TSTP Solution File: SEV157^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV157^5 : 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 : Tue Jul 19 18:05:08 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 146
% Syntax : Number of formulae : 185 ( 59 unt; 18 typ; 4 def)
% Number of atoms : 431 ( 4 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 2748 ( 616 ~; 48 |; 0 &;1381 @)
% ( 48 <=>; 655 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 205 ( 205 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 66 usr; 61 con; 0-2 aty)
% Number of variables : 657 ( 4 ^ 653 !; 0 ?; 657 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__14,type,
eigen__14: a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__12,type,
eigen__12: a > a > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__25,type,
eigen__25: a ).
thf(ty_eigen__7,type,
eigen__7: a > a > $o ).
thf(ty_eigen__24,type,
eigen__24: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__26,type,
eigen__26: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__19,type,
eigen__19: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__23,type,
eigen__23: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__7 @ eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__14 @ X1 )
=> ( eigen__12 @ eigen__14 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( eigen__0 @ eigen__8 @ eigen__10 )
=> ( eigen__1 @ eigen__8 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__4 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( eigen__0 @ eigen__14 @ eigen__19 )
=> ( eigen__1 @ eigen__14 @ eigen__19 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__12 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__24 @ eigen__25 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__1 @ eigen__8 @ X1 ) )
=> ( eigen__7 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__4 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__12 @ X1 @ X2 )
=> ~ ( eigen__12 @ X2 @ X3 ) )
=> ( eigen__12 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ( eigen__1 @ eigen__14 @ X1 )
=> ( eigen__12 @ eigen__14 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__1 @ eigen__14 @ eigen__19 )
=> ( eigen__12 @ eigen__14 @ eigen__19 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__12 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__26 @ eigen__23 @ X1 )
=> ~ ( eigen__26 @ X1 @ X2 ) )
=> ( eigen__26 @ eigen__23 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ~ ( ( eigen__26 @ eigen__23 @ eigen__24 )
=> ~ ( eigen__26 @ eigen__24 @ X1 ) )
=> ( eigen__26 @ eigen__23 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__0 @ eigen__8 @ eigen__10 )
=> ( eigen__7 @ eigen__8 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__26 @ eigen__23 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__26 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__26 @ X1 @ X2 )
=> ~ ( eigen__26 @ X2 @ X3 ) )
=> ( eigen__26 @ X1 @ X3 ) ) )
=> ( eigen__26 @ eigen__23 @ eigen__24 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__4 @ X1 @ X2 )
=> ~ ( eigen__4 @ X2 @ X3 ) )
=> ( eigen__4 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( eigen__26 @ eigen__23 @ eigen__24 )
=> ~ ( eigen__26 @ eigen__24 @ eigen__25 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__26 @ X1 @ X2 ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__26 @ X1 @ X2 )
=> ~ ( eigen__26 @ X2 @ X3 ) )
=> ( eigen__26 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__26 @ X1 @ X2 )
=> ~ ( eigen__26 @ X2 @ X3 ) )
=> ( eigen__26 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__12 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__14 @ X1 )
=> ( eigen__1 @ eigen__14 @ X1 ) )
=> ( eigen__12 @ eigen__14 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__7 @ eigen__8 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__26 @ eigen__23 @ eigen__24 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) )
=> ~ sP1 )
=> ( eigen__7 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP3
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP20
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( sP23
=> ~ sP10 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__26 @ eigen__24 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP2
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__7 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__1 @ eigen__14 @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__7 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( eigen__7 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a,X2: a] :
( ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__26 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__12 @ eigen__14 @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ sP28
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP29
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__0 @ eigen__8 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP23
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP4
=> sP40 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP21
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(cTHM250G_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X2 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X6 ) )
=> ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X7 ) ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X2 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X6 ) )
=> ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X7 ) ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM250G_pme]) ).
thf(h2,assumption,
~ ! [X1: a > a > $o,X2: a,X3: a] :
( ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ~ ( ~ ( ! [X4: a,X5: a] :
( ( ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( eigen__0 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( X1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X4 @ X5 ) )
=> ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( eigen__0 @ X8 @ X9 )
=> ( X1 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X4 @ X6 ) ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a] :
( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ~ ( ~ ( ! [X3: a,X4: a] :
( ( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X3 @ X4 ) )
=> ~ ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ! [X6: a > a > $o] :
( ~ ( ! [X7: a,X8: a] :
( ( ~ ( eigen__0 @ X7 @ X8 )
=> ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X7 @ X8 ) )
=> ~ ! [X7: a,X8: a,X9: a] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) )
=> ~ ( ~ ( ! [X2: a,X3: a] :
( ( ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__1 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X2 @ X3 ) )
=> ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( eigen__0 @ X6 @ X7 )
=> ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP35
=> ~ ( ~ ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) )
=> sP35 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP35,
introduced(assumption,[]) ).
thf(h7,assumption,
( ~ ( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) )
=> sP35 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP41,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h11,assumption,
sP3,
introduced(assumption,[]) ).
thf(h12,assumption,
sP19,
introduced(assumption,[]) ).
thf(h13,assumption,
( ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP35,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: a,X2: a] :
( ( ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ~ ( ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
=> ~ ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ~ ( ! [X5: a,X6: a] :
( ( ~ ( eigen__0 @ X5 @ X6 )
=> ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ( ~ sP47
=> sP48 )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
( ~ sP47
=> sP48 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__5 @ eigen__6 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP47,
introduced(assumption,[]) ).
thf(h22,assumption,
sP48,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( sP34
=> ~ sP1 )
=> sP38 ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( sP34
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP38,
introduced(assumption,[]) ).
thf(h26,assumption,
sP34,
introduced(assumption,[]) ).
thf(h27,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP34
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP33
| ~ sP2
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP16
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP16
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP37
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(8,plain,
( sP29
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(9,plain,
( ~ sP47
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP27
| sP42
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP42
| ~ sP29
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h24,h25,h23,h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h21,h26,h27,h25]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,12,h26,h27]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,13,h24,h25]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__7)],[h20,14,h23]) ).
thf(h28,assumption,
~ ( ~ ( sP13
=> ~ sP10 )
=> sP5 ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( sP13
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h31,assumption,
sP13,
introduced(assumption,[]) ).
thf(h32,assumption,
sP10,
introduced(assumption,[]) ).
thf(16,plain,
( sP4
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP13
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP24
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP45
| ~ sP4
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP12
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP12
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP11
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19]) ).
thf(23,plain,
( sP23
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(24,plain,
( ~ sP48
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP31
| sP44
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP44
| ~ sP23
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h32,h29,h30,h28,h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[16,17,18,19,20,21,22,23,24,25,26,h22,h31,h32,h30]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h29,27,h31,h32]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,28,h29,h30]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__12)],[h20,29,h28]) ).
thf(31,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h20,h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h21]),tab_imp(discharge,[h22])],[h19,15,30,h21,h22]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,31,h19,h20]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__6)],[h17,32,h18]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__5)],[h15,33,h17]) ).
thf(h33,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ eigen__23 @ X1 ) )
=> ~ ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ! [X3: a > a > $o] :
( ~ ( ! [X4: a,X5: a] :
( ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X4 @ X5 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) ) )
=> ( X3 @ eigen__23 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ! [X1: a] :
( ~ ( sP9
=> ~ ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__24 @ X1 ) ) )
=> ! [X2: a > a > $o] :
( ~ ( ! [X3: a,X4: a] :
( ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) )
=> ~ ! [X3: a,X4: a,X5: a] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) ) )
=> ( X2 @ eigen__23 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( ~ ( sP9
=> ~ sP6 )
=> ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__25 ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( sP9
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ! [X1: a > a > $o] :
( ~ ( ! [X2: a,X3: a] :
( ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X2 @ X3 ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ( X1 @ eigen__23 @ eigen__25 ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP9,
introduced(assumption,[]) ).
thf(h39,assumption,
sP6,
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( ~ sP21
=> sP17 ),
introduced(assumption,[]) ).
thf(h41,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h42,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h43,assumption,
sP39,
introduced(assumption,[]) ).
thf(h44,assumption,
sP22,
introduced(assumption,[]) ).
thf(35,plain,
( ~ sP22
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP14
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP15
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP30
| sP20
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP20
| ~ sP26
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP18
| sP21
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP6
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP46
| sP21
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP21
| ~ sP39
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h43,h44,h41,h42,h40,h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[35,36,37,38,39,40,41,42,43,44,h38,h39,h43,h44,h42]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h40,h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h41,45,h43,h44]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h41,h42])],[h40,46,h41,h42]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h38,h39,h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h40]),tab_negall(eigenvar,eigen__26)],[h37,47,h40]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h37,h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h38,h39])],[h36,48,h38,h39]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,49,h36,h37]) ).
thf(51,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h34,h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__25)],[h34,50,h35]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h33,h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__24)],[h33,51,h34]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__23)],[h16,52,h33]) ).
thf(54,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h13,34,53,h15,h16]) ).
thf(55,plain,
( ~ sP35
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP41
| sP28
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP28
| ~ sP3
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0])],[55,56,57,h11,h12,h10,h14]) ).
thf(59,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h7,54,58,h13,h14]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,59,h11,h12]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,60,h9,h10]) ).
thf(62,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__4)],[h6,61,h8]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,62,h6,h7]) ).
thf(64,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,63,h5]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,64,h4]) ).
thf(66,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,65,h3]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,66,h2]) ).
thf(68,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[67,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ~ ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ~ ( ~ ( ! [X5: a,X6: a] :
( ( ~ ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( X2 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ! [X7: a > a > $o] :
( ~ ( ! [X8: a,X9: a] :
( ( ~ ( X1 @ X8 @ X9 )
=> ( X2 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X9 ) )
=> ~ ! [X8: a,X9: a,X10: a] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a,X7: a] :
( ~ ( ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X6 ) )
=> ~ ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X6 @ X7 ) ) )
=> ! [X8: a > a > $o] :
( ~ ( ! [X9: a,X10: a] :
( ( ~ ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ( X8 @ X9 @ X10 ) )
=> ~ ! [X9: a,X10: a,X11: a] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X10 @ X11 ) )
=> ( X8 @ X9 @ X11 ) ) )
=> ( X8 @ X5 @ X7 ) ) ) )
=> ! [X5: a > a > $o] :
( ~ ( ! [X6: a,X7: a] :
( ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) )
=> ( X5 @ X6 @ X7 ) )
=> ~ ! [X6: a,X7: a,X8: a] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) ) )
=> ( X5 @ X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[67,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV157^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.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 : Tue Jun 28 12:00:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % Mode: mode213
% 0.19/0.49 % Inferences: 121
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------