TSTP Solution File: SEV244^6 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV244^6 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:05:32 EDT 2022
% Result : Theorem 80.40s 80.63s
% Output : Proof 80.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 104
% Syntax : Number of formulae : 120 ( 28 unt; 7 typ; 4 def)
% Number of atoms : 305 ( 10 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 633 ( 131 ~; 52 |; 0 &; 277 @)
% ( 43 <=>; 130 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 52 usr; 50 con; 0-2 aty)
% Number of variables : 138 ( 19 ^ 119 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__137,type,
eigen__137: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $i > $o ).
thf(ty_eigen__11,type,
eigen__11: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__114,type,
eigen__114: $i > $o ).
thf(ty_eigen__22,type,
eigen__22: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__137,definition,
( eigen__137
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__114 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__137])]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__1
@ ^ [X1: $i] :
~ ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__22,definition,
( eigen__22
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__11 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__22])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__114 @ X1 )
=> ( eigen__0 @ ( eigen__0 @ eigen__114 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( eigen__0 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__11 @ eigen__3 )
=> ( eigen__0 @ eigen__11 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__11 @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__22 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( eigen__114 @ X1 )
=> ( eigen__0 @ eigen__114 @ X1 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ ( eigen__0 @ eigen__114 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__0 @ eigen__114 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ ( eigen__0 @ eigen__114 ) @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__114 @ X1 )
=> ( eigen__0 @ eigen__114 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__0 @ eigen__11 @ eigen__3 )
=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ eigen__114 @ eigen__137 )
=> ~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__137 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: $i] :
( ( eigen__11 @ X1 )
=> ( eigen__0 @ eigen__11 @ X1 ) )
=> ~ ( eigen__11 @ eigen__22 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eigen__0 @ ( eigen__0 @ eigen__114 ) @ X1 )
=> ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0
@ ^ [X1: $i] :
~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) )
@ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( eigen__11 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__137 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__114 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__114 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( eigen__11 @ X1 )
=> ( eigen__0 @ eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__114 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP17
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP22
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( eigen__11 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__11 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0 @ eigen__11 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP18
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ! [X1: $i] :
( ( eigen__0 @ eigen__114 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__11 @ eigen__22 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__11 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP2
=> ~ ( eigen__0 @ eigen__114 @ eigen__137 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP9
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__114 @ X1 )
=> ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__114 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
=> ( eigen__0
@ ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( eigen__0 @ eigen__114 @ eigen__137 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP7
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP21
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP37
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP36
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__11 @ eigen__22 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(cTHM2A_pme,conjecture,
! [X1: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM2A_pme]) ).
thf(h3,assumption,
~ ( sP30
=> ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP30,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( eigen__0
@ ^ [X2: $i] :
~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( eigen__0 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) )
@ X1 )
= ( ~ ! [X2: $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 )
=> ( eigen__0 @ X2 @ X3 ) )
=> ~ ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1
!= ( ~ sP33 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
sP33,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| ~ sP21
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP29
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP29
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| ~ sP26
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP17
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__22]) ).
thf(8,plain,
( ~ sP23
| ~ sP17
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP25
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP30
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP4
| ~ sP31
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP21
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP40
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP40
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP18
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(16,plain,
( sP27
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP27
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP39
| ~ sP7
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP3
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( sP7
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).
thf(21,plain,
( ~ sP41
| ~ sP37
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP30
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP33
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,h4,h7,h8]) ).
thf(h11,assumption,
~ ( sP11
=> ~ sP36 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP11,
introduced(assumption,[]) ).
thf(h13,assumption,
sP36,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP32
| ~ sP2
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP19
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( sP13
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP13
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP24
| ~ sP22
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP34
| ~ sP9
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP2
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP15
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP8
| ~ sP11
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP35
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__137]) ).
thf(35,plain,
( ~ sP28
| ~ sP35
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP20
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP10
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP42
| ~ sP36
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP30
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP30
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP11
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h6,h4,h5,h3,h2,h1,h0])],[25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,h4,h9,h12,h13]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,42,h12,h13]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__114)],[h10,43,h11]) ).
thf(45,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h6,24,44,h7,h8,h9,h10]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,45,h6]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,46,h4,h5]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,47,h3]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[48,h1]) ).
thf(50,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[49,h0]) ).
thf(0,theorem,
! [X1: ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ! [X2: $i] :
( ( X1
@ ^ [X3: $i] :
~ ! [X4: $i > $o] :
( ! [X5: $i] :
( ( X4 @ X5 )
=> ( X1 @ X4 @ X5 ) )
=> ~ ( X4 @ X3 ) )
@ X2 )
= ( ~ ! [X3: $i > $o] :
( ! [X4: $i] :
( ( X3 @ X4 )
=> ( X1 @ X3 @ X4 ) )
=> ~ ( X3 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[48,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV244^6 : TPTP v8.1.0. Released v5.1.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n016.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 28 13:57:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 80.40/80.63 % SZS status Theorem
% 80.40/80.63 % Mode: mode484
% 80.40/80.63 % Inferences: 64452
% 80.40/80.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------