TSTP Solution File: SEV037^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV037^5 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:04:33 EDT 2022
% Result : Theorem 260.44s 260.55s
% Output : Proof 260.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $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 > b ).
thf(ty_eigen__2,type,
eigen__2: a > b > b > $o ).
thf(ty_eigen__16,type,
eigen__16: a ).
thf(ty_eigen__7,type,
eigen__7: a > b ).
thf(ty_eigen__15,type,
eigen__15: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > b ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__3,type,
eigen__3: a > b ).
thf(ty_eigen__17,type,
eigen__17: a ).
thf(ty_eigen__10,type,
eigen__10: a ).
thf(ty_eigen__8,type,
eigen__8: a > b ).
thf(ty_eigen__13,type,
eigen__13: a > b ).
thf(ty_eigen__9,type,
eigen__9: a > b ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 @ eigen__10 @ ( eigen__8 @ eigen__10 ) @ ( eigen__9 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__6 @ eigen__5 )
=> ~ ( ~ ( ! [X1: b,X2: b] :
( ( eigen__2 @ eigen__6 @ X1 @ X2 )
=> ( eigen__2 @ eigen__6 @ X2 @ X1 ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__2 @ eigen__6 @ X1 @ X2 )
=> ~ ( eigen__2 @ eigen__6 @ X2 @ X3 ) )
=> ( eigen__2 @ eigen__6 @ X1 @ X3 ) ) )
=> ( ( eigen__2 @ eigen__6 )
!= ( eigen__2 @ eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ ( eigen__8 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( eigen__0 @ eigen__10 @ X1 )
=> ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ ( eigen__8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__11 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ! [X1: b,X2: b] :
( ( eigen__2 @ eigen__10 @ X1 @ X2 )
=> ( eigen__2 @ eigen__10 @ X2 @ X1 ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__2 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__2 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__2 @ eigen__10 @ X1 @ X3 ) ) )
=> ( ( eigen__2 @ eigen__10 )
!= ( eigen__2 @ eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ eigen__14 @ eigen__15 )
=> ( eigen__2 @ eigen__14 @ ( eigen__12 @ eigen__14 ) @ ( eigen__13 @ eigen__15 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__10 @ eigen__11 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__0 @ eigen__10 @ eigen__11 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: b,X2: b] :
( ( eigen__2 @ eigen__6 @ X1 @ X2 )
=> ( eigen__2 @ eigen__6 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__7 @ X1 ) @ ( eigen__8 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__2 @ eigen__6 @ ( eigen__3 @ eigen__6 ) @ ( eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( eigen__0 @ eigen__10 @ X1 )
=> ( eigen__2 @ eigen__10 @ ( eigen__8 @ eigen__10 ) @ ( eigen__9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__12 @ X1 ) @ ( eigen__13 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0 @ eigen__10 @ eigen__10 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ ( eigen__9 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a] :
( ( eigen__0 @ eigen__10 @ X1 )
=> ~ ( ~ ( ! [X2: b,X3: b] :
( ( eigen__2 @ eigen__10 @ X2 @ X3 )
=> ( eigen__2 @ eigen__10 @ X3 @ X2 ) )
=> ~ ! [X2: b,X3: b,X4: b] :
( ~ ( ( eigen__2 @ eigen__10 @ X2 @ X3 )
=> ~ ( eigen__2 @ eigen__10 @ X3 @ X4 ) )
=> ( eigen__2 @ eigen__10 @ X2 @ X4 ) ) )
=> ( ( eigen__2 @ eigen__10 )
!= ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__2 @ eigen__6 @ ( eigen__4 @ eigen__5 ) @ ( eigen__3 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: b] :
( ( eigen__2 @ eigen__6 @ X1 )
= ( eigen__2 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__2 @ eigen__6 )
= ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__0 @ X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0 @ eigen__14 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__0 @ eigen__16 @ X1 )
= ( eigen__1 @ eigen__16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ! [X1: b,X2: b] :
( ( eigen__2 @ eigen__10 @ X1 @ X2 )
=> ( eigen__2 @ eigen__10 @ X2 @ X1 ) )
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__2 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__2 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__2 @ eigen__10 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP22
= ( eigen__2 @ eigen__5 @ ( eigen__4 @ eigen__5 ) @ ( eigen__3 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( eigen__1 @ eigen__16 @ eigen__17 )
=> ( eigen__2 @ eigen__16 @ ( eigen__12 @ eigen__16 ) @ ( eigen__13 @ eigen__17 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( eigen__0 @ eigen__10 @ eigen__11 )
=> ~ sP7 )
=> ( eigen__0 @ eigen__10 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ( sP5
=> ~ sP2 )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a,X2: a] :
( ( eigen__1 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__12 @ X1 ) @ ( eigen__13 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a] :
( ~ ( ( eigen__0 @ eigen__10 @ eigen__11 )
=> ~ ( eigen__0 @ eigen__11 @ X1 ) )
=> ( eigen__0 @ eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__0 @ eigen__10 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__10 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: b] :
( ~ ( sP5
=> ~ ( eigen__2 @ eigen__10 @ ( eigen__8 @ eigen__10 ) @ X1 ) )
=> ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( eigen__0 @ eigen__6 @ eigen__5 )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eigen__1 @ eigen__14 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: b] :
( ( eigen__2 @ eigen__6 @ ( eigen__3 @ eigen__6 ) @ X1 )
=> ( eigen__2 @ eigen__6 @ X1 @ ( eigen__3 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__1 @ eigen__16 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP26 = sP39 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__0 @ eigen__10 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__2 @ eigen__10 @ X1 @ X2 )
=> ~ ( eigen__2 @ eigen__10 @ X2 @ X3 ) )
=> ( eigen__2 @ eigen__10 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP5
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( eigen__2 @ eigen__14 @ ( eigen__12 @ eigen__14 ) @ ( eigen__13 @ eigen__15 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ X1 )
=> ~ ( eigen__2 @ eigen__10 @ X1 @ X2 ) )
=> ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: a] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__2 @ eigen__6 @ ( eigen__3 @ eigen__6 ) @ ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: a] :
( ( eigen__0 @ eigen__14 @ X1 )
=> ( eigen__2 @ eigen__14 @ ( eigen__12 @ eigen__14 ) @ ( eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP1
=> ( eigen__0 @ eigen__6 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: a] :
( ( eigen__0 @ eigen__10 @ X1 )
=> ( eigen__0 @ X1 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__3 @ X1 ) @ ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( eigen__2 @ eigen__5 @ ( eigen__4 @ eigen__5 ) @ ( eigen__3 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: a] :
( ( eigen__0 @ eigen__14 @ X1 )
= ( eigen__1 @ eigen__14 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP13
=> ~ ! [X1: b,X2: b,X3: b] :
( ~ ( ( eigen__2 @ eigen__6 @ X1 @ X2 )
=> ~ ( eigen__2 @ eigen__6 @ X2 @ X3 ) )
=> ( eigen__2 @ eigen__6 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( eigen__2 @ eigen__16 @ ( eigen__12 @ eigen__16 ) @ ( eigen__13 @ eigen__17 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP15
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: a] :
( ( eigen__1 @ eigen__16 @ X1 )
=> ( eigen__2 @ eigen__16 @ ( eigen__12 @ eigen__16 ) @ ( eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: b] :
( ( eigen__2 @ eigen__6 @ ( eigen__4 @ eigen__5 ) @ X1 )
= ( eigen__2 @ eigen__5 @ ( eigen__4 @ eigen__5 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ sP55
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( eigen__0 @ eigen__10 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__8 @ X1 ) @ ( eigen__9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( eigen__2 @ eigen__6 @ ( eigen__4 @ eigen__5 ) )
= ( eigen__2 @ eigen__5 @ ( eigen__4 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ( eigen__0 @ eigen__16 )
= ( eigen__1 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: a] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ~ ( ~ sP55
=> ( ( eigen__2 @ eigen__6 )
!= ( eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( eigen__0 @ eigen__14 )
= ( eigen__1 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP61
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( eigen__0 @ eigen__16 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( ~ ( ! [X3: b,X4: b] :
( ( eigen__2 @ X1 @ X3 @ X4 )
=> ( eigen__2 @ X1 @ X4 @ X3 ) )
=> ~ ! [X3: b,X4: b,X5: b] :
( ~ ( ( eigen__2 @ X1 @ X3 @ X4 )
=> ~ ( eigen__2 @ X1 @ X4 @ X5 ) )
=> ( eigen__2 @ X1 @ X3 @ X5 ) ) )
=> ( ( eigen__2 @ X1 )
!= ( eigen__2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP68 = sP41 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( eigen__0 @ eigen__6 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP61
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(cTHM516_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o,X3: a > b > b > $o] :
( ~ ( ~ ( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X1 @ X4 @ X5 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X1 @ X4 @ X6 ) ) )
=> ( X1 != X2 ) )
=> ( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ~ ( ~ ( ! [X6: b,X7: b] :
( ( X3 @ X4 @ X6 @ X7 )
=> ( X3 @ X4 @ X7 @ X6 ) )
=> ~ ! [X6: b,X7: b,X8: b] :
( ~ ( ( X3 @ X4 @ X6 @ X7 )
=> ~ ( X3 @ X4 @ X7 @ X8 ) )
=> ( X3 @ X4 @ X6 @ X8 ) ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) ) )
=> ~ ( ~ ( ! [X4: a > b,X5: a > b] :
( ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) )
=> ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X5 @ X6 ) @ ( X4 @ X7 ) ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X4 @ X7 ) @ ( X5 @ X8 ) ) )
=> ~ ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X5 @ X7 ) @ ( X6 @ X8 ) ) ) )
=> ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X4 @ X7 ) @ ( X6 @ X8 ) ) ) ) )
=> ( ( ^ [X4: a > b,X5: a > b] :
! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) )
!= ( ^ [X4: a > b,X5: a > b] :
! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o,X3: a > b > b > $o] :
( ~ ( ~ ( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X1 @ X4 @ X5 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X1 @ X4 @ X6 ) ) )
=> ( X1 != X2 ) )
=> ( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ~ ( ~ ( ! [X6: b,X7: b] :
( ( X3 @ X4 @ X6 @ X7 )
=> ( X3 @ X4 @ X7 @ X6 ) )
=> ~ ! [X6: b,X7: b,X8: b] :
( ~ ( ( X3 @ X4 @ X6 @ X7 )
=> ~ ( X3 @ X4 @ X7 @ X8 ) )
=> ( X3 @ X4 @ X6 @ X8 ) ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) ) )
=> ~ ( ~ ( ! [X4: a > b,X5: a > b] :
( ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) )
=> ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X5 @ X6 ) @ ( X4 @ X7 ) ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X4 @ X7 ) @ ( X5 @ X8 ) ) )
=> ~ ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X5 @ X7 ) @ ( X6 @ X8 ) ) ) )
=> ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X4 @ X7 ) @ ( X6 @ X8 ) ) ) ) )
=> ( ( ^ [X4: a > b,X5: a > b] :
! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) )
!= ( ^ [X4: a > b,X5: a > b] :
! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM516_pme]) ).
thf(h1,assumption,
~ ! [X1: a > a > $o,X2: a > b > b > $o] :
( ~ ( ~ ( sP4
=> ~ sP27 )
=> ( eigen__0 != X1 ) )
=> ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ~ ( ~ ( ! [X5: b,X6: b] :
( ( X2 @ X3 @ X5 @ X6 )
=> ( X2 @ X3 @ X6 @ X5 ) )
=> ~ ! [X5: b,X6: b,X7: b] :
( ~ ( ( X2 @ X3 @ X5 @ X6 )
=> ~ ( X2 @ X3 @ X6 @ X7 ) )
=> ( X2 @ X3 @ X5 @ X7 ) ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) ) )
=> ~ ( ~ ( ! [X3: a > b,X4: a > b] :
( ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) )
=> ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X4 @ X5 ) @ ( X3 @ X6 ) ) ) )
=> ~ ! [X3: a > b,X4: a > b,X5: a > b] :
( ~ ( ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X7 ) ) )
=> ~ ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) )
=> ! [X6: a,X7: a] :
( ( eigen__0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X7 ) ) ) ) )
=> ( ( ^ [X3: a > b,X4: a > b] :
! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) )
!= ( ^ [X3: a > b,X4: a > b] :
! [X5: a,X6: a] :
( ( X1 @ X5 @ X6 )
=> ( X2 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > b > b > $o] :
( ~ ( ~ ( sP4
=> ~ sP27 )
=> ~ sP12 )
=> ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ~ ( ~ ( ! [X4: b,X5: b] :
( ( X1 @ X2 @ X4 @ X5 )
=> ( X1 @ X2 @ X5 @ X4 ) )
=> ~ ! [X4: b,X5: b,X6: b] :
( ~ ( ( X1 @ X2 @ X4 @ X5 )
=> ~ ( X1 @ X2 @ X5 @ X6 ) )
=> ( X1 @ X2 @ X4 @ X6 ) ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) ) )
=> ~ ( ~ ( ! [X2: a > b,X3: a > b] :
( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X5 ) ) ) )
=> ~ ! [X2: a > b,X3: a > b,X4: a > b] :
( ~ ( ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
=> ~ ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) )
=> ! [X5: a,X6: a] :
( ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X6 ) ) ) ) )
=> ( ( ^ [X2: a > b,X3: a > b] :
! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) )
!= ( ^ [X2: a > b,X3: a > b] :
! [X4: a,X5: a] :
( ( eigen__1 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( sP4
=> ~ sP27 )
=> ~ sP12 )
=> ( sP69
=> ~ ( ~ ( ! [X1: a > b,X2: a > b] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X5 ) ) ) ) )
=> ( ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) )
!= ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP4
=> ~ sP27 )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP69
=> ~ ( ~ ( ! [X1: a > b,X2: a > b] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X5 ) ) ) ) )
=> ( ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) )
!= ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP4
=> ~ sP27 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(h9,assumption,
sP27,
introduced(assumption,[]) ).
thf(h10,assumption,
sP69,
introduced(assumption,[]) ).
thf(h11,assumption,
( ~ ( ! [X1: a > b,X2: a > b] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X5 ) ) ) ) )
=> ( ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) )
!= ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( ! [X1: a > b,X2: a > b] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X4 ) ) ) )
=> ~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) )
!= ( ^ [X1: a > b,X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: a > b,X2: a > b] :
( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) )
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X2 @ X3 ) @ ( X1 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: a > b,X2: a > b,X3: a > b] :
( ~ ( ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X2 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) )
=> ! [X4: a,X5: a] :
( ( eigen__0 @ X4 @ X5 )
=> ( eigen__2 @ X4 @ ( X1 @ X4 ) @ ( X3 @ X5 ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: a > b] :
( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__3 @ X2 ) @ ( X1 @ X3 ) ) )
=> ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( X1 @ X2 ) @ ( eigen__3 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP52
=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__4 @ X1 ) @ ( eigen__3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP52,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__4 @ X1 ) @ ( eigen__3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__2 @ eigen__5 @ ( eigen__4 @ eigen__5 ) @ ( eigen__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP1
=> sP53 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP1,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP53,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP30
| ~ sP22
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP59
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP63
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP23
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP24
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP60
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP60
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP40
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP57
| ~ sP15
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP55
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP3
| ~ sP71
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP38
| ~ sP71
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP65
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP48
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP4
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP25
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP50
| ~ sP1
| sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP69
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP52
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h20,h18,h19,h17,h16,h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h8,h10,h18,h22,h23]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h20,h18,h19,h17,h16,h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,21,h22,h23]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h20,h18,h19,h17,h16,h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__6)],[h20,22,h21]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h16,h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,23,h20]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h16,h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,24,h18,h19]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,25,h17]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h14,26,h16]) ).
thf(h24,assumption,
~ ! [X1: a > b,X2: a > b] :
( ~ ( ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( eigen__7 @ X3 ) @ ( X1 @ X4 ) ) )
=> ~ ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) )
=> ! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( eigen__7 @ X3 ) @ ( X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ! [X1: a > b] :
( ~ ( sP14
=> ~ ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__8 @ X2 ) @ ( X1 @ X3 ) ) ) )
=> ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__7 @ X2 ) @ ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ~ ( sP14
=> ~ sP62 )
=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__7 @ X1 ) @ ( eigen__9 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( sP14
=> ~ sP62 ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__2 @ X1 @ ( eigen__7 @ X1 ) @ ( eigen__9 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP14,
introduced(assumption,[]) ).
thf(h30,assumption,
sP62,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__10 @ X1 )
=> ( eigen__2 @ eigen__10 @ ( eigen__7 @ eigen__10 ) @ ( eigen__9 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( sP61
=> sP19 ),
introduced(assumption,[]) ).
thf(h33,assumption,
sP61,
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(28,plain,
( ~ sP37
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP33
| sP45
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP45
| ~ sP5
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP47
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP44
| sP47 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( sP29
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP8
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP32
| sP67
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP67
| ~ sP61
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP35
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP18
| ~ sP43
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP36
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP6
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP27
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP62
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP16
| sP72 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP72
| ~ sP61
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP69
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP21
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP10
| ~ sP61
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP4
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP51
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP11
| ~ sP61
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h34,h32,h31,h29,h30,h27,h28,h26,h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,h8,h9,h10,h29,h30,h33,h34]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h31,h29,h30,h27,h28,h26,h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h32,52,h33,h34]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h29,h30,h27,h28,h26,h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__11)],[h31,53,h32]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h29,h30,h27,h28,h26,h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__10)],[h28,54,h31]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h28,h26,h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h29,h30])],[h27,55,h29,h30]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,56,h27,h28]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__9)],[h25,57,h26]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__8)],[h24,58,h25]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__7)],[h15,59,h24]) ).
thf(61,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h12,27,60,h14,h15]) ).
thf(h35,assumption,
~ ! [X1: a > b] :
( ( ^ [X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__0 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) )
= ( ^ [X2: a > b] :
! [X3: a,X4: a] :
( ( eigen__1 @ X3 @ X4 )
=> ( eigen__2 @ X3 @ ( X1 @ X3 ) @ ( X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
( ^ [X1: a > b] :
! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__12 @ X2 ) @ ( X1 @ X3 ) ) ) )
!= ( ^ [X1: a > b] :
! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__12 @ X2 ) @ ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
~ ! [X1: a > b] :
( ( ! [X2: a,X3: a] :
( ( eigen__0 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__12 @ X2 ) @ ( X1 @ X3 ) ) ) )
= ( ! [X2: a,X3: a] :
( ( eigen__1 @ X2 @ X3 )
=> ( eigen__2 @ X2 @ ( eigen__12 @ X2 ) @ ( X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP17 != sP34,
introduced(assumption,[]) ).
thf(h39,assumption,
sP17,
introduced(assumption,[]) ).
thf(h40,assumption,
sP34,
introduced(assumption,[]) ).
thf(h41,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h42,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h43,assumption,
~ ! [X1: a] :
( ( eigen__1 @ eigen__14 @ X1 )
=> ( eigen__2 @ eigen__14 @ ( eigen__12 @ eigen__14 ) @ ( eigen__13 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
~ ( sP39
=> sP46 ),
introduced(assumption,[]) ).
thf(h45,assumption,
sP39,
introduced(assumption,[]) ).
thf(h46,assumption,
~ sP46,
introduced(assumption,[]) ).
thf(62,plain,
( ~ sP42
| sP26
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP54
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP66
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP20
| sP66 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP12
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP17
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP49
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP9
| ~ sP26
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h45,h46,h44,h43,h39,h40,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[62,63,64,65,66,67,68,69,h7,h39,h45,h46]) ).
thf(71,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h44,h43,h39,h40,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h45,h46])],[h44,70,h45,h46]) ).
thf(72,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h43,h39,h40,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__15)],[h43,71,h44]) ).
thf(73,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h39,h40,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h43]),tab_negall(eigenvar,eigen__14)],[h40,72,h43]) ).
thf(h47,assumption,
~ ! [X1: a] :
( ( eigen__0 @ eigen__16 @ X1 )
=> ( eigen__2 @ eigen__16 @ ( eigen__12 @ eigen__16 ) @ ( eigen__13 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h48,assumption,
~ ( sP68
=> sP56 ),
introduced(assumption,[]) ).
thf(h49,assumption,
sP68,
introduced(assumption,[]) ).
thf(h50,assumption,
~ sP56,
introduced(assumption,[]) ).
thf(74,plain,
( ~ sP70
| ~ sP68
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP28
| sP70 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP64
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP20
| sP64 ),
inference(all_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP12
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP58
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP31
| ~ sP41
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP34
| sP58 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h49,h50,h48,h47,h41,h42,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[74,75,76,77,78,79,80,81,h7,h49,h50,h42]) ).
thf(83,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h48,h47,h41,h42,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h49,h50])],[h48,82,h49,h50]) ).
thf(84,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h47,h41,h42,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h48]),tab_negall(eigenvar,eigen__17)],[h47,83,h48]) ).
thf(85,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h41,h42,h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h47]),tab_negall(eigenvar,eigen__16)],[h41,84,h47]) ).
thf(86,plain,
$false,
inference(tab_be,[status(thm),assumptions([h38,h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h39,h40]),tab_be(discharge,[h41,h42])],[h38,73,85,h39,h40,h41,h42]) ).
thf(87,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h37,h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h38]),tab_negall(eigenvar,eigen__13)],[h37,86,h38]) ).
thf(88,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h36,h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_fe(discharge,[h37])],[h36,87,h37]) ).
thf(89,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h35,h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__12)],[h35,88,h36]) ).
thf(90,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h13,h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_fe(discharge,[h35])],[h13,89,h35]) ).
thf(91,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h11,61,90,h12,h13]) ).
thf(92,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h5,91,h10,h11]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,92,h8,h9]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,93,h6,h7]) ).
thf(95,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,94,h4,h5]) ).
thf(96,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,95,h3]) ).
thf(97,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,96,h2]) ).
thf(98,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,97,h1]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o,X3: a > b > b > $o] :
( ~ ( ~ ( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ( X1 @ X5 @ X4 ) )
=> ~ ! [X4: a,X5: a,X6: a] :
( ~ ( ( X1 @ X4 @ X5 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X1 @ X4 @ X6 ) ) )
=> ( X1 != X2 ) )
=> ( ! [X4: a,X5: a] :
( ( X1 @ X4 @ X5 )
=> ~ ( ~ ( ! [X6: b,X7: b] :
( ( X3 @ X4 @ X6 @ X7 )
=> ( X3 @ X4 @ X7 @ X6 ) )
=> ~ ! [X6: b,X7: b,X8: b] :
( ~ ( ( X3 @ X4 @ X6 @ X7 )
=> ~ ( X3 @ X4 @ X7 @ X8 ) )
=> ( X3 @ X4 @ X6 @ X8 ) ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) ) )
=> ~ ( ~ ( ! [X4: a > b,X5: a > b] :
( ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) )
=> ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X5 @ X6 ) @ ( X4 @ X7 ) ) ) )
=> ~ ! [X4: a > b,X5: a > b,X6: a > b] :
( ~ ( ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X4 @ X7 ) @ ( X5 @ X8 ) ) )
=> ~ ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X5 @ X7 ) @ ( X6 @ X8 ) ) ) )
=> ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( X3 @ X7 @ ( X4 @ X7 ) @ ( X6 @ X8 ) ) ) ) )
=> ( ( ^ [X4: a > b,X5: a > b] :
! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) )
!= ( ^ [X4: a > b,X5: a > b] :
! [X6: a,X7: a] :
( ( X2 @ X6 @ X7 )
=> ( X3 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[98,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV037^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.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 : 600
% 0.13/0.34 % DateTime : Tue Jun 28 17:27:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 260.44/260.55 % SZS status Theorem
% 260.44/260.55 % Mode: mode493
% 260.44/260.55 % Inferences: 2927
% 260.44/260.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------