TSTP Solution File: ALG292^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG292^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:33:53 EDT 2023
% Result : Theorem 0.19s 0.69s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 75
% Syntax : Number of formulae : 101 ( 42 unt; 12 typ; 1 def)
% Number of atoms : 277 ( 163 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1665 ( 485 ~; 16 |; 0 &; 705 @)
% ( 17 <=>; 442 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 25 con; 0-2 aty)
% Number of variables : 412 ( 1 ^; 411 !; 0 ?; 412 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_eigen__5,type,
eigen__5: a > $o ).
thf(ty_eigen__37,type,
eigen__37: a ).
thf(ty_eigen__3,type,
eigen__3: a > a ).
thf(ty_eigen__20,type,
eigen__20: a ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__19,type,
eigen__19: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__2,type,
eigen__2: a > a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__37,definition,
( eigen__37
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__20 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) )
=> ( eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__37])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__4 @ ( eigen__1 @ eigen__7 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) )
=> ( eigen__5 @ X2 ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X1 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: a > $o] :
( ~ ( ( X1 @ eigen__19 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eigen__2 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ( eigen__3 @ X2 )
!= eigen__37 ) ) )
=> ( eigen__5 @ eigen__37 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: a > $o] :
( ~ ( ( X1 @ eigen__20 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eigen__2 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ( eigen__3 @ X2 )
!= eigen__37 ) ) )
=> ( eigen__5 @ eigen__37 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__7 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) )
=> ( eigen__5 @ X1 ) )
=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ( X3 @ eigen__7 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X1 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__20 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) )
=> ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: a > $o] :
( ~ ( ( X1 @ eigen__20 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eigen__2 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ( eigen__3 @ X2 )
!= eigen__37 ) ) )
=> ! [X1: a > $o] :
( ~ ( ( X1 @ eigen__19 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eigen__2 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ( eigen__3 @ X2 )
!= eigen__37 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o] :
( ~ ( ( X1 @ eigen__19 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eigen__2 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ( eigen__3 @ X2 )
!= eigen__37 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__19 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) )
=> ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__20 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) )
=> ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__19 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ( X2 @ eigen__7 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X2 @ ( eigen__2 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( ( eigen__3 @ X3 )
!= X1 ) ) )
=> ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ~ ( ( X1 @ eigen__20 )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eigen__2 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( ( eigen__3 @ X2 )
!= eigen__37 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) )
=> ( eigen__5 @ X2 ) )
=> ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( eigen__2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( eigen__3 @ X5 )
!= X3 ) ) )
=> ! [X4: a > $o] :
( ~ ( ( X4 @ X1 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( eigen__2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( eigen__3 @ X5 )
!= X3 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X2 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ( X3 @ eigen__7 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X1 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__4 @ ( eigen__1 @ eigen__20 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__5 @ eigen__37 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP6
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cPU_X238A_pme,conjecture,
! [X1: a,X2: a > a > a,X3: a > a,X4: a > a,X5: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X3 @ X1 )
= X1 )
=> ( ( X4 @ X1 )
!= X1 ) )
=> ~ ! [X6: a,X7: a] :
( ( X3 @ ( X2 @ X6 @ X7 ) )
= X6 ) )
=> ~ ! [X6: a,X7: a] :
( ( X4 @ ( X2 @ X6 @ X7 ) )
= X7 ) )
=> ~ ! [X6: a] :
( ( X6 != X1 )
= ( X6
= ( X2 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) ) ) )
=> ~ ! [X6: a > $o] :
( ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X3 @ X8 ) ) ) )
=> ( X6 @ X1 ) ) )
=> ! [X6: a > $o,X7: a] :
( ( ~ ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X4 @ X11 )
!= X9 ) ) )
=> ( X6 @ X9 ) )
=> ~ ( X5 @ ( X2 @ X8 @ X7 ) ) ) )
= ( ~ ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X4 @ X11 )
!= X9 ) ) )
=> ( X6 @ X9 ) )
=> ! [X9: a] :
( ! [X10: a] :
( ! [X11: a > $o] :
( ~ ( ( X11 @ X9 )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( X3 @ X12 ) ) ) )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( ( X4 @ X12 )
!= X10 ) ) )
=> ! [X11: a > $o] :
( ~ ( ( X11 @ X8 )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( X3 @ X12 ) ) ) )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( ( X4 @ X12 )
!= X10 ) ) ) )
=> ~ ( X5 @ ( X2 @ X9 @ X7 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: a,X2: a > a > a,X3: a > a,X4: a > a,X5: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X3 @ X1 )
= X1 )
=> ( ( X4 @ X1 )
!= X1 ) )
=> ~ ! [X6: a,X7: a] :
( ( X3 @ ( X2 @ X6 @ X7 ) )
= X6 ) )
=> ~ ! [X6: a,X7: a] :
( ( X4 @ ( X2 @ X6 @ X7 ) )
= X7 ) )
=> ~ ! [X6: a] :
( ( X6 != X1 )
= ( X6
= ( X2 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) ) ) )
=> ~ ! [X6: a > $o] :
( ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X3 @ X8 ) ) ) )
=> ( X6 @ X1 ) ) )
=> ! [X6: a > $o,X7: a] :
( ( ~ ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X4 @ X11 )
!= X9 ) ) )
=> ( X6 @ X9 ) )
=> ~ ( X5 @ ( X2 @ X8 @ X7 ) ) ) )
= ( ~ ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X4 @ X11 )
!= X9 ) ) )
=> ( X6 @ X9 ) )
=> ! [X9: a] :
( ! [X10: a] :
( ! [X11: a > $o] :
( ~ ( ( X11 @ X9 )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( X3 @ X12 ) ) ) )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( ( X4 @ X12 )
!= X10 ) ) )
=> ! [X11: a > $o] :
( ~ ( ( X11 @ X8 )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( X3 @ X12 ) ) ) )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( ( X4 @ X12 )
!= X10 ) ) ) )
=> ~ ( X5 @ ( X2 @ X9 @ X7 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_X238A_pme]) ).
thf(h2,assumption,
~ ! [X1: a > a > a,X2: a > a,X3: a > a,X4: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= eigen__0 )
=> ( ( X3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X5: a,X6: a] :
( ( X2 @ ( X1 @ X5 @ X6 ) )
= X5 ) )
=> ~ ! [X5: a,X6: a] :
( ( X3 @ ( X1 @ X5 @ X6 ) )
= X6 ) )
=> ~ ! [X5: a] :
( ( X5 != eigen__0 )
= ( X5
= ( X1 @ ( X2 @ X5 ) @ ( X3 @ X5 ) ) ) ) )
=> ~ ! [X5: a > $o] :
( ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X2 @ X7 ) ) ) )
=> ( X5 @ eigen__0 ) ) )
=> ! [X5: a > $o,X6: a] :
( ( ~ ! [X7: a] :
( ! [X8: a] :
( ! [X9: a > $o] :
( ~ ( ( X9 @ X7 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( X9 @ ( X2 @ X10 ) ) ) )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( ( X3 @ X10 )
!= X8 ) ) )
=> ( X5 @ X8 ) )
=> ~ ( X4 @ ( X1 @ X7 @ X6 ) ) ) )
= ( ~ ! [X7: a] :
( ! [X8: a] :
( ! [X9: a > $o] :
( ~ ( ( X9 @ X7 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( X9 @ ( X2 @ X10 ) ) ) )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( ( X3 @ X10 )
!= X8 ) ) )
=> ( X5 @ X8 ) )
=> ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X2 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X3 @ X11 )
!= X9 ) ) )
=> ! [X10: a > $o] :
( ~ ( ( X10 @ X7 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X2 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X3 @ X11 )
!= X9 ) ) ) )
=> ~ ( X4 @ ( X1 @ X8 @ X6 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a > a,X2: a > a,X3: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= eigen__0 )
=> ( ( X2 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X4: a,X5: a] :
( ( X1 @ ( eigen__1 @ X4 @ X5 ) )
= X4 ) )
=> ~ ! [X4: a,X5: a] :
( ( X2 @ ( eigen__1 @ X4 @ X5 ) )
= X5 ) )
=> ~ ! [X4: a] :
( ( X4 != eigen__0 )
= ( X4
= ( eigen__1 @ ( X1 @ X4 ) @ ( X2 @ X4 ) ) ) ) )
=> ~ ! [X4: a > $o] :
( ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X1 @ X6 ) ) ) )
=> ( X4 @ eigen__0 ) ) )
=> ! [X4: a > $o,X5: a] :
( ( ~ ! [X6: a] :
( ! [X7: a] :
( ! [X8: a > $o] :
( ~ ( ( X8 @ X6 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( X8 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( ( X2 @ X9 )
!= X7 ) ) )
=> ( X4 @ X7 ) )
=> ~ ( X3 @ ( eigen__1 @ X6 @ X5 ) ) ) )
= ( ~ ! [X6: a] :
( ! [X7: a] :
( ! [X8: a > $o] :
( ~ ( ( X8 @ X6 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( X8 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( ( X2 @ X9 )
!= X7 ) ) )
=> ( X4 @ X7 ) )
=> ! [X7: a] :
( ! [X8: a] :
( ! [X9: a > $o] :
( ~ ( ( X9 @ X7 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( X9 @ ( X1 @ X10 ) ) ) )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( ( X2 @ X10 )
!= X8 ) ) )
=> ! [X9: a > $o] :
( ~ ( ( X9 @ X6 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( X9 @ ( X1 @ X10 ) ) ) )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ( ( X2 @ X10 )
!= X8 ) ) ) )
=> ~ ( X3 @ ( eigen__1 @ X7 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a > a,X2: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( X1 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X3: a,X4: a] :
( ( eigen__2 @ ( eigen__1 @ X3 @ X4 ) )
= X3 ) )
=> ~ ! [X3: a,X4: a] :
( ( X1 @ ( eigen__1 @ X3 @ X4 ) )
= X4 ) )
=> ~ ! [X3: a] :
( ( X3 != eigen__0 )
= ( X3
= ( eigen__1 @ ( eigen__2 @ X3 ) @ ( X1 @ X3 ) ) ) ) )
=> ~ ! [X3: a > $o] :
( ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( eigen__2 @ X5 ) ) ) )
=> ( X3 @ eigen__0 ) ) )
=> ! [X3: a > $o,X4: a] :
( ( ~ ! [X5: a] :
( ! [X6: a] :
( ! [X7: a > $o] :
( ~ ( ( X7 @ X5 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( eigen__2 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( ( X1 @ X8 )
!= X6 ) ) )
=> ( X3 @ X6 ) )
=> ~ ( X2 @ ( eigen__1 @ X5 @ X4 ) ) ) )
= ( ~ ! [X5: a] :
( ! [X6: a] :
( ! [X7: a > $o] :
( ~ ( ( X7 @ X5 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( eigen__2 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( ( X1 @ X8 )
!= X6 ) ) )
=> ( X3 @ X6 ) )
=> ! [X6: a] :
( ! [X7: a] :
( ! [X8: a > $o] :
( ~ ( ( X8 @ X6 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( X8 @ ( eigen__2 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( ( X1 @ X9 )
!= X7 ) ) )
=> ! [X8: a > $o] :
( ~ ( ( X8 @ X5 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( X8 @ ( eigen__2 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ( ( X1 @ X9 )
!= X7 ) ) ) )
=> ~ ( X2 @ ( eigen__1 @ X6 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__2 @ ( eigen__1 @ X2 @ X3 ) )
= X2 ) )
=> ~ ! [X2: a,X3: a] :
( ( eigen__3 @ ( eigen__1 @ X2 @ X3 ) )
= X3 ) )
=> ~ ! [X2: a] :
( ( X2 != eigen__0 )
= ( X2
= ( eigen__1 @ ( eigen__2 @ X2 ) @ ( eigen__3 @ X2 ) ) ) ) )
=> ~ ! [X2: a > $o] :
( ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( eigen__2 @ X4 ) ) ) )
=> ( X2 @ eigen__0 ) ) )
=> ! [X2: a > $o,X3: a] :
( ( ~ ! [X4: a] :
( ! [X5: a] :
( ! [X6: a > $o] :
( ~ ( ( X6 @ X4 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( eigen__2 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( ( eigen__3 @ X7 )
!= X5 ) ) )
=> ( X2 @ X5 ) )
=> ~ ( X1 @ ( eigen__1 @ X4 @ X3 ) ) ) )
= ( ~ ! [X4: a] :
( ! [X5: a] :
( ! [X6: a > $o] :
( ~ ( ( X6 @ X4 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( eigen__2 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( ( eigen__3 @ X7 )
!= X5 ) ) )
=> ( X2 @ X5 ) )
=> ! [X5: a] :
( ! [X6: a] :
( ! [X7: a > $o] :
( ~ ( ( X7 @ X5 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( eigen__2 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( ( eigen__3 @ X8 )
!= X6 ) ) )
=> ! [X7: a > $o] :
( ~ ( ( X7 @ X4 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( X7 @ ( eigen__2 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ( ( eigen__3 @ X8 )
!= X6 ) ) ) )
=> ~ ( X1 @ ( eigen__1 @ X5 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__3 @ ( eigen__1 @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != eigen__0 )
= ( X1
= ( eigen__1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( eigen__2 @ X3 ) ) ) )
=> ( X1 @ eigen__0 ) ) )
=> ! [X1: a > $o,X2: a] :
( ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( eigen__2 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( eigen__3 @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X3 @ X2 ) ) ) )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( eigen__2 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( eigen__3 @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ! [X4: a] :
( ! [X5: a] :
( ! [X6: a > $o] :
( ~ ( ( X6 @ X4 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( eigen__2 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( ( eigen__3 @ X7 )
!= X5 ) ) )
=> ! [X6: a > $o] :
( ~ ( ( X6 @ X3 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( eigen__2 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( ( eigen__3 @ X7 )
!= X5 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X4 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__3 @ ( eigen__1 @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != eigen__0 )
= ( X1
= ( eigen__1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( eigen__2 @ X3 ) ) ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a > $o,X2: a] :
( ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( eigen__2 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( eigen__3 @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X3 @ X2 ) ) ) )
= ( ~ ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( eigen__2 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( eigen__3 @ X6 )
!= X4 ) ) )
=> ( X1 @ X4 ) )
=> ! [X4: a] :
( ! [X5: a] :
( ! [X6: a > $o] :
( ~ ( ( X6 @ X4 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( eigen__2 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( ( eigen__3 @ X7 )
!= X5 ) ) )
=> ! [X6: a > $o] :
( ~ ( ( X6 @ X3 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( X6 @ ( eigen__2 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ( ( eigen__3 @ X7 )
!= X5 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X4 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__3 @ ( eigen__1 @ X1 @ X2 ) )
= X2 ) )
=> ~ ! [X1: a] :
( ( X1 != eigen__0 )
= ( X1
= ( eigen__1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a > $o] :
( ~ ! [X2: a] :
( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( eigen__2 @ X3 ) ) ) )
=> ( X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= X1 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__3 @ ( eigen__1 @ X1 @ X2 ) )
= X2 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a] :
( ( X1 != eigen__0 )
= ( X1
= ( eigen__1 @ ( eigen__2 @ X1 ) @ ( eigen__3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) )
=> ~ ! [X1: a,X2: a] :
( ( eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
! [X1: a,X2: a] :
( ( eigen__3 @ ( eigen__1 @ X1 @ X2 ) )
= X2 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ( ( eigen__2 @ eigen__0 )
= eigen__0 )
=> ( ( eigen__3 @ eigen__0 )
!= eigen__0 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: a,X2: a] :
( ( eigen__2 @ ( eigen__1 @ X1 @ X2 ) )
= X1 ),
introduced(assumption,[]) ).
thf(h17,assumption,
( ( eigen__2 @ eigen__0 )
= eigen__0 ),
introduced(assumption,[]) ).
thf(h18,assumption,
( ( eigen__3 @ eigen__0 )
= eigen__0 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( eigen__2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( eigen__3 @ X5 )
!= X3 ) ) )
=> ( eigen__5 @ X3 ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X2 @ X1 ) ) ) )
= ( ~ ! [X2: a] :
( ! [X3: a] :
( ! [X4: a > $o] :
( ~ ( ( X4 @ X2 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X4 @ ( eigen__2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( ( eigen__3 @ X5 )
!= X3 ) ) )
=> ( eigen__5 @ X3 ) )
=> ! [X3: a] :
( ! [X4: a] :
( ! [X5: a > $o] :
( ~ ( ( X5 @ X3 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( eigen__2 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( eigen__3 @ X6 )
!= X4 ) ) )
=> ! [X5: a > $o] :
( ~ ( ( X5 @ X2 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( X5 @ ( eigen__2 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ( ( eigen__3 @ X6 )
!= X4 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X3 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
( ~ sP2 != ~ sP13 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h23,assumption,
sP2,
introduced(assumption,[]) ).
thf(h24,assumption,
sP13,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( sP11
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP11,
introduced(assumption,[]) ).
thf(h27,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP11
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h25,h21,h22,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,h26,h27,h22]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h21,h22,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,4,h26,h27]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__7)],[h21,5,h25]) ).
thf(h28,assumption,
~ ( sP9
=> ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ( X3 @ eigen__19 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X1 @ eigen__6 ) ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP9,
introduced(assumption,[]) ).
thf(h30,assumption,
~ ! [X1: a] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) )
=> ! [X3: a > $o] :
( ~ ( ( X3 @ eigen__19 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X3 @ ( eigen__2 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( ( eigen__3 @ X4 )
!= X2 ) ) ) )
=> ~ ( eigen__4 @ ( eigen__1 @ X1 @ eigen__6 ) ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP10
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP10,
introduced(assumption,[]) ).
thf(h33,assumption,
sP15,
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP7
| ~ sP12
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| ~ sP8
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP4
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP6
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__37]) ).
thf(14,plain,
( ~ sP17
| ~ sP6
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h32,h33,h31,h29,h30,h28,h23,h24,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0])],[7,8,9,10,11,12,13,14,15,h23,h29,h32,h33]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h29,h30,h28,h23,h24,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,16,h32,h33]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h29,h30,h28,h23,h24,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__20)],[h30,17,h31]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h23,h24,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,18,h29,h30]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__19)],[h24,19,h28]) ).
thf(21,plain,
$false,
inference(tab_be,[status(thm),assumptions([h20,h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h21,h22]),tab_be(discharge,[h23,h24])],[h20,6,20,h21,h22,h23,h24]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__6)],[h19,21,h20]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__5)],[h8,22,h19]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,23,h17,h18]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,24,h15,h16]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,25,h13,h14]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,26,h11,h12]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,27,h9,h10]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,28,h7,h8]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__4)],[h5,29,h6]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,30,h5]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,31,h4]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,32,h3]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,33,h2]) ).
thf(35,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[34,h0]) ).
thf(0,theorem,
! [X1: a,X2: a > a > a,X3: a > a,X4: a > a,X5: a > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( X3 @ X1 )
= X1 )
=> ( ( X4 @ X1 )
!= X1 ) )
=> ~ ! [X6: a,X7: a] :
( ( X3 @ ( X2 @ X6 @ X7 ) )
= X6 ) )
=> ~ ! [X6: a,X7: a] :
( ( X4 @ ( X2 @ X6 @ X7 ) )
= X7 ) )
=> ~ ! [X6: a] :
( ( X6 != X1 )
= ( X6
= ( X2 @ ( X3 @ X6 ) @ ( X4 @ X6 ) ) ) ) )
=> ~ ! [X6: a > $o] :
( ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X3 @ X8 ) ) ) )
=> ( X6 @ X1 ) ) )
=> ! [X6: a > $o,X7: a] :
( ( ~ ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X4 @ X11 )
!= X9 ) ) )
=> ( X6 @ X9 ) )
=> ~ ( X5 @ ( X2 @ X8 @ X7 ) ) ) )
= ( ~ ! [X8: a] :
( ! [X9: a] :
( ! [X10: a > $o] :
( ~ ( ( X10 @ X8 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( X10 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ( ( X4 @ X11 )
!= X9 ) ) )
=> ( X6 @ X9 ) )
=> ! [X9: a] :
( ! [X10: a] :
( ! [X11: a > $o] :
( ~ ( ( X11 @ X9 )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( X3 @ X12 ) ) ) )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( ( X4 @ X12 )
!= X10 ) ) )
=> ! [X11: a > $o] :
( ~ ( ( X11 @ X8 )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( X11 @ ( X3 @ X12 ) ) ) )
=> ~ ! [X12: a] :
( ( X11 @ X12 )
=> ( ( X4 @ X12 )
!= X10 ) ) ) )
=> ~ ( X5 @ ( X2 @ X9 @ X7 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[34,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG292^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:21:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.69 % SZS status Theorem
% 0.19/0.69 % Mode: cade22grackle2xfee4
% 0.19/0.69 % Steps: 7175
% 0.19/0.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------