TSTP Solution File: SYO225^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO225^5 : 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 : n023.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 : Fri Sep 1 04:45:57 EDT 2023
% Result : Theorem 20.28s 20.55s
% Output : Proof 20.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__3,type,
eigen__3: g > g > g ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__1,type,
eigen__1: b > a ).
thf(ty_eigen__2,type,
eigen__2: g > $o ).
thf(ty_eigen__13,type,
eigen__13: g ).
thf(ty_eigen__9,type,
eigen__9: g ).
thf(ty_eigen__5,type,
eigen__5: b > b > b ).
thf(ty_eigen__7,type,
eigen__7: a > a > a ).
thf(ty_eigen__12,type,
eigen__12: a ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(ty_eigen__8,type,
eigen__8: g ).
thf(ty_eigen__11,type,
eigen__11: a ).
thf(ty_eigen__10,type,
eigen__10: g ).
thf(ty_eigen__0,type,
eigen__0: g > b ).
thf(ty_eigen__14,type,
eigen__14: g ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__2 @ eigen__13 )
=> ~ ( eigen__2 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__4 @ ( eigen__0 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( eigen__4 @ ( eigen__0 @ eigen__8 ) )
=> ~ sP3 )
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( eigen__2 @ eigen__8 )
=> ~ sP1 )
=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__9 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ~ ( ( eigen__6 @ eigen__11 )
=> ~ ( eigen__6 @ X1 ) )
=> ( eigen__6 @ ( eigen__7 @ eigen__11 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__4 @ ( eigen__0 @ eigen__10 ) )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: g] :
( ~ ( ( eigen__2 @ eigen__8 )
=> ~ ( eigen__2 @ X1 ) )
=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ X1 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__2 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__9 ) )
= ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__6 @ X1 )
=> ~ ( eigen__6 @ X2 ) )
=> ( eigen__6 @ ( eigen__7 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__2 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP8
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP13
=> ( eigen__4 @ ( eigen__0 @ eigen__10 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__6 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP1
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__6 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__2 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( sP19
=> ~ sP22 )
=> ( eigen__6 @ ( eigen__7 @ eigen__11 @ eigen__12 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__9 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( sP23
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__6 @ ( eigen__7 @ eigen__11 @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__2 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__4 @ ( eigen__0 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__9 ) ) )
= ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( eigen__2 @ ( eigen__3 @ eigen__13 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: b] :
( ~ ( sP8
=> ~ ( eigen__4 @ X1 ) )
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ X1 ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__9 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP19
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X1 @ X2 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP23
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: g] :
( ~ ( sP29
=> ~ ( eigen__2 @ X1 ) )
=> ( eigen__2 @ ( eigen__3 @ eigen__13 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP2
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(cTHM126_CORRECTED_pme,conjecture,
! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g > g,X5: b > $o,X6: b > b > b,X7: a > $o,X8: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X1 @ ( X4 @ X9 @ X10 ) )
= ( X6 @ ( X1 @ X9 ) @ ( X1 @ X10 ) ) ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( ( X2 @ ( X6 @ X9 @ X10 ) )
= ( X8 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ~ ( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ~ ( X3 @ X9 ) )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g > g,X5: b > $o,X6: b > b > b,X7: a > $o,X8: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X1 @ ( X4 @ X9 @ X10 ) )
= ( X6 @ ( X1 @ X9 ) @ ( X1 @ X10 ) ) ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( ( X2 @ ( X6 @ X9 @ X10 ) )
= ( X8 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ~ ( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ~ ( X3 @ X9 ) )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM126_CORRECTED_pme]) ).
thf(h1,assumption,
~ ! [X1: b > a,X2: g > $o,X3: g > g > g,X4: b > $o,X5: b > b > b,X6: a > $o,X7: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( eigen__0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( eigen__0 @ X8 ) @ ( eigen__0 @ X9 ) ) ) ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X6 @ X8 )
=> ~ ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X6 @ X8 )
=> ~ ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ~ ( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ~ ( X2 @ X8 ) )
=> ~ ( X2 @ X9 ) )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) @ ( X1 @ ( eigen__0 @ X9 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: g > $o,X2: g > g > g,X3: b > $o,X4: b > b > b,X5: a > $o,X6: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( X1 @ ( X2 @ X7 @ X8 ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__0 @ ( X2 @ X7 @ X8 ) )
= ( X4 @ ( eigen__0 @ X7 ) @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( ( eigen__1 @ ( X4 @ X7 @ X8 ) )
= ( X6 @ ( eigen__1 @ X7 ) @ ( eigen__1 @ X8 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( X1 @ ( X2 @ X7 @ X8 ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X5 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ~ ( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ~ ( X1 @ X7 ) )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 @ X8 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) @ ( eigen__1 @ ( eigen__0 @ X8 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: g > g > g,X2: b > $o,X3: b > b > b,X4: a > $o,X5: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( eigen__2 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( ( eigen__0 @ ( X1 @ X6 @ X7 ) )
= ( X3 @ ( eigen__0 @ X6 ) @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( ( eigen__1 @ ( X3 @ X6 @ X7 ) )
= ( X5 @ ( eigen__1 @ X6 ) @ ( eigen__1 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( eigen__2 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X4 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ~ ( eigen__2 @ X6 ) )
=> ~ ( eigen__2 @ X7 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 @ X7 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: b > $o,X2: b > b > b,X3: a > $o,X4: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X5 @ X6 ) )
= ( X2 @ ( eigen__0 @ X5 ) @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( ( eigen__1 @ ( X2 @ X5 @ X6 ) )
= ( X4 @ ( eigen__1 @ X5 ) @ ( eigen__1 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP20
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X3 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ~ ( eigen__2 @ X5 ) )
=> ~ ( eigen__2 @ X6 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 @ X6 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: b > b > b,X2: a > $o,X3: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X4 @ X5 ) )
= ( X1 @ ( eigen__0 @ X4 ) @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( ( eigen__1 @ ( X1 @ X4 @ X5 ) )
= ( X3 @ ( eigen__1 @ X4 ) @ ( eigen__1 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP20
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( X2 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ~ ( eigen__2 @ X4 ) )
=> ~ ( eigen__2 @ X5 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a > $o,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X3 @ X4 ) )
= ( X2 @ ( eigen__1 @ X3 ) @ ( eigen__1 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP20
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ~ ( eigen__2 @ X3 ) )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__6 @ X3 ) )
=> ( eigen__6 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ sP11 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__4 @ X2 )
=> ~ ( eigen__4 @ X3 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X2 @ X3 ) )
= ( X1 @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP20
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__6 @ X3 ) )
=> ( eigen__6 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X2: g,X3: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ~ ( eigen__2 @ X2 ) )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ sP37 )
=> ~ ( ~ ( ~ ( sP20
=> ~ sP15 )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) )
=> ~ ! [X1: g,X2: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ~ ( eigen__2 @ X1 ) )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ sP37 ),
introduced(assumption,[]) ).
thf(h10,assumption,
( ~ ( ~ ( sP20
=> ~ sP15 )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) )
=> ~ ! [X1: g,X2: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ~ ( eigen__2 @ X1 ) )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 )
=> ~ sP15 )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP37,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 )
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP11,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP15,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 )
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP5,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( sP20
=> ~ sP32 )
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP32,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP20
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP20,
introduced(assumption,[]) ).
thf(h23,assumption,
( ~ ( sP20
=> ~ sP15 )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: g,X2: g] :
( ~ ( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ~ ( eigen__2 @ X1 ) )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
( sP20
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP39,
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP40,
introduced(assumption,[]) ).
thf(h31,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h33,assumption,
sP29,
introduced(assumption,[]) ).
thf(h34,assumption,
sP16,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP29
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP40
| sP2
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP39
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP20
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h33,h34,h31,h32,h30,h29,h27,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,h22,h33,h34,h32]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h32,h30,h29,h27,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h31,5,h33,h34]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h29,h27,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,6,h31,h32]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h29,h27,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__14)],[h29,7,h30]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h27,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h29]),tab_negall(eigenvar,eigen__13)],[h27,8,h29]) ).
thf(h35,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h36,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h37,assumption,
~ sP36,
introduced(assumption,[]) ).
thf(h38,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h39,assumption,
sP19,
introduced(assumption,[]) ).
thf(h40,assumption,
sP22,
introduced(assumption,[]) ).
thf(10,plain,
( ~ sP36
| ~ sP19
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP24
| sP36
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP7
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP15
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h39,h40,h37,h38,h36,h35,h28,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[10,11,12,13,h16,h39,h40,h38]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h36,h35,h28,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h39,h40])],[h37,14,h39,h40]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h35,h28,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h37,h38])],[h36,15,h37,h38]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h35,h28,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__12)],[h35,16,h36]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h28,h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__11)],[h28,17,h35]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h25,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h27]),tab_imp(discharge,[h28])],[h25,9,18,h27,h28]) ).
thf(h41,assumption,
~ ( sP13
=> sP25 ),
introduced(assumption,[]) ).
thf(h42,assumption,
sP13,
introduced(assumption,[]) ).
thf(h43,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(20,plain,
( ~ sP18
| ~ sP13
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP9
| ~ sP30
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP32
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP11
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h42,h43,h41,h26,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[20,21,22,23,h20,h14,h42,h43]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h26,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h42,h43])],[h41,24,h42,h43]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h41]),tab_negall(eigenvar,eigen__10)],[h26,25,h41]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h23,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h25]),tab_imp(discharge,[h26])],[h23,19,26,h25,h26]) ).
thf(h44,assumption,
~ ! [X1: g] :
( ~ ( ~ ( ~ ( sP23
=> ~ ( eigen__2 @ X1 ) )
=> ~ sP23 )
=> ~ ( eigen__2 @ X1 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( ~ ( ~ ( ~ sP27
=> ~ sP23 )
=> ~ sP1 )
=> sP26 ),
introduced(assumption,[]) ).
thf(h46,assumption,
~ ( ~ ( ~ sP27
=> ~ sP23 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h47,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h48,assumption,
~ ( ~ sP27
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h49,assumption,
sP1,
introduced(assumption,[]) ).
thf(h50,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h51,assumption,
sP23,
introduced(assumption,[]) ).
thf(28,plain,
( sP31
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP10
| sP26
| ~ sP31
| ~ sP10 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP35
| sP14 ),
inference(symeq,[status(thm)],]) ).
thf(31,plain,
( ~ sP27
| ~ sP23
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP17
| ~ sP8
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP6
| sP27
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP4
| sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP21
| ~ sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP38
| ~ sP23
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP34
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP32
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP32
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP5
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP37
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h51,h49,h50,h51,h48,h49,h46,h47,h45,h44,h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,h20,h18,h12,h51,h49,h47]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h50,h51,h48,h49,h46,h47,h45,h44,h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h51,h49])],[h50,43,h51,h49]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h48,h49,h46,h47,h45,h44,h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h50,h51])],[h48,44,h50,h51]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h47,h45,h44,h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h48,h49])],[h46,45,h48,h49]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h44,h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h46,h47])],[h45,46,h46,h47]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h44,h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__9)],[h44,47,h45]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__8)],[h24,48,h44]) ).
thf(50,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h22,h20,h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h24])],[h10,27,49,h23,h24]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h20,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h20])],[h21,50,h22,h20]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h20])],[h19,51,h21,h20]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,52,h19,h20]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,53,h17,h18]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,54,h15,h16]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,55,h13,h14]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,56,h11,h12]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,57,h9,h10]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__7)],[h7,58,h8]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__6)],[h6,59,h7]) ).
thf(61,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__5)],[h5,60,h6]) ).
thf(62,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__4)],[h4,61,h5]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,62,h4]) ).
thf(64,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,63,h3]) ).
thf(65,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,64,h2]) ).
thf(66,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,65,h1]) ).
thf(0,theorem,
! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g > g,X5: b > $o,X6: b > b > b,X7: a > $o,X8: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X1 @ ( X4 @ X9 @ X10 ) )
= ( X6 @ ( X1 @ X9 ) @ ( X1 @ X10 ) ) ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( ( X2 @ ( X6 @ X9 @ X10 ) )
= ( X8 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ~ ( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ~ ( X3 @ X9 ) )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[66,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SYO225^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 01:28:11 EDT 2023
% 0.13/0.33 % CPUTime :
% 20.28/20.55 % SZS status Theorem
% 20.28/20.55 % Mode: cade22grackle2x798d
% 20.28/20.55 % Steps: 1267
% 20.28/20.55 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------