TSTP Solution File: GRA030^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GRA030^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : 600s
% DateTime : Sat Jul 16 07:21:40 EDT 2022
% Result : Theorem 26.02s 26.45s
% Output : Proof 26.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 526
% Syntax : Number of formulae : 557 ( 39 unt; 23 typ; 25 def)
% Number of atoms : 1951 ( 145 equ; 0 cnn)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 2653 ( 899 ~; 526 |; 0 &; 578 @)
% ( 195 <=>; 455 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 242 ( 242 >; 0 *; 0 +; 0 <<)
% Number of symbols : 225 ( 223 usr; 212 con; 0-2 aty)
% Number of variables : 168 ( 25 ^ 143 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: ( $o > $o ) > $o ).
thf(ty_eigen__14,type,
eigen__14: $o ).
thf(ty_eigen__12,type,
eigen__12: $o > $o ).
thf(ty_eigen__2,type,
eigen__2: $o > $o ).
thf(ty_eigen__16,type,
eigen__16: $o ).
thf(ty_eigen__25,type,
eigen__25: $o ).
thf(ty_eigen__7,type,
eigen__7: ( $o > $o ) > $o ).
thf(ty_eigen__24,type,
eigen__24: $o ).
thf(ty_eigen__1,type,
eigen__1: $o > $o ).
thf(ty_eigen__15,type,
eigen__15: $o ).
thf(ty_eigen__0,type,
eigen__0: $o > $o ).
thf(ty_eigen__21,type,
eigen__21: $o ).
thf(ty_eigen__4,type,
eigen__4: $o > $o ).
thf(ty_eigen__5,type,
eigen__5: ( $o > $o ) > $o ).
thf(ty_eigen__19,type,
eigen__19: $o ).
thf(ty_eigen__11,type,
eigen__11: $o > $o ).
thf(ty_eigen__3,type,
eigen__3: $o > $o ).
thf(ty_eigen__17,type,
eigen__17: $o ).
thf(ty_eigen__8,type,
eigen__8: ( $o > $o ) > $o ).
thf(ty_eigen__13,type,
eigen__13: ( $o > $o ) > $o ).
thf(ty_eigen__20,type,
eigen__20: $o ).
thf(ty_eigen__28,type,
eigen__28: $o ).
thf(ty_eigen__23,type,
eigen__23: $o ).
thf(h0,assumption,
! [X1: ( $o > $o ) > $o,X2: $o > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: ( $o > $o ) > $o] :
( ~ ( ( X3 @ X1 )
=> ( X3 @ X2 ) )
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__0 )
=> ( X3 @ eigen__1 ) )
=> ( X3 @ eigen__2 ) )
=> ( X3 @ X1 ) )
=> ( X3 @ X2 ) )
=> ( X4 @ eigen__0 ) )
=> ~ ( X4 @ eigen__1 ) )
=> ( X4 @ eigen__2 ) )
=> ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( X5 @ eigen__0 ) )
=> ( X5 @ eigen__1 ) )
=> ~ ( X5 @ eigen__2 ) )
=> ( X5 @ X1 ) )
=> ( X5 @ X2 ) )
=> ( X6 @ eigen__0 ) )
=> ( X6 @ eigen__1 ) )
=> ( X6 @ eigen__2 ) )
=> ~ ( X6 @ X1 ) )
=> ( X6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o,X8: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 @ eigen__0 )
=> ( X5 @ X1 ) )
=> ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( X5 @ X4 ) )
=> ( X6 @ eigen__0 ) )
=> ~ ( X6 @ X1 ) )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( X7 @ eigen__0 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) )
=> ( X7 @ X4 ) )
=> ( X8 @ eigen__0 ) )
=> ( X8 @ X1 ) )
=> ( X8 @ X2 ) )
=> ~ ( X8 @ X3 ) )
=> ( X8 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__3 @ X1 )
!= ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__3 @ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(h2,assumption,
! [X1: ( ( $o > $o ) > $o ) > $o,X2: ( $o > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__2
@ ^ [X1: ( $o > $o ) > $o] :
~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__5 @ eigen__0 )
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) )
=> ( eigen__5 @ eigen__3 ) )
=> ( eigen__5 @ eigen__4 ) )
=> ( X1 @ eigen__0 ) )
=> ~ ( X1 @ eigen__1 ) )
=> ( X1 @ eigen__2 ) )
=> ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__0 ) )
=> ( X2 @ eigen__1 ) )
=> ~ ( X2 @ eigen__2 ) )
=> ( X2 @ eigen__3 ) )
=> ( X2 @ eigen__4 ) )
=> ( X3 @ eigen__0 ) )
=> ( X3 @ eigen__1 ) )
=> ( X3 @ eigen__2 ) )
=> ~ ( X3 @ eigen__3 ) )
=> ( X3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__3 @ X1 )
!= ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: $o > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o,X8: ( $o > $o ) > $o,X9: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X6 @ X1 )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( X6 @ X5 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) )
=> ( X7 @ X4 ) )
=> ( X7 @ X5 ) )
=> ( X8 @ X1 ) )
=> ( X8 @ X2 ) )
=> ~ ( X8 @ X3 ) )
=> ( X8 @ X4 ) )
=> ( X8 @ X5 ) )
=> ( X9 @ X1 ) )
=> ( X9 @ X2 ) )
=> ( X9 @ X3 ) )
=> ~ ( X9 @ X4 ) )
=> ( X9 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $o > $o] :
~ ~ $false ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: ( $o > $o ) > $o] :
( ~ ( ( X2 @ eigen__11 )
=> ( X2 @ X1 ) )
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__2
@ ^ [X1: ( $o > $o ) > $o] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__5 @ eigen__0 )
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) )
=> ( eigen__5 @ eigen__3 ) )
=> ( eigen__5 @ eigen__4 ) )
=> ( eigen__6 @ eigen__0 ) )
=> ~ ( eigen__6 @ eigen__1 ) )
=> ( eigen__6 @ eigen__2 ) )
=> ( eigen__6 @ eigen__3 ) )
=> ( eigen__6 @ eigen__4 ) )
=> ( eigen__7 @ eigen__0 ) )
=> ( eigen__7 @ eigen__1 ) )
=> ~ ( eigen__7 @ eigen__2 ) )
=> ( eigen__7 @ eigen__3 ) )
=> ( eigen__7 @ eigen__4 ) )
=> ( X1 @ eigen__0 ) )
=> ( X1 @ eigen__1 ) )
=> ( X1 @ eigen__2 ) )
=> ~ ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__21,definition,
( eigen__21
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__2 @ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__21])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ eigen__0 )
=> ( X4 @ eigen__1 ) )
=> ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ eigen__0 ) )
=> ~ ( X5 @ eigen__1 ) )
=> ( X5 @ X1 ) )
=> ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( X6 @ eigen__0 ) )
=> ( X6 @ eigen__1 ) )
=> ~ ( X6 @ X1 ) )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X7 @ eigen__0 ) )
=> ( X7 @ eigen__1 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__23,definition,
( eigen__23
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__23])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__2
@ ^ [X1: ( $o > $o ) > $o] :
~ ( ~ ( ( X1 @ eigen__11 )
=> ( X1 @ eigen__12 ) )
=> ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__0 )
=> ( X2 @ eigen__1 ) )
=> ( X2 @ eigen__2 ) )
=> ( X2 @ eigen__3 ) )
=> ( X2 @ X1 ) )
=> ( X3 @ eigen__0 ) )
=> ~ ( X3 @ eigen__1 ) )
=> ( X3 @ eigen__2 ) )
=> ( X3 @ eigen__3 ) )
=> ( X3 @ X1 ) )
=> ( X4 @ eigen__0 ) )
=> ( X4 @ eigen__1 ) )
=> ~ ( X4 @ eigen__2 ) )
=> ( X4 @ eigen__3 ) )
=> ( X4 @ X1 ) )
=> ( X5 @ eigen__0 ) )
=> ( X5 @ eigen__1 ) )
=> ( X5 @ eigen__2 ) )
=> ~ ( X5 @ eigen__3 ) )
=> ( X5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__3 @ X1 )
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__20,definition,
( eigen__20
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__2 @ X1 )
!= ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__20])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o] : ~ $false ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__25,definition,
( eigen__25
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__25])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__2
@ ^ [X1: ( $o > $o ) > $o] :
~ ! [X2: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__5 @ eigen__0 )
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) )
=> ( eigen__5 @ eigen__3 ) )
=> ( eigen__5 @ eigen__4 ) )
=> ( eigen__6 @ eigen__0 ) )
=> ~ ( eigen__6 @ eigen__1 ) )
=> ( eigen__6 @ eigen__2 ) )
=> ( eigen__6 @ eigen__3 ) )
=> ( eigen__6 @ eigen__4 ) )
=> ( X1 @ eigen__0 ) )
=> ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__2 ) )
=> ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__0 ) )
=> ( X2 @ eigen__1 ) )
=> ( X2 @ eigen__2 ) )
=> ~ ( X2 @ eigen__3 ) )
=> ( X2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__0 @ X1 )
!= ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__2
@ ^ [X1: ( $o > $o ) > $o] :
~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__0 )
=> ( X1 @ eigen__1 ) )
=> ( X1 @ eigen__2 ) )
=> ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__0 ) )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 @ eigen__2 ) )
=> ( X2 @ eigen__3 ) )
=> ( X2 @ eigen__4 ) )
=> ( X3 @ eigen__0 ) )
=> ( X3 @ eigen__1 ) )
=> ~ ( X3 @ eigen__2 ) )
=> ( X3 @ eigen__3 ) )
=> ( X3 @ eigen__4 ) )
=> ( X4 @ eigen__0 ) )
=> ( X4 @ eigen__1 ) )
=> ( X4 @ eigen__2 ) )
=> ~ ( X4 @ eigen__3 ) )
=> ( X4 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__24,definition,
( eigen__24
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__24])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__1
@ ^ [X1: $o] :
( ( eigen__2 @ X1 )
!= ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: $o > $o,X2: $o > $o] : ~ $false
=> ~ ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o] :
( ~ ( ( X3 @ X1 )
=> ( X3 @ X2 ) )
=> ~ $false ) )
=> ~ ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: $o > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o,X8: ( $o > $o ) > $o,X9: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X6 @ X1 )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( X6 @ X5 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) )
=> ( X7 @ X4 ) )
=> ( X7 @ X5 ) )
=> ( X8 @ X1 ) )
=> ( X8 @ X2 ) )
=> ~ ( X8 @ X3 ) )
=> ( X8 @ X4 ) )
=> ( X8 @ X5 ) )
=> ( X9 @ X1 ) )
=> ( X9 @ X2 ) )
=> ( X9 @ X3 ) )
=> ~ ( X9 @ X4 ) )
=> ( X9 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__5 @ eigen__0 )
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) )
=> ( eigen__5 @ eigen__3 ) )
=> ( eigen__5 @ eigen__4 ) )
=> ( eigen__6 @ eigen__0 ) )
=> ~ ( eigen__6 @ eigen__1 ) )
=> ( eigen__6 @ eigen__2 ) )
=> ( eigen__6 @ eigen__3 ) )
=> ( eigen__6 @ eigen__4 ) )
=> ( eigen__7 @ eigen__0 ) )
=> ( eigen__7 @ eigen__1 ) )
=> ~ ( eigen__7 @ eigen__2 ) )
=> ( eigen__7 @ eigen__3 ) )
=> ( eigen__7 @ eigen__4 ) )
=> ( eigen__8 @ eigen__0 ) )
=> ( eigen__8 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__6 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__3 @ eigen__14 )
= ( eigen__4 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__7 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> eigen__17 ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__28 )
= ( eigen__4 @ eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__7 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__19 = eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o,X8: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 @ eigen__0 )
=> ( X5 @ X1 ) )
=> ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( X5 @ X4 ) )
=> ( X6 @ eigen__0 ) )
=> ~ ( X6 @ X1 ) )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( X7 @ eigen__0 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) )
=> ( X7 @ X4 ) )
=> ( X8 @ eigen__0 ) )
=> ( X8 @ X1 ) )
=> ( X8 @ X2 ) )
=> ~ ( X8 @ X3 ) )
=> ( X8 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__7 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP6 = eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__6 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__14 = eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__23 = eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> eigen__19 ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $o > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__0 )
=> ( X2 @ eigen__1 ) )
=> ( X2 @ eigen__2 ) )
=> ( X2 @ eigen__3 ) )
=> ( X2 @ X1 ) )
=> ( X3 @ eigen__0 ) )
=> ~ ( X3 @ eigen__1 ) )
=> ( X3 @ eigen__2 ) )
=> ( X3 @ eigen__3 ) )
=> ( X3 @ X1 ) )
=> ( X4 @ eigen__0 ) )
=> ( X4 @ eigen__1 ) )
=> ~ ( X4 @ eigen__2 ) )
=> ( X4 @ eigen__3 ) )
=> ( X4 @ X1 ) )
=> ( X5 @ eigen__0 ) )
=> ( X5 @ eigen__1 ) )
=> ( X5 @ eigen__2 ) )
=> ~ ( X5 @ eigen__3 ) )
=> ( X5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__5 @ eigen__0 )
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) )
=> ( eigen__5 @ eigen__3 ) )
=> ( eigen__5 @ eigen__4 ) )
=> ( eigen__6 @ eigen__0 ) )
=> ~ ( eigen__6 @ eigen__1 ) )
=> ( eigen__6 @ eigen__2 ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> eigen__28 ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__21 = eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__16 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__2 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__24 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__3 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__3 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__23 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__7 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__3 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $o > $o,X2: ( $o > $o ) > $o] :
( ~ ( ( X2 @ eigen__11 )
=> ( X2 @ X1 ) )
=> ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( eigen__3 @ eigen__15 )
= ( eigen__2 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__14 = eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $o] :
( ( eigen__2 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $o] :
( ( sP22 = X1 )
=> ( X1 = sP22 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $o > $o,X2: $o > $o] : ~ $false ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__1 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__20 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: ( $o > $o ) > $o] :
( ~ ( ( X1 @ eigen__11 )
=> ( X1 @ eigen__12 ) )
=> ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__0 @ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> eigen__15 ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__20 = sP46 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__23 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ( sP22 = eigen__25 )
=> ( eigen__25 = sP22 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP22 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP21
=> sP3 )
=> sP12 )
=> sP31 )
=> ~ sP8 )
=> ( eigen__7 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__6 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( eigen__1 @ eigen__23 )
= ( eigen__3 @ eigen__23 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP22 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> eigen__14 ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP19 = sP46 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ ( ~ sP51
=> sP5 )
=> ( eigen__8 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> $false ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP6 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( sP32
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) )
=> ( eigen__5 @ eigen__3 ) )
=> ( eigen__5 @ eigen__4 ) )
=> sP52 )
=> ~ ( eigen__6 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP46 = eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ ( ~ ( ~ sP21
=> sP3 )
=> sP12 )
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ ( ( eigen__13 @ eigen__11 )
=> ( eigen__13 @ eigen__12 ) )
=> ~ sP58 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $o] :
( ( eigen__3 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( eigen__24 = eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( eigen__4 @ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( eigen__2 @ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( eigen__1 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( eigen__24 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP27 = sP40 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( eigen__4 @ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP6 = sP46 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( eigen__20 = eigen__23 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ sP21
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( eigen__21 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( ( eigen__1 @ eigen__25 )
= ( eigen__0 @ eigen__25 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( eigen__3 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( sP6 = eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( eigen__25 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( sP19 = sP22 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( sP55 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o] :
( ~ ( ( X3 @ X1 )
=> ( X3 @ X2 ) )
=> ~ sP58 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( eigen__16 = eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( eigen__16 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( sP22 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( eigen__2 @ eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ~ ( sP32
=> ( eigen__5 @ eigen__1 ) )
=> ( eigen__5 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> eigen__16 ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( sP19 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( eigen__21 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( eigen__1 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: $o] :
( ( eigen__2 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( eigen__24 = sP22 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( sP54
=> sP95 ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( eigen__8 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( eigen__8 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( eigen__24 = eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( eigen__23 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( eigen__20 = sP89 ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( eigen__21 = sP46 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( sP55 = sP22 ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( eigen__6 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( sP46 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( eigen__25 = eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( sP46 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> eigen__23 ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP74
=> ( X1 @ eigen__0 ) )
=> ( X1 @ eigen__1 ) )
=> ~ ( X1 @ eigen__2 ) )
=> ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__0 ) )
=> ( X2 @ eigen__1 ) )
=> ( X2 @ eigen__2 ) )
=> ~ ( X2 @ eigen__3 ) )
=> ( X2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( eigen__24 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ( eigen__20 = eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( eigen__3 @ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__0 )
=> ( X3 @ eigen__1 ) )
=> ( X3 @ eigen__2 ) )
=> ( X3 @ X1 ) )
=> ( X3 @ X2 ) )
=> ( X4 @ eigen__0 ) )
=> ~ ( X4 @ eigen__1 ) )
=> ( X4 @ eigen__2 ) )
=> ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( X5 @ eigen__0 ) )
=> ( X5 @ eigen__1 ) )
=> ~ ( X5 @ eigen__2 ) )
=> ( X5 @ X1 ) )
=> ( X5 @ X2 ) )
=> ( X6 @ eigen__0 ) )
=> ( X6 @ eigen__1 ) )
=> ( X6 @ eigen__2 ) )
=> ~ ( X6 @ X1 ) )
=> ( X6 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ( eigen__3 @ sP108 ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( sP22 = eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( eigen__0 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__0 )
=> ( X1 @ eigen__1 ) )
=> ( X1 @ eigen__2 ) )
=> ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__0 ) )
=> ~ ( X2 @ eigen__1 ) )
=> ( X2 @ eigen__2 ) )
=> ( X2 @ eigen__3 ) )
=> ( X2 @ eigen__4 ) )
=> ( X3 @ eigen__0 ) )
=> ( X3 @ eigen__1 ) )
=> ~ ( X3 @ eigen__2 ) )
=> ( X3 @ eigen__3 ) )
=> ( X3 @ eigen__4 ) )
=> ( X4 @ eigen__0 ) )
=> ( X4 @ eigen__1 ) )
=> ( X4 @ eigen__2 ) )
=> ~ ( X4 @ eigen__3 ) )
=> ( X4 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( eigen__8 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ! [X1: $o] :
( ( eigen__3 @ X1 )
= ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( eigen__3 @ sP46 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( sP19 = eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ! [X1: $o] :
( ( eigen__3 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> eigen__24 ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( sP87
= ( eigen__1 @ eigen__20 ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( sP89 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( sP22 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( eigen__1 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( eigen__0 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( eigen__20 = eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( ~ sP74
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> eigen__25 ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ( sP126
=> sP103 ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( eigen__8 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( eigen__4 @ sP55 ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( ( sP22 = eigen__21 )
=> ( eigen__21 = sP22 ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( ~ ( ~ sP2
=> sP133 )
=> ~ sP98 ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ( eigen__3 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ( sP39
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ! [X1: $o > $o] : ~ sP58 ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ( sP86
=> sP81 ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( eigen__4 @ sP123 ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ( eigen__8 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ( sP55 = sP123 ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ! [X1: ( $o > $o ) > ( $o > $o ) > $o] :
( ~ ( ! [X2: $o > $o,X3: $o > $o] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o] :
( ~ ( ( X4 @ X2 )
=> ( X4 @ X3 ) )
=> ~ ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: $o > $o,X6: $o > $o,X7: ( $o > $o ) > $o,X8: ( $o > $o ) > $o,X9: ( $o > $o ) > $o,X10: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X7 @ X2 )
=> ( X7 @ X3 ) )
=> ( X7 @ X4 ) )
=> ( X7 @ X5 ) )
=> ( X7 @ X6 ) )
=> ( X8 @ X2 ) )
=> ~ ( X8 @ X3 ) )
=> ( X8 @ X4 ) )
=> ( X8 @ X5 ) )
=> ( X8 @ X6 ) )
=> ( X9 @ X2 ) )
=> ( X9 @ X3 ) )
=> ~ ( X9 @ X4 ) )
=> ( X9 @ X5 ) )
=> ( X9 @ X6 ) )
=> ( X10 @ X2 ) )
=> ( X10 @ X3 ) )
=> ( X10 @ X4 ) )
=> ~ ( X10 @ X5 ) )
=> ( X10 @ X6 ) )
=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X4 @ X2 ) )
=> ( X1 @ X4 @ X3 ) )
=> ( X1 @ X5 @ X2 ) )
=> ( X1 @ X5 @ X3 ) )
=> ( X1 @ X5 @ X4 ) )
=> ( X1 @ X6 @ X2 ) )
=> ( X1 @ X6 @ X3 ) )
=> ( X1 @ X6 @ X4 ) )
=> ( X1 @ X6 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ! [X1: $o] :
( ( eigen__3 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( sP89 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( sP131 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ( sP55 = sP89 ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( ~ sP60
=> ( eigen__6 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( ~ sP88
=> ( eigen__5 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ( sP108 = sP131 ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ( sP46 = eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ( eigen__1 @ sP108 ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ eigen__0 )
=> ( X4 @ eigen__1 ) )
=> ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ eigen__0 ) )
=> ~ ( X5 @ eigen__1 ) )
=> ( X5 @ X1 ) )
=> ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( X6 @ eigen__0 ) )
=> ( X6 @ eigen__1 ) )
=> ~ ( X6 @ X1 ) )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X7 @ eigen__0 ) )
=> ( X7 @ eigen__1 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ! [X1: $o] :
( ( eigen__0 @ X1 )
= ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( sP131 = sP22 ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ( eigen__21 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP150
=> sP92 )
=> ( X1 @ eigen__0 ) )
=> ~ ( X1 @ eigen__1 ) )
=> ( X1 @ eigen__2 ) )
=> ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) )
=> ( X2 @ eigen__0 ) )
=> ( X2 @ eigen__1 ) )
=> ~ ( X2 @ eigen__2 ) )
=> ( X2 @ eigen__3 ) )
=> ( X2 @ eigen__4 ) )
=> ( X3 @ eigen__0 ) )
=> ( X3 @ eigen__1 ) )
=> ( X3 @ eigen__2 ) )
=> ~ ( X3 @ eigen__3 ) )
=> ( X3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ( sP46 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ( sP46 = eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ~ sP62
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( sP89 = sP46 ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ( sP67 = sP66 ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ( sP6 = eigen__21 ) ),
introduced(definition,[new_symbols(definition,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ! [X1: $o] :
( ( eigen__2 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ( ~ sP136
=> sP97 ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> eigen__21 ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ( sP123 = sP89 ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> eigen__20 ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( sP50
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ! [X1: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ sP51
=> sP5 )
=> ( X1 @ eigen__0 ) )
=> ( X1 @ eigen__1 ) )
=> ( X1 @ eigen__2 ) )
=> ~ ( X1 @ eigen__3 ) )
=> ( X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ( ( eigen__1 @ sP123 )
= sP141 ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ( sP22 = sP168 ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ( eigen__2 @ sP168 ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( eigen__2 @ sP46 ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ( eigen__1 @ sP123 ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ( sP32
=> ( eigen__5 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( eigen__3 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ( sP170 = sP19 ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ( sP19 = sP123 ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: $o > $o,X6: ( $o > $o ) > $o,X7: ( $o > $o ) > $o,X8: ( $o > $o ) > $o,X9: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( X6 @ X1 )
=> ( X6 @ X2 ) )
=> ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( X6 @ X5 ) )
=> ( X7 @ X1 ) )
=> ~ ( X7 @ X2 ) )
=> ( X7 @ X3 ) )
=> ( X7 @ X4 ) )
=> ( X7 @ X5 ) )
=> ( X8 @ X1 ) )
=> ( X8 @ X2 ) )
=> ~ ( X8 @ X3 ) )
=> ( X8 @ X4 ) )
=> ( X8 @ X5 ) )
=> ( X9 @ X1 ) )
=> ( X9 @ X2 ) )
=> ( X9 @ X3 ) )
=> ~ ( X9 @ X4 ) )
=> ( X9 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( sP175 = sP13 ) ),
introduced(definition,[new_symbols(definition,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ( ~ sP150
=> sP92 ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ( eigen__1 @ sP170 ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ~ sP51
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ( sP131 = sP168 ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ( sP6 = sP131 ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ~ sP184
=> sP52 ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ( sP55 = sP46 ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ( sP131 = sP89 ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ( ~ sP2
=> sP133 ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ( sP112 = sP17 ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ( sP168 = sP22 ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(ramsey_l_2_5_4,conjecture,
~ sP144 ).
thf(h3,negated_conjecture,
sP144,
inference(assume_negation,[status(cth)],[ramsey_l_2_5_4]) ).
thf(1,plain,
( sP126
| ~ sP22
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP126
| sP22
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP132
| ~ sP126
| sP103 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP38
| sP132 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP86
| ~ sP22
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP86
| sP22
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP140
| ~ sP86
| sP81 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP38
| sP140 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP54
| ~ sP22
| ~ sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP54
| sP22
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP96
| ~ sP54
| sP95 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP38
| sP96 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP50
| ~ sP22
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP50
| sP22
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP171
| ~ sP50
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP38
| sP171 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( sP174
| ~ sP22
| ~ sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP174
| sP22
| sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP135
| ~ sP174
| sP195 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP38
| sP135 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP115
| ~ sP22
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP115
| sP22
| sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP49
| ~ sP115
| sP157 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP38
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP11
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( sP188
| ~ sP6
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP188
| sP6
| sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP23
| ~ sP168
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP23
| sP168
| sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP84
| ~ sP89
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP84
| sP89
| sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP111
| ~ sP170
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP111
| sP170
| sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP151
| ~ sP108
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP99
| ~ sP123
| ~ sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP99
| sP123
| sP131 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP147
| ~ sP131
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP147
| sP131
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP187
| ~ sP131
| ~ sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP187
| sP131
| sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP191
| ~ sP131
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP191
| sP131
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP80
| ~ sP131
| ~ sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP80
| sP131
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP106
| ~ sP131
| ~ sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP106
| sP131
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP143
| ~ sP55
| ~ sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP143
| sP55
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( sP181
| ~ sP19
| ~ sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP181
| sP19
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP24
| ~ sP89
| ~ sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP24
| sP89
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP41
| ~ sP170
| ~ sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP41
| sP170
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP48
| sP108
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP110
| ~ sP123
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP110
| sP123
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP69
| ~ sP123
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP69
| sP123
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP169
| ~ sP123
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP169
| sP123
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( sP26
| ~ sP123
| ~ sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP26
| sP123
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( sP65
| sP123
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( sP36
| sP55
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( sP73
| sP170
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( sP18
| sP108
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP30
| ~ sP108
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( sP100
| sP108
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( sP165
| ~ sP6
| ~ sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP165
| sP6
| sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP161
| ~ sP46
| ~ sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP161
| sP46
| sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( sP121
| ~ sP19
| ~ sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( sP121
| sP19
| sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
( sP129
| ~ sP170
| ~ sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( sP129
| sP170
| sP168 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( sP76
| ~ sP168
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( sP76
| sP168
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( sP102
| ~ sP168
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( sP102
| sP168
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( sP158
| ~ sP168
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP158
| sP168
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP91
| ~ sP168
| ~ sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( sP91
| sP168
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( sP85
| ~ sP89
| ~ sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( sP85
| sP89
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( sP153
| ~ sP46
| ~ sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(89,plain,
( sP153
| sP46
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( sP90
| ~ sP19
| ~ sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( sP90
| sP19
| sP170 ),
inference(prop_rule,[status(thm)],]) ).
thf(92,plain,
( sP101
| ~ sP170
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(93,plain,
( sP101
| sP170
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP47
| ~ sP170
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( sP47
| sP170
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( sP180
| ~ sP170
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(97,plain,
( sP180
| sP170
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( sP16
| ~ sP55
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(99,plain,
( sP16
| sP55
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(100,plain,
( sP107
| ~ sP46
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(101,plain,
( sP107
| sP46
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(102,plain,
( sP9
| ~ sP19
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(103,plain,
( sP9
| sP19
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(104,plain,
( sP56
| ~ sP19
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(105,plain,
( sP56
| sP19
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(106,plain,
( sP82
| ~ sP55
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(107,plain,
( sP82
| sP55
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(108,plain,
( sP160
| ~ sP46
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(109,plain,
( sP160
| sP46
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(110,plain,
( sP146
| sP89
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(111,plain,
( sP59
| ~ sP6
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(112,plain,
( sP59
| sP6
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(113,plain,
( sP72
| ~ sP6
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(114,plain,
( sP72
| sP6
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(115,plain,
( sP79
| ~ sP6
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(116,plain,
( sP79
| sP6
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(117,plain,
( sP148
| ~ sP55
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(118,plain,
( sP148
| sP55
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(119,plain,
( sP61
| ~ sP46
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(120,plain,
( sP61
| sP46
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(121,plain,
( sP125
| ~ sP89
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(122,plain,
( sP125
| sP89
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(123,plain,
( sP163
| ~ sP89
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(124,plain,
( sP163
| sP89
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(125,plain,
( sP190
| ~ sP55
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(126,plain,
( sP190
| sP55
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(127,plain,
( sP105
| ~ sP46
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(128,plain,
( sP105
| sP46
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(129,plain,
( ~ sP134
| sP71
| ~ sP103 ),
inference(mating_rule,[status(thm)],]) ).
thf(130,plain,
( ~ sP66
| sP71
| ~ sP81 ),
inference(mating_rule,[status(thm)],]) ).
thf(131,plain,
( ~ sP141
| sP71
| ~ sP95 ),
inference(mating_rule,[status(thm)],]) ).
thf(132,plain,
( ~ sP17
| sP45
| ~ sP14 ),
inference(mating_rule,[status(thm)],]) ).
thf(133,plain,
( ~ sP13
| sP45
| ~ sP195 ),
inference(mating_rule,[status(thm)],]) ).
thf(134,plain,
( ~ sP116
| sP45
| ~ sP157 ),
inference(mating_rule,[status(thm)],]) ).
thf(135,plain,
( ~ sP71
| sP134
| ~ sP126 ),
inference(mating_rule,[status(thm)],]) ).
thf(136,plain,
( ~ sP71
| sP66
| ~ sP86 ),
inference(mating_rule,[status(thm)],]) ).
thf(137,plain,
( ~ sP71
| sP141
| ~ sP54 ),
inference(mating_rule,[status(thm)],]) ).
thf(138,plain,
( ~ sP45
| sP17
| ~ sP50 ),
inference(mating_rule,[status(thm)],]) ).
thf(139,plain,
( ~ sP45
| sP13
| ~ sP174 ),
inference(mating_rule,[status(thm)],]) ).
thf(140,plain,
( ~ sP45
| sP116
| ~ sP115 ),
inference(mating_rule,[status(thm)],]) ).
thf(141,plain,
( sP7
| ~ sP45
| ~ sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(142,plain,
( sP7
| sP45
| sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(143,plain,
( sP156
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__28]) ).
thf(144,plain,
( sP128
| ~ sP156 ),
inference(prop_rule,[status(thm)],]) ).
thf(145,plain,
( ~ sP17
| sP116
| ~ sP188 ),
inference(mating_rule,[status(thm)],]) ).
thf(146,plain,
( ~ sP13
| sP116
| ~ sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(147,plain,
( ~ sP40
| sP93
| ~ sP84 ),
inference(mating_rule,[status(thm)],]) ).
thf(148,plain,
( ~ sP185
| sP93
| ~ sP111 ),
inference(mating_rule,[status(thm)],]) ).
thf(149,plain,
( ~ sP154
| sP93
| ~ sP151 ),
inference(mating_rule,[status(thm)],]) ).
thf(150,plain,
( ~ sP177
| sP93
| ~ sP99 ),
inference(mating_rule,[status(thm)],]) ).
thf(151,plain,
( ~ sP116
| sP17
| ~ sP147 ),
inference(mating_rule,[status(thm)],]) ).
thf(152,plain,
( ~ sP116
| sP13
| ~ sP187 ),
inference(mating_rule,[status(thm)],]) ).
thf(153,plain,
( ~ sP93
| sP40
| ~ sP191 ),
inference(mating_rule,[status(thm)],]) ).
thf(154,plain,
( ~ sP93
| sP185
| ~ sP80 ),
inference(mating_rule,[status(thm)],]) ).
thf(155,plain,
( ~ sP93
| sP177
| ~ sP106 ),
inference(mating_rule,[status(thm)],]) ).
thf(156,plain,
( sP77
| ~ sP93
| ~ sP116 ),
inference(prop_rule,[status(thm)],]) ).
thf(157,plain,
( sP77
| sP93
| sP116 ),
inference(prop_rule,[status(thm)],]) ).
thf(158,plain,
( sP152
| ~ sP77 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__25]) ).
thf(159,plain,
( sP75
| ~ sP152 ),
inference(prop_rule,[status(thm)],]) ).
thf(160,plain,
( ~ sP134
| sP141
| ~ sP143 ),
inference(mating_rule,[status(thm)],]) ).
thf(161,plain,
( ~ sP66
| sP141
| ~ sP181 ),
inference(mating_rule,[status(thm)],]) ).
thf(162,plain,
( ~ sP40
| sP177
| ~ sP24 ),
inference(mating_rule,[status(thm)],]) ).
thf(163,plain,
( ~ sP185
| sP177
| ~ sP41 ),
inference(mating_rule,[status(thm)],]) ).
thf(164,plain,
( ~ sP154
| sP177
| ~ sP48 ),
inference(mating_rule,[status(thm)],]) ).
thf(165,plain,
( ~ sP141
| sP134
| ~ sP110 ),
inference(mating_rule,[status(thm)],]) ).
thf(166,plain,
( ~ sP141
| sP66
| ~ sP69 ),
inference(mating_rule,[status(thm)],]) ).
thf(167,plain,
( ~ sP177
| sP40
| ~ sP169 ),
inference(mating_rule,[status(thm)],]) ).
thf(168,plain,
( ~ sP177
| sP185
| ~ sP26 ),
inference(mating_rule,[status(thm)],]) ).
thf(169,plain,
( ~ sP177
| sP154
| ~ sP65 ),
inference(mating_rule,[status(thm)],]) ).
thf(170,plain,
( sP173
| ~ sP177
| ~ sP141 ),
inference(prop_rule,[status(thm)],]) ).
thf(171,plain,
( sP173
| sP177
| sP141 ),
inference(prop_rule,[status(thm)],]) ).
thf(172,plain,
( sP29
| ~ sP173 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__24]) ).
thf(173,plain,
( sP68
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(174,plain,
( ~ sP28
| sP114
| ~ sP36 ),
inference(mating_rule,[status(thm)],]) ).
thf(175,plain,
( ~ sP185
| sP154
| ~ sP73 ),
inference(mating_rule,[status(thm)],]) ).
thf(176,plain,
( ~ sP114
| sP28
| ~ sP18 ),
inference(mating_rule,[status(thm)],]) ).
thf(177,plain,
( ~ sP114
| sP112
| ~ sP30 ),
inference(mating_rule,[status(thm)],]) ).
thf(178,plain,
( ~ sP154
| sP185
| ~ sP100 ),
inference(mating_rule,[status(thm)],]) ).
thf(179,plain,
( sP53
| ~ sP154
| ~ sP114 ),
inference(prop_rule,[status(thm)],]) ).
thf(180,plain,
( sP53
| sP154
| sP114 ),
inference(prop_rule,[status(thm)],]) ).
thf(181,plain,
( sP194
| ~ sP53 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__23]) ).
thf(182,plain,
( sP127
| ~ sP194 ),
inference(prop_rule,[status(thm)],]) ).
thf(183,plain,
( ~ sP17
| sP13
| ~ sP165 ),
inference(mating_rule,[status(thm)],]) ).
thf(184,plain,
( ~ sP176
| sP175
| ~ sP161 ),
inference(mating_rule,[status(thm)],]) ).
thf(185,plain,
( ~ sP67
| sP175
| ~ sP121 ),
inference(mating_rule,[status(thm)],]) ).
thf(186,plain,
( ~ sP87
| sP175
| ~ sP129 ),
inference(mating_rule,[status(thm)],]) ).
thf(187,plain,
( ~ sP13
| sP17
| ~ sP76 ),
inference(mating_rule,[status(thm)],]) ).
thf(188,plain,
( ~ sP175
| sP176
| ~ sP102 ),
inference(mating_rule,[status(thm)],]) ).
thf(189,plain,
( ~ sP175
| sP67
| ~ sP158 ),
inference(mating_rule,[status(thm)],]) ).
thf(190,plain,
( ~ sP175
| sP87
| ~ sP91 ),
inference(mating_rule,[status(thm)],]) ).
thf(191,plain,
( sP183
| ~ sP175
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(192,plain,
( sP183
| sP175
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(193,plain,
( sP94
| ~ sP183 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__21]) ).
thf(194,plain,
( sP44
| ~ sP94 ),
inference(prop_rule,[status(thm)],]) ).
thf(195,plain,
( ~ sP40
| sP185
| ~ sP85 ),
inference(mating_rule,[status(thm)],]) ).
thf(196,plain,
( ~ sP176
| sP87
| ~ sP153 ),
inference(mating_rule,[status(thm)],]) ).
thf(197,plain,
( ~ sP67
| sP87
| ~ sP90 ),
inference(mating_rule,[status(thm)],]) ).
thf(198,plain,
( ~ sP185
| sP40
| ~ sP101 ),
inference(mating_rule,[status(thm)],]) ).
thf(199,plain,
( ~ sP87
| sP176
| ~ sP47 ),
inference(mating_rule,[status(thm)],]) ).
thf(200,plain,
( ~ sP87
| sP67
| ~ sP180 ),
inference(mating_rule,[status(thm)],]) ).
thf(201,plain,
( sP124
| ~ sP87
| ~ sP185 ),
inference(prop_rule,[status(thm)],]) ).
thf(202,plain,
( sP124
| sP87
| sP185 ),
inference(prop_rule,[status(thm)],]) ).
thf(203,plain,
( sP166
| ~ sP124 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__20]) ).
thf(204,plain,
( sP42
| ~ sP166 ),
inference(prop_rule,[status(thm)],]) ).
thf(205,plain,
( ~ sP134
| sP66
| ~ sP16 ),
inference(mating_rule,[status(thm)],]) ).
thf(206,plain,
( ~ sP176
| sP67
| ~ sP107 ),
inference(mating_rule,[status(thm)],]) ).
thf(207,plain,
( ~ sP66
| sP134
| ~ sP9 ),
inference(mating_rule,[status(thm)],]) ).
thf(208,plain,
( ~ sP67
| sP176
| ~ sP56 ),
inference(mating_rule,[status(thm)],]) ).
thf(209,plain,
( sP164
| ~ sP67
| ~ sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(210,plain,
( sP164
| sP67
| sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(211,plain,
( sP37
| ~ sP164 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).
thf(212,plain,
( sP25
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(213,plain,
( ~ sP28
| sP112
| ~ sP82 ),
inference(mating_rule,[status(thm)],]) ).
thf(214,plain,
( ~ sP120
| sP112
| ~ sP160 ),
inference(mating_rule,[status(thm)],]) ).
thf(215,plain,
( ~ sP27
| sP112
| ~ sP146 ),
inference(mating_rule,[status(thm)],]) ).
thf(216,plain,
( ~ sP112
| sP28
| ~ sP59 ),
inference(mating_rule,[status(thm)],]) ).
thf(217,plain,
( ~ sP112
| sP120
| ~ sP72 ),
inference(mating_rule,[status(thm)],]) ).
thf(218,plain,
( ~ sP112
| sP27
| ~ sP79 ),
inference(mating_rule,[status(thm)],]) ).
thf(219,plain,
( sP193
| ~ sP112
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(220,plain,
( sP193
| sP112
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(221,plain,
( sP145
| ~ sP193 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__17]) ).
thf(222,plain,
( sP33
| ~ sP145 ),
inference(prop_rule,[status(thm)],]) ).
thf(223,plain,
( ~ sP28
| sP27
| ~ sP148 ),
inference(mating_rule,[status(thm)],]) ).
thf(224,plain,
( ~ sP120
| sP27
| ~ sP61 ),
inference(mating_rule,[status(thm)],]) ).
thf(225,plain,
( ~ sP27
| sP28
| ~ sP125 ),
inference(mating_rule,[status(thm)],]) ).
thf(226,plain,
( ~ sP27
| sP120
| ~ sP163 ),
inference(mating_rule,[status(thm)],]) ).
thf(227,plain,
( sP70
| ~ sP27
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(228,plain,
( sP70
| sP27
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(229,plain,
( sP64
| ~ sP70 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__16]) ).
thf(230,plain,
( sP179
| ~ sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(231,plain,
( ~ sP28
| sP120
| ~ sP190 ),
inference(mating_rule,[status(thm)],]) ).
thf(232,plain,
( ~ sP120
| sP28
| ~ sP105 ),
inference(mating_rule,[status(thm)],]) ).
thf(233,plain,
( sP35
| ~ sP120
| ~ sP176 ),
inference(prop_rule,[status(thm)],]) ).
thf(234,plain,
( sP35
| sP120
| sP176 ),
inference(prop_rule,[status(thm)],]) ).
thf(235,plain,
( sP119
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__15]) ).
thf(236,plain,
( sP78
| ~ sP119 ),
inference(prop_rule,[status(thm)],]) ).
thf(237,plain,
( sP4
| ~ sP28
| ~ sP134 ),
inference(prop_rule,[status(thm)],]) ).
thf(238,plain,
( sP4
| sP28
| sP134 ),
inference(prop_rule,[status(thm)],]) ).
thf(239,plain,
sP11,
inference(eq_sym,[status(thm)],]) ).
thf(240,plain,
( sP122
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14]) ).
thf(241,plain,
( sP137
| ~ sP122 ),
inference(prop_rule,[status(thm)],]) ).
thf(242,plain,
( sP63
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(243,plain,
( sP43
| ~ sP63 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__13]) ).
thf(244,plain,
( sP34
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(245,plain,
( sP83
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(246,plain,
~ sP58,
inference(prop_rule,[status(thm)],]) ).
thf(247,plain,
( sP139
| sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(248,plain,
( sP39
| ~ sP139 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(249,plain,
( ~ sP32
| sP92
| ~ sP128 ),
inference(mating_rule,[status(thm)],]) ).
thf(250,plain,
( sP178
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(251,plain,
( sP88
| ~ sP178 ),
inference(prop_rule,[status(thm)],]) ).
thf(252,plain,
( ~ sP104
| sP52
| ~ sP75 ),
inference(mating_rule,[status(thm)],]) ).
thf(253,plain,
( sP150
| ~ sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(254,plain,
( ~ sP104
| sP3
| ~ sP68 ),
inference(mating_rule,[status(thm)],]) ).
thf(255,plain,
( ~ sP104
| sP15
| ~ sP127 ),
inference(mating_rule,[status(thm)],]) ).
thf(256,plain,
( sP184
| ~ sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf(257,plain,
( sP184
| ~ sP150 ),
inference(prop_rule,[status(thm)],]) ).
thf(258,plain,
( sP189
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(259,plain,
( sP189
| ~ sP184 ),
inference(prop_rule,[status(thm)],]) ).
thf(260,plain,
( sP60
| sP104 ),
inference(prop_rule,[status(thm)],]) ).
thf(261,plain,
( sP60
| ~ sP189 ),
inference(prop_rule,[status(thm)],]) ).
thf(262,plain,
( sP149
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(263,plain,
( ~ sP8
| sP12
| ~ sP44 ),
inference(mating_rule,[status(thm)],]) ).
thf(264,plain,
( sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(265,plain,
( sP21
| ~ sP149 ),
inference(prop_rule,[status(thm)],]) ).
thf(266,plain,
( ~ sP8
| sP31
| ~ sP42 ),
inference(mating_rule,[status(thm)],]) ).
thf(267,plain,
( sP74
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(268,plain,
( sP74
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(269,plain,
( ~ sP8
| sP5
| ~ sP25 ),
inference(mating_rule,[status(thm)],]) ).
thf(270,plain,
( sP130
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(271,plain,
( sP130
| ~ sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(272,plain,
( sP62
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(273,plain,
( sP62
| ~ sP130 ),
inference(prop_rule,[status(thm)],]) ).
thf(274,plain,
( sP162
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(275,plain,
( sP162
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(276,plain,
( ~ sP98
| sP118
| ~ sP33 ),
inference(mating_rule,[status(thm)],]) ).
thf(277,plain,
( sP51
| ~ sP162 ),
inference(prop_rule,[status(thm)],]) ).
thf(278,plain,
( ~ sP98
| sP142
| ~ sP179 ),
inference(mating_rule,[status(thm)],]) ).
thf(279,plain,
( sP186
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(280,plain,
( sP186
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(281,plain,
( ~ sP98
| sP133
| ~ sP78 ),
inference(mating_rule,[status(thm)],]) ).
thf(282,plain,
( sP57
| ~ sP118 ),
inference(prop_rule,[status(thm)],]) ).
thf(283,plain,
( sP57
| ~ sP186 ),
inference(prop_rule,[status(thm)],]) ).
thf(284,plain,
( ~ sP98
| sP97
| ~ sP137 ),
inference(mating_rule,[status(thm)],]) ).
thf(285,plain,
( sP2
| ~ sP142 ),
inference(prop_rule,[status(thm)],]) ).
thf(286,plain,
( sP2
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(287,plain,
( sP192
| ~ sP133 ),
inference(prop_rule,[status(thm)],]) ).
thf(288,plain,
( sP192
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(289,plain,
( sP136
| sP98 ),
inference(prop_rule,[status(thm)],]) ).
thf(290,plain,
( sP136
| ~ sP192 ),
inference(prop_rule,[status(thm)],]) ).
thf(291,plain,
( sP167
| ~ sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf(292,plain,
( sP167
| ~ sP136 ),
inference(prop_rule,[status(thm)],]) ).
thf(293,plain,
( sP172
| ~ sP167 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__8]) ).
thf(294,plain,
( sP109
| ~ sP172 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__7]) ).
thf(295,plain,
( sP159
| ~ sP109 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__6]) ).
thf(296,plain,
( sP117
| ~ sP159 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).
thf(297,plain,
( sP20
| ~ sP117 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(298,plain,
( sP113
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(299,plain,
( sP155
| ~ sP113 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(300,plain,
( sP10
| ~ sP155 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(301,plain,
( sP182
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(302,plain,
( ~ sP138
| ~ sP39
| ~ sP83 ),
inference(prop_rule,[status(thm)],]) ).
thf(303,plain,
( ~ sP1
| sP138
| ~ sP182 ),
inference(prop_rule,[status(thm)],]) ).
thf(304,plain,
( ~ sP144
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(305,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,h3]) ).
thf(306,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[305,h2]) ).
thf(307,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[306,h1]) ).
thf(308,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[307,h0]) ).
thf(0,theorem,
~ sP144,
inference(contra,[status(thm),contra(discharge,[h3])],[305,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA030^1 : TPTP v8.1.0. Released v3.6.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 23:33:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 26.02/26.45 % SZS status Theorem
% 26.02/26.45 % Mode: mode454
% 26.02/26.45 % Inferences: 1113
% 26.02/26.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------