TSTP Solution File: SYO069^4.003 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO069^4.003 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 : Thu Jul 21 19:30:04 EDT 2022
% Result : Theorem 252.84s 253.00s
% Output : Proof 252.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 231
% Syntax : Number of formulae : 244 ( 34 unt; 19 typ; 28 def)
% Number of atoms : 1153 ( 28 equ; 0 cnn)
% Maximal formula atoms : 71 ( 5 avg)
% Number of connectives : 2313 ( 291 ~; 118 |; 0 &;1148 @)
% ( 93 <=>; 661 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 135 ( 132 usr; 124 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 411 ( 36 ^ 375 !; 0 ?; 411 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_a0,type,
a0: $i > $o ).
thf(ty_a3,type,
a3: $i > $o ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__35,type,
eigen__35: $i ).
thf(ty_a2,type,
a2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_b3,type,
b3: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_b2,type,
b2: $i > $o ).
thf(ty_eigen__55,type,
eigen__55: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_b1,type,
b1: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_b0,type,
b0: $i > $o ).
thf(ty_eigen__50,type,
eigen__50: $i ).
thf(ty_f,type,
f: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__55,definition,
( eigen__55
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__55])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__50,definition,
( eigen__50
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__15 @ X1 )
=> ( b0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__50])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__35,definition,
( eigen__35
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__11 @ X1 )
=> ( a3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__35])]) ).
thf(sP1,plain,
( sP1
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a0 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__6 @ eigen__11 )
=> ~ ( irel @ eigen__11 @ X1 ) )
=> ( irel @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( irel @ eigen__16 @ eigen__55 )
=> ( a2 @ eigen__55 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a0 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a3 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( f @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( irel @ eigen__11 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__6 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__6 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( b0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__6 @ eigen__16 )
=> ~ ( irel @ eigen__16 @ X1 ) )
=> ( irel @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( irel @ eigen__6 @ eigen__16 )
=> ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( b1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( b3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( b0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( irel @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( irel @ eigen__1 @ eigen__6 )
=> ( sP12
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> sP10 )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a0 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a3 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( f @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a3 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ~ ( sP9
=> ~ ( irel @ eigen__1 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( irel @ eigen__6 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( irel @ eigen__11 @ eigen__35 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( sP23
=> ~ ( irel @ eigen__16 @ eigen__55 ) )
=> ( irel @ eigen__6 @ eigen__55 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( irel @ eigen__6 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP17
=> ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( irel @ eigen__1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP26
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( irel @ eigen__6 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP12
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( irel @ eigen__0 @ eigen__6 )
=> ~ ( sP7
=> sP19 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( irel @ eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a3 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a0 @ X1 ) ) )
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP4
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ ( sP27
=> ~ sP24 )
=> ( irel @ eigen__6 @ eigen__35 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( f @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> sP22 )
=> sP37 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( sP31
=> ~ ( irel @ eigen__15 @ eigen__50 ) )
=> ( irel @ eigen__6 @ eigen__50 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP35
=> ~ sP40 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( irel @ eigen__15 @ eigen__50 )
=> ( b0 @ eigen__50 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( irel @ eigen__6 @ eigen__55 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP47
=> ( a2 @ eigen__55 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ ( sP9
=> ~ sP29 )
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP27
=> ( ! [X1: $i] :
( ( irel @ eigen__11 @ X1 )
=> ( b2 @ X1 ) )
=> sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP44
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( a3 @ eigen__35 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP27
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ! [X1: $i] :
( ( irel @ eigen__11 @ X1 )
=> ( b2 @ X1 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a0 @ X1 ) ) )
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP9
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) ) )
=> sP6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: $i] :
( ~ ( sP31
=> ~ ( irel @ eigen__15 @ X1 ) )
=> ( irel @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP9
=> ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( f @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( a2 @ eigen__55 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( irel @ eigen__6 @ eigen__50 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP42
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP43
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP9
=> ~ ( sP51
=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a3 @ X1 ) ) )
=> sP1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( b1 @ X1 ) )
=> sP69 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP9
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( sP7
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( b0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( irel @ eigen__6 @ eigen__35 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP23
=> ~ ( irel @ eigen__16 @ eigen__55 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) ) )
=> sP58 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( sP75
=> sP53 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( sP63
=> ( b0 @ eigen__50 ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( sP51
=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a3 @ X1 ) ) )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( irel @ eigen__15 @ eigen__50 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( b0 @ eigen__50 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( irel @ eigen__16 @ eigen__55 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( sP16
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( sP31
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( sP31
=> ~ sP84 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( sP24
=> sP53 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a3 @ X1 ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
iand = mand ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
ivalid = !! ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(con,conjecture,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ).
thf(h1,negated_conjecture,
~ sP71,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( ~ sP11
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP39
| sP54
| sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP54
| ~ sP27
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP59
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP41
| sP90
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP90
| ~ sP31
| ~ sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP25
| sP77
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP77
| ~ sP23
| ~ sP87 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP33
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP21
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP49
| sP72
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP72
| ~ sP9
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP81
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP48
| ~ sP47
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP12
| sP80 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP80
| ~ sP63
| sP85 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP2
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP68
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP68
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP5
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP5
| sP87 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP22
| sP79 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP79
| ~ sP75
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP46
| ~ sP85 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP46
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP69
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__55]) ).
thf(31,plain,
( sP91
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP91
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP74
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__50]) ).
thf(34,plain,
( sP70
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP8
| ~ sP91 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__35]) ).
thf(36,plain,
( sP15
| ~ sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP14
| ~ sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP14
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP55
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP89
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP89
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP50
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP50
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP20
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP52
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(46,plain,
( sP30
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP30
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP83
| ~ sP89 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(49,plain,
( ~ sP26
| ~ sP52
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP56
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP93
| ~ sP50 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(52,plain,
( ~ sP42
| ~ sP83
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP37
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP65
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP65
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP7
| ~ sP93
| sP81 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP19
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP19
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP73
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP73
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP40
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP45
| ~ sP35
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP34
| ~ sP35
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP4
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP86
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( sP36
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( sP6
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP6
| sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( sP58
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( sP78
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP32
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP32
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP18
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( sP18
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP64
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP28
| ~ sP17
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP51
| ~ sP44
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( sP43
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(79,plain,
( ~ sP66
| ~ sP43
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( sP1
| sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( sP92
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( sP82
| ~ sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP82
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( ~ sP86
| sP67 ),
inference(all_rule,[status(thm)],]) ).
thf(85,plain,
( ~ sP67
| ~ sP9
| ~ sP82 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( sP16
| ~ sP76 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( sP16
| sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP4
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP57
| ~ sP9
| ~ sP78 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( sP60
| ~ sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( sP60
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(92,plain,
( sP76
| ~ sP60 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(93,plain,
( sP38
| ~ sP76 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP38
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP88
| ~ sP16
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( sP71
| sP88 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(trans_axiom,axiom,
sP68 ).
thf(refl_axiom,axiom,
sP2 ).
thf(97,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,trans_axiom,refl_axiom,h1]) ).
thf(98,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[97,h0]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[97,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYO069^4.003 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.08/0.29 % Computer : n006.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Sat Jul 9 15:37:51 EDT 2022
% 0.08/0.29 % CPUTime :
% 252.84/253.00 % SZS status Theorem
% 252.84/253.00 % Mode: mode519
% 252.84/253.00 % Inferences: 12408
% 252.84/253.00 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------