > a,X3 : (a > b > $o) > a,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > b > a > b,X4 : (a > b > $o) > a] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y3)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | ((X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X3 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ Y1)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X4 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3) @ (X1 @ Y1 @ Y2 @ Y3))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X4 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5) @ (X1 @ Y3 @ Y4 @ Y5))))))))) @ Y2 @ Y1)))))))) != (X3 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X3 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ Y1))))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ Y1)))))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2)))))))) | (X3 != X4) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X4)))) != (^[Y0 : b]: ((^[Y1 : a]: (X3)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f222])).
% 1.56/1.63 thf(f222,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b > a > a,X3 : (a > b > $o) > a,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > b > a > b,X4 : (a > b > $o) > a] : (((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X4 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X0 @ Y1 @ Y2 @ Y3) @ (X1 @ Y1 @ Y2 @ Y3))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X4 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X0 @ Y3 @ Y4 @ Y5) @ (X1 @ Y3 @ Y4 @ Y5))))))))) @ Y2 @ Y1)))))))) != (X3 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X3 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: ((^[Y5 : a]: (Y4)))))) @ Y0 @ Y1 @ Y2)))))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y3)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X1))))) | (X3 != X4) | ((^[Y0 : b]: ((^[Y1 : a]: (X4)))) != (^[Y0 : b]: ((^[Y1 : a]: (X3))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X2)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | ((X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X3 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: ((^[Y5 : a]: (Y4)))))) @ Y0 @ Y1 @ Y2))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: ((^[Y5 : a]: (Y4)))))) @ Y0 @ Y1 @ Y2))))))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f221])).
% 1.56/1.63 thf(f221,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b > a > b,X3 : (a > b > $o) > b > a > b,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > b > a > a,X4 : (a > b > $o) > a,X5 : (a > b > $o) > a] : (((^[Y0 : b]: ((^[Y1 : a]: (Y0)))) != (X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X4 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2)))))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X1 @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2))))))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2)))))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X4 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((X4 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X4 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X5 @ Y1) @ (sK10 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ (X1 @ Y1 @ Y2 @ Y3) @ (X3 @ Y1 @ Y2 @ Y3))))))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X5 @ Y3) @ (sK10 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5) @ (X3 @ Y3 @ Y4 @ Y5))))))))) @ Y2 @ Y1))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (X4 != X5) | ((^[Y0 : b]: ((^[Y1 : a]: (X3)))) != (^[Y0 : b]: ((^[Y1 : a]: (X2))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X5)))) != (^[Y0 : b]: ((^[Y1 : a]: (X4)))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f220])).
% 1.56/1.63 thf(f220,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b > a > b,X3 : (a > b > $o) > b > a > b,X0 : (a > b > $o) > b > a > a,X1 : (a > b > $o) > b > a > a,X4 : (a > b > $o) > a,X5 : (a > b > $o) > a] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (X1 @ Y2 @ Y3 @ Y4)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (X0 @ Y2 @ Y3 @ Y4))))))))))) | (X4 != X5) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (X3 @ Y2 @ Y3 @ Y4)))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (X2 @ Y2 @ Y3 @ Y4))))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X5)))) != (^[Y0 : b]: ((^[Y1 : a]: (X4))))) | ((X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X4 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (Y1))))) | ((^[Y0 : b]: ((^[Y1 : a]: (Y0)))) != (X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X4 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2)))))))))))) | ((X4 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X4 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X5 @ Y1) @ (sK10 @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: ((^[Y6 : a]: (Y4 @ (X1 @ Y4 @ Y5 @ Y6) @ (X3 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y1))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X5 @ Y3) @ (sK10 @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: (sF4 @ ((^[Y6 : a > b > $o]: ((^[Y7 : b]: ((^[Y8 : a]: (Y6 @ (X1 @ Y6 @ Y7 @ Y8) @ (X3 @ Y6 @ Y7 @ Y8))))))) @ Y4 @ Y5))))) @ Y3))))) @ Y2 @ Y1))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ ((^[Y1 : a > b > $o]: ((^[Y2 : b]: (sF4 @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: ((^[Y5 : a]: (Y3 @ (X1 @ Y3 @ Y4 @ Y5) @ (X3 @ Y3 @ Y4 @ Y5))))))) @ Y1 @ Y2))))) @ Y0))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X0 @ Y0 @ Y1 @ Y2) @ (X2 @ Y0 @ Y1 @ Y2))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f219])).
% 1.56/1.63 thf(f219,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b > a > a,X3 : (a > b > $o) > b > a > b,X0 : (a > b > $o) > a,X1 : (a > b > $o) > a,X4 : (a > b > $o) > b > $o] : (((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4) @ (X3 @ Y2 @ Y3 @ Y4))))))))))) != (^[Y0 : b]: ((^[Y1 : a]: (X4))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2))))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (sK10 @ (X4 @ Y1))))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (sK10 @ (X4 @ Y3))))) @ Y2 @ Y1))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (Y0)))) != (X3 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2)))))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ (X4 @ Y0))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2)))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (Y1)))) != (X2 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ (X2 @ Y0 @ Y1 @ Y2) @ (X3 @ Y0 @ Y1 @ Y2)))))))))))) | ((^[Y0 : b]: ((^[Y1 : a]: (X1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X0))))) | (X0 != X1)) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f218])).
% 1.56/1.63 thf(f218,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b > a > a,X3 : (a > b > $o) > b > a > b,X0 : (a > b > $o) > a,X1 : (a > b > $o) > a,X4 : (a > b > $o) > b > $o] : (((^[Y0 : b]: ((^[Y1 : a]: (Y0)))) != (^[Y0 : b]: ((^[Y1 : a]: (X3 @ (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X1 @ Y2) @ (sK10 @ (^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: ((^[Y6 : a]: (Y4 @ (X2 @ Y4 @ Y5 @ Y6) @ (X3 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3)))))))) @ Y0 @ Y1))))) | (X0 != X1) | ((^[Y0 : b]: ((^[Y1 : a]: (Y1)))) != (^[Y0 : b]: ((^[Y1 : a]: (X2 @ (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X1 @ Y2) @ (sK10 @ (^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: ((^[Y6 : a]: (Y4 @ (X2 @ Y4 @ Y5 @ Y6) @ (X3 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3)))))))) @ Y0 @ Y1))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: ((^[Y3 : b]: (sF4 @ ((^[Y4 : a > b > $o]: ((^[Y5 : b]: ((^[Y6 : a]: (Y4 @ (X2 @ Y4 @ Y5 @ Y6) @ (X3 @ Y4 @ Y5 @ Y6))))))) @ Y2 @ Y3))))))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (X4 @ Y2))))))) | ((^[Y0 : a > b > $o]: (sK10 @ (X4 @ Y0))) != (^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4) @ (X3 @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1)))))) | ((^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (X1 @ Y2)))))) != (^[Y0 : b]: ((^[Y1 : a]: ((^[Y2 : a > b > $o]: (X0 @ Y2))))))) | ((sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ ((^[Y2 : a > b > $o]: (sK10 @ (X4 @ Y2))) @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ ((^[Y4 : a > b > $o]: (sK10 @ (X4 @ Y4))) @ Y3)))) @ Y2 @ Y1)))))))) != (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: ((^[Y4 : a]: (Y2 @ (X2 @ Y2 @ Y3 @ Y4) @ (X3 @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(equality_resolution,[status(thm)],[f215])).
% 1.56/1.63 thf(f215,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b,X3 : (a > b > $o) > b > a > $o,X0 : (a > b > $o) > a,X1 : (a > b > $o) > a] : (((^[Y0 : b]: ((^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X2 @ Y2)))) @ Y1 @ Y0)))) != (X3 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (X3 @ Y0 @ Y1)))))))))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ (sK10 @ (^[Y1 : b]: (sF4 @ (X3 @ Y0 @ Y1))))))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X2 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X2 @ Y3)))) @ Y2 @ Y1))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ (^[Y1 : b]: (sF4 @ (X3 @ Y0 @ Y1))))) != X2) | (X0 != X1)) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f214])).
% 1.56/1.63 thf(f214,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b,X3 : (a > b > $o) > b > a > $o,X0 : (a > b > $o) > a,X1 : (a > b > $o) > a] : (((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ ((^[Y1 : a > b > $o]: (sK10 @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: (sF4 @ (X3 @ Y2 @ Y3))))) @ Y1))) @ Y0)))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X2 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X2 @ Y3)))) @ Y2 @ Y1))))))))) | ((^[Y0 : a > b > $o]: (X1 @ Y0)) != (^[Y0 : a > b > $o]: (X0 @ Y0))) | ((^[Y0 : b]: (X3 @ (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ ((^[Y2 : a > b > $o]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: (sF4 @ (X3 @ Y3 @ Y4))))) @ Y2))) @ Y1))))) @ Y0)) != (^[Y0 : b]: ((^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X2 @ Y2)))) @ Y1 @ Y0))))) | ((^[Y0 : a > b > $o]: (sK10 @ ((^[Y1 : a > b > $o]: ((^[Y2 : b]: (sF4 @ (X3 @ Y1 @ Y2))))) @ Y0))) != (^[Y0 : a > b > $o]: (X2 @ Y0)))) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.56/1.63 thf(f212,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b,X3 : (a > b > $o) > b > a > $o,X0 : (a > b > $o) > a,X1 : (a > b > $o) > a] : (((^[Y0 : a > b > $o]: (X1 @ Y0)) != (^[Y0 : a > b > $o]: (X0 @ Y0))) | ((X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X1 @ Y0) @ ((^[Y1 : a > b > $o]: (sK10 @ ((^[Y2 : a > b > $o]: ((^[Y3 : b]: (sF4 @ (X3 @ Y2 @ Y3))))) @ Y1))) @ Y0)))))) != (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X2 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X2 @ Y3)))) @ Y2 @ Y1))))))))) | ((^[Y0 : a > b > $o]: (sK10 @ ((^[Y1 : a > b > $o]: ((^[Y2 : b]: (sF4 @ (X3 @ Y1 @ Y2))))) @ Y0))) != (^[Y0 : a > b > $o]: (X2 @ Y0))) | ((^[Y0 : b]: (X3 @ (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ ((^[Y2 : a > b > $o]: (sK10 @ ((^[Y3 : a > b > $o]: ((^[Y4 : b]: (sF4 @ (X3 @ Y3 @ Y4))))) @ Y2))) @ Y1))))) @ Y0)) != (^[Y0 : b]: ((^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X2 @ Y2)))) @ Y1 @ Y0))))) | ($true = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(constrained_superposition,[status(thm)],[f209,f170])).
% 1.56/1.63 thf(f170,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (((sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))) = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f169])).
% 1.56/1.63 thf(f169,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (((sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))) = $false) | ($true = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(boolean_simplification,[status(thm)],[f161])).
% 1.56/1.63 thf(f161,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : ((((sF3 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) => $true) = $false) | ((sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))) = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(cases_simplifying,[status(thm)],[f158])).
% 1.56/1.63 thf(f158,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($false = ((sF3 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))) => (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f157])).
% 1.56/1.63 thf(f157,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : ((((^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.56/1.63 thf(f153,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : ((((^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) = $false) | ($true = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(superposition,[status(thm)],[f105,f141])).
% 1.56/1.63 thf(f141,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($false = (sF2 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.56/1.63 thf(f140,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($false = ((^[Y0 : (a > b > $o) > b]: (sF2 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (Y0 @ Y1)))))) @ X1))) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.56/1.63 thf(f137,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = $false) | ($false = ((^[Y0 : (a > b > $o) > b]: (sF2 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (Y0 @ Y1)))))) @ X1))) ) | ~spl8_1),
% 1.56/1.63 inference(superposition,[status(thm)],[f134,f133])).
% 1.56/1.63 thf(f133,plain,(
% 1.56/1.63 ( ! [X1 : (a > b > $o) > a] : (((sF1 @ (^[Y0 : (a > b > $o) > b]: (sF2 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (Y0 @ Y1))))))) = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(backward_demodulation,[status(thm)],[f50,f124])).
% 1.56/1.63 thf(f124,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a] : (((sF5 @ X0) = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.56/1.63 thf(f121,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a] : (($true = $false) | ((sF5 @ X0) = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(superposition,[status(thm)],[f45,f117])).
% 1.56/1.63 thf(f117,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > a,X1 : ((a > b > $o) > a) > $o] : (($true = (sF0 @ X1)) | ($false = (X1 @ X2))) )),
% 1.56/1.63 inference(pi_clausification,[status(thm)],[f57])).
% 1.56/1.63 thf(f57,plain,(
% 1.56/1.63 ( ! [X1 : ((a > b > $o) > a) > $o] : (($false = (?? @ ((a > b > $o) > a) @ X1)) | ($true = (sF0 @ X1))) )),
% 1.56/1.63 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.56/1.63 thf(f47,plain,(
% 1.56/1.63 ( ! [X1 : ((a > b > $o) > a) > $o] : (((sF0 @ X1) = (?? @ ((a > b > $o) > a) @ X1))) )),
% 1.56/1.63 inference(argument_congruence,[status(thm)],[f7])).
% 1.56/1.63 thf(f7,definition,(
% 1.56/1.63 (?? @ ((a > b > $o) > a) = sF0)),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f45,plain,(
% 1.56/1.63 ($false = (sF0 @ sF5)) | ~spl8_1),
% 1.56/1.63 inference(forward_demodulation,[status(thm)],[f13,f23])).
% 1.56/1.63 thf(f23,plain,(
% 1.56/1.63 (sF6 = $false) | ~spl8_1),
% 1.56/1.63 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.56/1.63 thf(f21,definition,(
% 1.56/1.63 spl8_1 <=> (sF6 = $false)),
% 1.56/1.63 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.56/1.63 thf(f13,definition,(
% 1.56/1.63 (sF6 = (sF0 @ sF5))),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f50,plain,(
% 1.56/1.63 ( ! [X1 : (a > b > $o) > a] : (((sF1 @ (^[Y0 : (a > b > $o) > b]: (sF2 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X1 @ Y1) @ (Y0 @ Y1))))))) = (sF5 @ X1))) )),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.56/1.63 thf(f49,plain,(
% 1.56/1.63 ( ! [X1 : (a > b > $o) > a] : (((sF5 @ X1) = ((^[Y0 : (a > b > $o) > a]: (sF1 @ (^[Y1 : (a > b > $o) > b]: (sF2 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))) @ X1))) )),
% 1.56/1.63 inference(argument_congruence,[status(thm)],[f12])).
% 1.56/1.63 thf(f12,definition,(
% 1.56/1.63 ((^[Y0 : (a > b > $o) > a]: (sF1 @ (^[Y1 : (a > b > $o) > b]: (sF2 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))) = sF5)),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f134,plain,(
% 1.56/1.63 ( ! [X2 : (a > b > $o) > b,X1 : ((a > b > $o) > b) > $o] : (($true = (sF1 @ X1)) | ($false = (X1 @ X2))) )),
% 1.56/1.63 inference(pi_clausification,[status(thm)],[f59])).
% 1.56/1.63 thf(f59,plain,(
% 1.56/1.63 ( ! [X1 : ((a > b > $o) > b) > $o] : (($false = (?? @ ((a > b > $o) > b) @ X1)) | ($true = (sF1 @ X1))) )),
% 1.56/1.63 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.56/1.63 thf(f48,plain,(
% 1.56/1.63 ( ! [X1 : ((a > b > $o) > b) > $o] : (((sF1 @ X1) = (?? @ ((a > b > $o) > b) @ X1))) )),
% 1.56/1.63 inference(argument_congruence,[status(thm)],[f8])).
% 1.56/1.63 thf(f8,definition,(
% 1.56/1.63 (?? @ ((a > b > $o) > b) = sF1)),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f105,plain,(
% 1.56/1.63 ( ! [X1 : (a > b > $o) > $o] : (((sF2 @ X1) = $true) | ((X1 @ (sK12 @ X1)) = $false)) )),
% 1.56/1.63 inference(sigma_clausification,[status(thm)],[f55])).
% 1.56/1.63 thf(f55,plain,(
% 1.56/1.63 ( ! [X1 : (a > b > $o) > $o] : (($false = (!! @ (a > b > $o) @ X1)) | ((sF2 @ X1) = $true)) )),
% 1.56/1.63 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.56/1.63 thf(f46,plain,(
% 1.56/1.63 ( ! [X1 : (a > b > $o) > $o] : (((sF2 @ X1) = (!! @ (a > b > $o) @ X1))) )),
% 1.56/1.63 inference(argument_congruence,[status(thm)],[f9])).
% 1.56/1.63 thf(f9,definition,(
% 1.56/1.63 (sF2 = !! @ (a > b > $o))),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f209,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1)))))))) @ (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f208])).
% 1.56/1.63 thf(f208,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = ((^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))) @ (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f206])).
% 1.56/1.63 thf(f206,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = ((^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1))))))) @ (sK11 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1)))))))))) | ($true = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(superposition,[status(thm)],[f197,f77])).
% 1.56/1.63 thf(f77,plain,(
% 1.56/1.63 ( ! [X1 : a > $o] : (($false = (sF4 @ X1)) | ((X1 @ (sK11 @ X1)) = $true)) )),
% 1.56/1.63 inference(sigma_clausification,[status(thm)],[f53])).
% 1.56/1.63 thf(f53,plain,(
% 1.56/1.63 ( ! [X1 : a > $o] : (((?? @ a @ X1) = $true) | ($false = (sF4 @ X1))) )),
% 1.56/1.63 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.56/1.63 thf(f44,plain,(
% 1.56/1.63 ( ! [X1 : a > $o] : (((?? @ a @ X1) = (sF4 @ X1))) )),
% 1.56/1.63 inference(argument_congruence,[status(thm)],[f11])).
% 1.56/1.63 thf(f11,definition,(
% 1.56/1.63 (?? @ a = sF4)),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f197,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = (sF4 @ (^[Y0 : a]: (sK12 @ (^[Y1 : a > b > $o]: ((sF3 @ (^[Y2 : b]: (sF4 @ (^[Y3 : a]: (Y1 @ Y3 @ Y2))))) => (Y1 @ (X0 @ Y1) @ (X1 @ Y1)))) @ Y0 @ (sK10 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (sK12 @ (^[Y3 : a > b > $o]: ((sF3 @ (^[Y4 : b]: (sF4 @ (^[Y5 : a]: (Y3 @ Y5 @ Y4))))) => (Y3 @ (X0 @ Y3) @ (X1 @ Y3)))) @ Y2 @ Y1)))))))))) ) | ~spl8_1),
% 1.56/1.63 inference(beta_eta_normalization,[status(thm)],[f196])).
% 1.56/1.63 thf(f196,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = ((^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))) @ (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))))))) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f194])).
% 1.56/1.63 thf(f194,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = ((^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0)))) @ (sK10 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))))) | ($true = $false)) ) | ~spl8_1),
% 1.56/1.63 inference(superposition,[status(thm)],[f172,f65])).
% 1.56/1.63 thf(f65,plain,(
% 1.56/1.63 ( ! [X1 : b > $o] : (($false = (sF3 @ X1)) | ((X1 @ (sK10 @ X1)) = $true)) )),
% 1.56/1.63 inference(sigma_clausification,[status(thm)],[f51])).
% 1.56/1.63 thf(f51,plain,(
% 1.56/1.63 ( ! [X1 : b > $o] : (($true = (?? @ b @ X1)) | ($false = (sF3 @ X1))) )),
% 1.56/1.63 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.56/1.63 thf(f43,plain,(
% 1.56/1.63 ( ! [X1 : b > $o] : (((?? @ b @ X1) = (sF3 @ X1))) )),
% 1.56/1.63 inference(argument_congruence,[status(thm)],[f10])).
% 1.56/1.63 thf(f10,definition,(
% 1.56/1.63 (sF3 = ?? @ b)),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f172,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = (sF3 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))))) ) | ~spl8_1),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.56/1.63 thf(f171,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($true = $false) | ($true = (sF3 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))))) ) | ~spl8_1),
% 1.56/1.63 inference(boolean_simplification,[status(thm)],[f160])).
% 1.56/1.63 thf(f160,plain,(
% 1.56/1.63 ( ! [X0 : (a > b > $o) > a,X1 : (a > b > $o) > b] : (($false = ($false => (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))) @ (X0 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0)))))) @ (X1 @ (sK12 @ (^[Y0 : a > b > $o]: ((sF3 @ (^[Y1 : b]: (sF4 @ (^[Y2 : a]: (Y0 @ Y2 @ Y1))))) => (Y0 @ (X0 @ Y0) @ (X1 @ Y0))))))))) | ($true = (sF3 @ (^[Y0 : b]: (sF4 @ (^[Y1 : a]: (sK12 @ (^[Y2 : a > b > $o]: ((sF3 @ (^[Y3 : b]: (sF4 @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (X0 @ Y2) @ (X1 @ Y2)))) @ Y1 @ Y0))))))) ) | ~spl8_1),
% 1.56/1.63 inference(cases_simplifying,[status(thm)],[f158])).
% 1.56/1.63 thf(f41,plain,(
% 1.56/1.63 ~spl8_2 | ~spl8_4),
% 1.56/1.63 inference(avatar_contradiction_clause,[status(thm)],[f40])).
% 1.56/1.63 thf(f40,plain,(
% 1.56/1.63 $false | (~spl8_2 | ~spl8_4)),
% 1.56/1.63 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.56/1.63 thf(f39,plain,(
% 1.56/1.63 ($true = $false) | (~spl8_2 | ~spl8_4)),
% 1.56/1.63 inference(forward_demodulation,[status(thm)],[f36,f27])).
% 1.56/1.63 thf(f27,plain,(
% 1.56/1.63 (sF7 = $false) | ~spl8_2),
% 1.56/1.63 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.56/1.63 thf(f25,definition,(
% 1.56/1.63 spl8_2 <=> (sF7 = $false)),
% 1.56/1.63 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.56/1.63 thf(f36,plain,(
% 1.56/1.63 (sF7 = $true) | ~spl8_4),
% 1.56/1.63 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.56/1.63 thf(f34,definition,(
% 1.56/1.63 spl8_4 <=> (sF7 = $true)),
% 1.56/1.63 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.56/1.63 thf(f38,plain,(
% 1.56/1.63 spl8_4),
% 1.56/1.63 inference(avatar_split_clause,[status(thm)],[f15,f34])).
% 1.56/1.63 thf(f15,plain,(
% 1.56/1.63 (sF7 = $true)),
% 1.56/1.63 inference(definition_folding,[status(thm)],[f6,f14,f13,f12,f11,f10,f9,f8,f7])).
% 1.56/1.63 thf(f14,definition,(
% 1.56/1.63 ((~ sF6) = sF7)),
% 1.56/1.63 introduced(definition,[],[function_definition])).
% 1.56/1.63 thf(f6,plain,(
% 1.56/1.63 ($true = (~ (?? @ ((a > b > $o) > a) @ (^[Y0 : (a > b > $o) > a]: (?? @ ((a > b > $o) > b) @ (^[Y1 : (a > b > $o) > b]: (!! @ (a > b > $o) @ (^[Y2 : a > b > $o]: ((?? @ b @ (^[Y3 : b]: (?? @ a @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))))))),
% 1.56/1.63 inference(cnf_transformation,[status(thm)],[f5])).
% 1.56/1.63 thf(f5,plain,(
% 1.56/1.63 ($true = (~ (?? @ ((a > b > $o) > a) @ (^[Y0 : (a > b > $o) > a]: (?? @ ((a > b > $o) > b) @ (^[Y1 : (a > b > $o) > b]: (!! @ (a > b > $o) @ (^[Y2 : a > b > $o]: ((?? @ b @ (^[Y3 : b]: (?? @ a @ (^[Y4 : a]: (Y2 @ Y4 @ Y3))))) => (Y2 @ (Y0 @ Y2) @ (Y1 @ Y2)))))))))))),
% 1.56/1.63 inference(fool_elimination,[status(thm)],[f4])).
% 1.56/1.63 thf(f4,plain,(
% 1.56/1.63 ~? [X0 : (a > b > $o) > b,X1 : (a > b > $o) > a] : ! [X2 : a > b > $o] : (? [X3 : a,X4 : b] : (X2 @ X3 @ X4) => (X2 @ (X1 @ X2) @ (X0 @ X2)))),
% 1.56/1.63 inference(rectify,[status(thm)],[f2])).
% 1.56/1.63 thf(f2,negated_conjecture,(
% 1.56/1.63 ~? [X1 : (a > b > $o) > b,X0 : (a > b > $o) > a] : ! [X2 : a > b > $o] : (? [X3 : a,X4 : b] : (X2 @ X3 @ X4) => (X2 @ (X0 @ X2) @ (X1 @ X2)))),
% 1.56/1.63 inference(negated_conjecture,[status(cth)],[f1])).
% 1.56/1.63 thf(f1,conjecture,(
% 1.56/1.63 ? [X1 : (a > b > $o) > b,X0 : (a > b > $o) > a] : ! [X2 : a > b > $o] : (? [X3 : a,X4 : b] : (X2 @ X3 @ X4) => (X2 @ (X0 @ X2) @ (X1 @ X2)))),
% 1.56/1.63 file('/export/starexec/sandbox/tmp/tmp.eE209qcMJe/DTF2THF_26135.p',claim)).
% 1.56/1.63 thf(f28,plain,(
% 1.56/1.63 spl8_1 | spl8_2),
% 1.56/1.63 inference(avatar_split_clause,[status(thm)],[f19,f25,f21])).
% 1.56/1.63 thf(f19,plain,(
% 1.56/1.63 (sF7 = $false) | (sF6 = $false)),
% 1.56/1.63 inference(boolean_simplification,[status(thm)],[f16])).
% 1.56/1.63 thf(f16,plain,(
% 1.56/1.63 (sF6 = $false) | ((~ $true) = sF7)),
% 1.56/1.63 inference(cases_simplifying,[status(thm)],[f14])).
% 1.56/1.63 % SZS output end Proof for DTF2THF_26135
% 1.56/1.63 % (26333)------------------------------
% 1.56/1.63 % (26333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.56/1.63 % (26333)Termination reason: Refutation
% 1.56/1.63
% 1.56/1.63 % (26333)Memory used [KB]: 7164
% 1.56/1.63 % (26333)Time elapsed: 0.065 s
% 1.56/1.63 % (26333)Instructions burned: 184 (million)
% 1.56/1.63 % (26333)------------------------------
% 1.56/1.63 % (26333)------------------------------
% 1.56/1.63 % (26241)Success in time 0.344 s
%------------------------------------------------------------------------------