TSTP Solution File: SEV192^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV192^5 : 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 : Thu Aug 31 19:32:57 EDT 2023
% Result : Theorem 20.25s 20.60s
% Output : Proof 20.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_c,type,
c: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b ).
thf(ty_eigen__61,type,
eigen__61: b ).
thf(ty_eigen__5,type,
eigen__5: c > b > $o ).
thf(ty_eigen__0,type,
eigen__0: ( c > b > $o ) > $o ).
thf(ty_eigen__60,type,
eigen__60: b ).
thf(ty_eigen__70,type,
eigen__70: c > b > $o ).
thf(ty_eigen__1,type,
eigen__1: c ).
thf(ty_eigen__62,type,
eigen__62: c > b > $o ).
thf(ty_eigen__4,type,
eigen__4: b ).
thf(ty_cP,type,
cP: b > b > b ).
thf(ty_eigen__3,type,
eigen__3: b ).
thf(ty_c0,type,
c0: b ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( sP1
=> ( eigen__5 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__70 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__5 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__70 @ eigen__1 @ c0 )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__70 @ eigen__1 @ X2 )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ( eigen__70 @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ( eigen__5 @ eigen__1 @ eigen__2 )
=> ~ sP4 )
=> ~ ! [X1: b > b > b > $o] :
( ! [X2: b,X3: b,X4: b] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: b,X6: b,X7: b,X8: b,X9: b,X10: b] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ eigen__2 @ eigen__3 @ eigen__4 ) ) )
=> ( eigen__5 @ eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b > b > b > $o] :
( ! [X2: b,X3: b,X4: b] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: b,X6: b,X7: b,X8: b,X9: b,X10: b] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ eigen__60 @ eigen__61 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__62 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: b] :
( ~ ( ( eigen__62 @ eigen__1 @ X1 )
=> ~ ! [X2: b > b > b > $o] :
( ! [X3: b,X4: b,X5: b] :
( ( ~ ( ( ( X3 = c0 )
=> ( X4 != X5 ) )
=> ~ ( ( X4 = c0 )
=> ( X3 != X5 ) ) )
=> ~ ! [X6: b,X7: b,X8: b,X9: b,X10: b,X11: b] :
( ~ ( ~ ( ~ ( ( X3
= ( cP @ X6 @ X7 ) )
=> ( X4
!= ( cP @ X8 @ X9 ) ) )
=> ( X5
!= ( cP @ X10 @ X11 ) ) )
=> ~ ( X2 @ X6 @ X8 @ X10 ) )
=> ~ ( X2 @ X7 @ X9 @ X11 ) ) )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ( X2 @ eigen__60 @ X1 @ X1 ) ) )
=> ( eigen__62 @ eigen__1 @ eigen__60 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__62 @ eigen__1 @ eigen__61 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ( eigen__62 @ eigen__1 @ c0 )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__62 @ eigen__1 @ X2 )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ( eigen__62 @ eigen__1 @ X1 ) ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ~ ( ( eigen__62 @ eigen__1 @ X1 )
=> ~ ( eigen__62 @ eigen__1 @ X2 ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X1 @ X2 @ X3 ) ) )
=> ( eigen__62 @ eigen__1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ! [X2: c] :
~ ( ~ ( ( X1 @ X2 @ c0 )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ( X1 @ X2 @ X3 ) ) )
=> ~ ! [X3: b,X4: b,X5: b] :
( ~ ( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X3 @ X4 @ X5 ) ) )
=> ( X1 @ X2 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: c] :
~ ( ~ ( ( eigen__62 @ X1 @ c0 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__62 @ X1 @ X3 )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ( eigen__62 @ X1 @ X2 ) ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ~ ( ( eigen__62 @ X1 @ X2 )
=> ~ ( eigen__62 @ X1 @ X3 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X2 @ X3 @ X4 ) ) )
=> ( eigen__62 @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__62 @ eigen__1 @ X2 )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ( eigen__62 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__62 @ eigen__1 @ c0 )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP1
=> ! [X1: c] :
~ ( ~ ( ( eigen__5 @ X1 @ c0 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__5 @ X1 @ X3 )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ( eigen__5 @ X1 @ X2 ) ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ~ ( ( eigen__5 @ X1 @ X2 )
=> ~ ( eigen__5 @ X1 @ X3 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X2 @ X3 @ X4 ) ) )
=> ( eigen__5 @ X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP9
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__5 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: c] :
~ ( ~ ( ( eigen__70 @ X1 @ c0 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__70 @ X1 @ X3 )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ( eigen__70 @ X1 @ X2 ) ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ~ ( ( eigen__70 @ X1 @ X2 )
=> ~ ( eigen__70 @ X1 @ X3 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X2 @ X3 @ X4 ) ) )
=> ( eigen__70 @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP5
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ~ ( ( eigen__70 @ eigen__1 @ X1 )
=> ~ ( eigen__70 @ eigen__1 @ X2 ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X1 @ X2 @ X3 ) ) )
=> ( eigen__70 @ eigen__1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: b,X2: b,X3: b] :
( ~ ( ~ ( ( eigen__5 @ eigen__1 @ X1 )
=> ~ ( eigen__5 @ eigen__1 @ X2 ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X1 @ X2 @ X3 ) ) )
=> ( eigen__5 @ eigen__1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: b > b > b > $o] :
( ! [X2: b,X3: b,X4: b] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: b,X6: b,X7: b,X8: b,X9: b,X10: b] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ eigen__2 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP3
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__5 @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP1
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: c] :
~ ( ~ ( ( eigen__5 @ X1 @ c0 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__5 @ X1 @ X3 )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ( eigen__5 @ X1 @ X2 ) ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ~ ( ( eigen__5 @ X1 @ X2 )
=> ~ ( eigen__5 @ X1 @ X3 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X2 @ X3 @ X4 ) ) )
=> ( eigen__5 @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP11
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP20
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__70 @ eigen__1 @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( eigen__5 @ eigen__1 @ c0 )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__5 @ eigen__1 @ X2 )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ( eigen__5 @ eigen__1 @ X1 ) ) )
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ sP29
=> ( eigen__62 @ eigen__1 @ eigen__60 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP30
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: b,X2: b] :
( ~ ( ~ ( sP20
=> ~ ( eigen__5 @ eigen__1 @ X1 ) )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ eigen__2 @ X1 @ X2 ) ) )
=> ( eigen__5 @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__62 @ eigen__1 @ eigen__60 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: b] :
( ~ ( ~ sP30
=> ~ ! [X2: b > b > b > $o] :
( ! [X3: b,X4: b,X5: b] :
( ( ~ ( ( ( X3 = c0 )
=> ( X4 != X5 ) )
=> ~ ( ( X4 = c0 )
=> ( X3 != X5 ) ) )
=> ~ ! [X6: b,X7: b,X8: b,X9: b,X10: b,X11: b] :
( ~ ( ~ ( ~ ( ( X3
= ( cP @ X6 @ X7 ) )
=> ( X4
!= ( cP @ X8 @ X9 ) ) )
=> ( X5
!= ( cP @ X10 @ X11 ) ) )
=> ~ ( X2 @ X6 @ X8 @ X10 ) )
=> ~ ( X2 @ X7 @ X9 @ X11 ) ) )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ( X2 @ eigen__2 @ eigen__3 @ X1 ) ) )
=> ( eigen__5 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP9
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(cCS_DUC_RELNS_pme,conjecture,
! [X1: ( c > b > $o ) > $o] :
( ! [X2: c > b > $o] :
( ( X1 @ X2 )
=> ! [X3: c] :
~ ( ~ ( ( X2 @ X3 @ c0 )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( X2 @ X3 @ X5 )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X4 @ X5 @ X5 ) ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ~ ! [X4: b,X5: b,X6: b] :
( ~ ( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ~ ! [X7: b > b > b > $o] :
( ! [X8: b,X9: b,X10: b] :
( ( ~ ( ( ( X8 = c0 )
=> ( X9 != X10 ) )
=> ~ ( ( X9 = c0 )
=> ( X8 != X10 ) ) )
=> ~ ! [X11: b,X12: b,X13: b,X14: b,X15: b,X16: b] :
( ~ ( ~ ( ~ ( ( X8
= ( cP @ X11 @ X12 ) )
=> ( X9
!= ( cP @ X13 @ X14 ) ) )
=> ( X10
!= ( cP @ X15 @ X16 ) ) )
=> ~ ( X7 @ X11 @ X13 @ X15 ) )
=> ~ ( X7 @ X12 @ X14 @ X16 ) ) )
=> ( X7 @ X8 @ X9 @ X10 ) )
=> ( X7 @ X4 @ X5 @ X6 ) ) )
=> ( X2 @ X3 @ X6 ) ) ) )
=> ! [X2: c] :
~ ( ~ ( ! [X3: c > b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 @ c0 ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ! [X5: c > b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: c > b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b,X5: b] :
( ~ ( ~ ( ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X3 ) )
=> ~ ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X4 ) ) )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X3 @ X4 @ X5 ) ) )
=> ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X5 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: ( c > b > $o ) > $o] :
( ! [X2: c > b > $o] :
( ( X1 @ X2 )
=> ! [X3: c] :
~ ( ~ ( ( X2 @ X3 @ c0 )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( X2 @ X3 @ X5 )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X4 @ X5 @ X5 ) ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ~ ! [X4: b,X5: b,X6: b] :
( ~ ( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ~ ! [X7: b > b > b > $o] :
( ! [X8: b,X9: b,X10: b] :
( ( ~ ( ( ( X8 = c0 )
=> ( X9 != X10 ) )
=> ~ ( ( X9 = c0 )
=> ( X8 != X10 ) ) )
=> ~ ! [X11: b,X12: b,X13: b,X14: b,X15: b,X16: b] :
( ~ ( ~ ( ~ ( ( X8
= ( cP @ X11 @ X12 ) )
=> ( X9
!= ( cP @ X13 @ X14 ) ) )
=> ( X10
!= ( cP @ X15 @ X16 ) ) )
=> ~ ( X7 @ X11 @ X13 @ X15 ) )
=> ~ ( X7 @ X12 @ X14 @ X16 ) ) )
=> ( X7 @ X8 @ X9 @ X10 ) )
=> ( X7 @ X4 @ X5 @ X6 ) ) )
=> ( X2 @ X3 @ X6 ) ) ) )
=> ! [X2: c] :
~ ( ~ ( ! [X3: c > b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 @ c0 ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ! [X5: c > b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: c > b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b,X5: b] :
( ~ ( ~ ( ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X3 ) )
=> ~ ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X4 ) ) )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X3 @ X4 @ X5 ) ) )
=> ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cCS_DUC_RELNS_pme]) ).
thf(h1,assumption,
~ ( sP14
=> ! [X1: c] :
~ ( ~ ( ! [X2: c > b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 @ c0 ) )
=> ~ ! [X2: b,X3: b] :
( ~ ( ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ X1 @ X3 ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ X1 @ X2 ) ) ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ~ ( ! [X5: c > b > $o] :
( ( eigen__0 @ X5 )
=> ( X5 @ X1 @ X2 ) )
=> ~ ! [X5: c > b > $o] :
( ( eigen__0 @ X5 )
=> ( X5 @ X1 @ X3 ) ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X2 @ X3 @ X4 ) ) )
=> ! [X5: c > b > $o] :
( ( eigen__0 @ X5 )
=> ( X5 @ X1 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP14,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: c] :
~ ( ~ ( ! [X2: c > b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ X1 @ c0 ) )
=> ~ ! [X2: b,X3: b] :
( ~ ( ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ X1 @ X3 ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X2 @ X3 @ X3 ) ) )
=> ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ X1 @ X2 ) ) ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ~ ( ! [X5: c > b > $o] :
( ( eigen__0 @ X5 )
=> ( X5 @ X1 @ X2 ) )
=> ~ ! [X5: c > b > $o] :
( ( eigen__0 @ X5 )
=> ( X5 @ X1 @ X3 ) ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X2 @ X3 @ X4 ) ) )
=> ! [X5: c > b > $o] :
( ( eigen__0 @ X5 )
=> ( X5 @ X1 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ ( ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ c0 ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X2 ) )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X1 ) ) ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ~ ( ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ eigen__1 @ X1 ) )
=> ~ ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ eigen__1 @ X2 ) ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X1 @ X2 @ X3 ) ) )
=> ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ eigen__1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ c0 ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X2 ) )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b,X2: b,X3: b] :
( ~ ( ~ ( ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ eigen__1 @ X1 ) )
=> ~ ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ eigen__1 @ X2 ) ) )
=> ~ ! [X4: b > b > b > $o] :
( ! [X5: b,X6: b,X7: b] :
( ( ~ ( ( ( X5 = c0 )
=> ( X6 != X7 ) )
=> ~ ( ( X6 = c0 )
=> ( X5 != X7 ) ) )
=> ~ ! [X8: b,X9: b,X10: b,X11: b,X12: b,X13: b] :
( ~ ( ~ ( ~ ( ( X5
= ( cP @ X8 @ X9 ) )
=> ( X6
!= ( cP @ X10 @ X11 ) ) )
=> ( X7
!= ( cP @ X12 @ X13 ) ) )
=> ~ ( X4 @ X8 @ X10 @ X12 ) )
=> ~ ( X4 @ X9 @ X11 @ X13 ) ) )
=> ( X4 @ X5 @ X6 @ X7 ) )
=> ( X4 @ X1 @ X2 @ X3 ) ) )
=> ! [X4: c > b > $o] :
( ( eigen__0 @ X4 )
=> ( X4 @ eigen__1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ c0 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: b,X2: b] :
( ~ ( ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X2 ) )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ X1 @ X2 @ X2 ) ) )
=> ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP3
=> sP31 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP3,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP31,
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP22
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP21
| ~ sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP25
| ~ sP3
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h5,h4,h2,h3,h1,h0])],[1,2,3,4,5,h2,h10,h11]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,6,h10,h11]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__70)],[h7,7,h9]) ).
thf(h12,assumption,
~ ! [X1: b] :
( ~ ( ! [X2: c > b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ eigen__1 @ X1 ) )
=> ~ ! [X2: b > b > b > $o] :
( ! [X3: b,X4: b,X5: b] :
( ( ~ ( ( ( X3 = c0 )
=> ( X4 != X5 ) )
=> ~ ( ( X4 = c0 )
=> ( X3 != X5 ) ) )
=> ~ ! [X6: b,X7: b,X8: b,X9: b,X10: b,X11: b] :
( ~ ( ~ ( ~ ( ( X3
= ( cP @ X6 @ X7 ) )
=> ( X4
!= ( cP @ X8 @ X9 ) ) )
=> ( X5
!= ( cP @ X10 @ X11 ) ) )
=> ~ ( X2 @ X6 @ X8 @ X10 ) )
=> ~ ( X2 @ X7 @ X9 @ X11 ) ) )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ( X2 @ eigen__60 @ X1 @ X1 ) ) )
=> ! [X2: c > b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ eigen__1 @ eigen__60 ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP12
=> ~ sP8 )
=> ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__60 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP12
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__60 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP12,
introduced(assumption,[]) ).
thf(h17,assumption,
sP8,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP9
=> sP37 ),
introduced(assumption,[]) ).
thf(h19,assumption,
sP9,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP37,
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP29
| ~ sP11
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP33
| sP29
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP17
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP13
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| ~ sP9
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP39
| ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP14
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP12
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h16,h17,h14,h15,h13,h12,h8,h5,h4,h2,h3,h1,h0])],[9,10,11,12,13,14,15,16,17,18,19,h2,h16,h17,h19,h20]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h14,h15,h13,h12,h8,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,20,h19,h20]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h14,h15,h13,h12,h8,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__62)],[h15,21,h18]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h12,h8,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,22,h16,h17]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h8,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,23,h14,h15]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h8,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__61)],[h12,24,h13]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__60)],[h8,25,h12]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,8,26,h7,h8]) ).
thf(h21,assumption,
~ ! [X1: b,X2: b] :
( ~ ( ~ ( sP7
=> ~ ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X1 ) ) )
=> ~ ! [X3: b > b > b > $o] :
( ! [X4: b,X5: b,X6: b] :
( ( ~ ( ( ( X4 = c0 )
=> ( X5 != X6 ) )
=> ~ ( ( X5 = c0 )
=> ( X4 != X6 ) ) )
=> ~ ! [X7: b,X8: b,X9: b,X10: b,X11: b,X12: b] :
( ~ ( ~ ( ~ ( ( X4
= ( cP @ X7 @ X8 ) )
=> ( X5
!= ( cP @ X9 @ X10 ) ) )
=> ( X6
!= ( cP @ X11 @ X12 ) ) )
=> ~ ( X3 @ X7 @ X9 @ X11 ) )
=> ~ ( X3 @ X8 @ X10 @ X12 ) ) )
=> ( X3 @ X4 @ X5 @ X6 ) )
=> ( X3 @ eigen__2 @ X1 @ X2 ) ) )
=> ! [X3: c > b > $o] :
( ( eigen__0 @ X3 )
=> ( X3 @ eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ! [X1: b] :
( ~ ( ~ ( sP7
=> ~ sP36 )
=> ~ ! [X2: b > b > b > $o] :
( ! [X3: b,X4: b,X5: b] :
( ( ~ ( ( ( X3 = c0 )
=> ( X4 != X5 ) )
=> ~ ( ( X4 = c0 )
=> ( X3 != X5 ) ) )
=> ~ ! [X6: b,X7: b,X8: b,X9: b,X10: b,X11: b] :
( ~ ( ~ ( ~ ( ( X3
= ( cP @ X6 @ X7 ) )
=> ( X4
!= ( cP @ X8 @ X9 ) ) )
=> ( X5
!= ( cP @ X10 @ X11 ) ) )
=> ~ ( X2 @ X6 @ X8 @ X10 ) )
=> ~ ( X2 @ X7 @ X9 @ X11 ) ) )
=> ( X2 @ X3 @ X4 @ X5 ) )
=> ( X2 @ eigen__2 @ eigen__3 @ X1 ) ) )
=> ! [X2: c > b > $o] :
( ( eigen__0 @ X2 )
=> ( X2 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( ~ ( ~ ( sP7
=> ~ sP36 )
=> ~ sP24 )
=> ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__4 ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ( ~ ( sP7
=> ~ sP36 )
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ! [X1: c > b > $o] :
( ( eigen__0 @ X1 )
=> ( X1 @ eigen__1 @ eigen__4 ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( sP7
=> ~ sP36 ),
introduced(assumption,[]) ).
thf(h27,assumption,
sP24,
introduced(assumption,[]) ).
thf(h28,assumption,
sP7,
introduced(assumption,[]) ).
thf(h29,assumption,
sP36,
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( sP1
=> sP26 ),
introduced(assumption,[]) ).
thf(h31,assumption,
sP1,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(28,plain,
( ~ sP30
| ~ sP20
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP34
| sP30
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP6
| sP34
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP38
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP35
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP23
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( sP32
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP28
| ~ sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP18
| ~ sP1
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP27
| ~ sP1
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP2
| ~ sP1
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP14
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP7
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP36
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h32,h30,h28,h29,h26,h27,h24,h25,h23,h22,h21,h6,h4,h2,h3,h1,h0])],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,h2,h28,h29,h27,h31,h32]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h28,h29,h26,h27,h24,h25,h23,h22,h21,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,42,h31,h32]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h23,h22,h21,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__5)],[h25,43,h30]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h23,h22,h21,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h26,44,h28,h29]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h23,h22,h21,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h24,45,h26,h27]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h22,h21,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,46,h24,h25]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h22,h21,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__4)],[h22,47,h23]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__3)],[h21,48,h22]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__2)],[h6,49,h21]) ).
thf(51,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,27,50,h5,h6]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,51,h4]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,52,h2,h3]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,53,h1]) ).
thf(0,theorem,
! [X1: ( c > b > $o ) > $o] :
( ! [X2: c > b > $o] :
( ( X1 @ X2 )
=> ! [X3: c] :
~ ( ~ ( ( X2 @ X3 @ c0 )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( X2 @ X3 @ X5 )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X4 @ X5 @ X5 ) ) )
=> ( X2 @ X3 @ X4 ) ) )
=> ~ ! [X4: b,X5: b,X6: b] :
( ~ ( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ~ ! [X7: b > b > b > $o] :
( ! [X8: b,X9: b,X10: b] :
( ( ~ ( ( ( X8 = c0 )
=> ( X9 != X10 ) )
=> ~ ( ( X9 = c0 )
=> ( X8 != X10 ) ) )
=> ~ ! [X11: b,X12: b,X13: b,X14: b,X15: b,X16: b] :
( ~ ( ~ ( ~ ( ( X8
= ( cP @ X11 @ X12 ) )
=> ( X9
!= ( cP @ X13 @ X14 ) ) )
=> ( X10
!= ( cP @ X15 @ X16 ) ) )
=> ~ ( X7 @ X11 @ X13 @ X15 ) )
=> ~ ( X7 @ X12 @ X14 @ X16 ) ) )
=> ( X7 @ X8 @ X9 @ X10 ) )
=> ( X7 @ X4 @ X5 @ X6 ) ) )
=> ( X2 @ X3 @ X6 ) ) ) )
=> ! [X2: c] :
~ ( ~ ( ! [X3: c > b > $o] :
( ( X1 @ X3 )
=> ( X3 @ X2 @ c0 ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ! [X5: c > b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X2 @ X4 ) )
=> ~ ! [X5: b > b > b > $o] :
( ! [X6: b,X7: b,X8: b] :
( ( ~ ( ( ( X6 = c0 )
=> ( X7 != X8 ) )
=> ~ ( ( X7 = c0 )
=> ( X6 != X8 ) ) )
=> ~ ! [X9: b,X10: b,X11: b,X12: b,X13: b,X14: b] :
( ~ ( ~ ( ~ ( ( X6
= ( cP @ X9 @ X10 ) )
=> ( X7
!= ( cP @ X11 @ X12 ) ) )
=> ( X8
!= ( cP @ X13 @ X14 ) ) )
=> ~ ( X5 @ X9 @ X11 @ X13 ) )
=> ~ ( X5 @ X10 @ X12 @ X14 ) ) )
=> ( X5 @ X6 @ X7 @ X8 ) )
=> ( X5 @ X3 @ X4 @ X4 ) ) )
=> ! [X5: c > b > $o] :
( ( X1 @ X5 )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b,X5: b] :
( ~ ( ~ ( ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X3 ) )
=> ~ ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X4 ) ) )
=> ~ ! [X6: b > b > b > $o] :
( ! [X7: b,X8: b,X9: b] :
( ( ~ ( ( ( X7 = c0 )
=> ( X8 != X9 ) )
=> ~ ( ( X8 = c0 )
=> ( X7 != X9 ) ) )
=> ~ ! [X10: b,X11: b,X12: b,X13: b,X14: b,X15: b] :
( ~ ( ~ ( ~ ( ( X7
= ( cP @ X10 @ X11 ) )
=> ( X8
!= ( cP @ X12 @ X13 ) ) )
=> ( X9
!= ( cP @ X14 @ X15 ) ) )
=> ~ ( X6 @ X10 @ X12 @ X14 ) )
=> ~ ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) )
=> ( X6 @ X3 @ X4 @ X5 ) ) )
=> ! [X6: c > b > $o] :
( ( X1 @ X6 )
=> ( X6 @ X2 @ X5 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[54,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV192^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.30 % Computer : n010.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Aug 24 03:12:51 EDT 2023
% 0.09/0.30 % CPUTime :
% 20.25/20.60 % SZS status Theorem
% 20.25/20.60 % Mode: cade22grackle2x798d
% 20.25/20.60 % Steps: 1798
% 20.25/20.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------