TSTP Solution File: SYO515^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO515^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : Thu Jul 21 19:33:09 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 138
% Syntax : Number of formulae : 152 ( 19 unt; 9 typ; 8 def)
% Number of atoms : 504 ( 76 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 575 ( 274 ~; 102 |; 0 &; 83 @)
% ( 57 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 67 con; 0-2 aty)
% Number of variables : 93 ( 72 ^ 21 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $o ).
thf(ty_eigen__14,type,
eigen__14: $o ).
thf(ty_eigen__2,type,
eigen__2: $o ).
thf(ty_eigen__1,type,
eigen__1: $o > $o ).
thf(ty_eigen__0,type,
eigen__0: ( $o > $o ) > $o ).
thf(ty_eigen__5,type,
eigen__5: $o ).
thf(ty_eigen__11,type,
eigen__11: $o ).
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(ty_eigen__8,type,
eigen__8: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $o] :
( ( ~ X1 )
!= ( ~ ( ~ ( eigen__0
@ ^ [X2: $o] : $false )
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $o] :
( $false
!= ( ~ ( ~ ( eigen__0
@ ^ [X2: $o] : $false )
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $o] :
( ( eigen__1 @ X1 )
!= ( ~ ( ~ ( eigen__0
@ ^ [X2: $o] : $false )
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $o] :
( ( ~ $false )
!= ( ~ ( ~ ( eigen__0
@ ^ [X2: $o] : $false )
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0
@ ^ [X1: $o] : $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o] :
( ( ~ X1 )
= ( ~ ( ~ sP2
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= ( ~ ( ~ sP2
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ $false )
= ( ~ ( ~ sP2
=> ~ ( ~ ( eigen__0
@ ^ [X1: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__14 = sP6 )
=> ( sP6 = eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: $o] : ~ $false )
= ( ^ [X1: $o] :
~ ( ~ sP2
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ $false )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__14 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ^ [X1: $o] : ~ X1 )
= ( ^ [X1: $o] :
~ ( ~ sP2
=> ~ ( ~ ( eigen__0
@ ^ [X2: $o] : ~ sP13 )
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__1 @ sP6 )
= sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0
@ ^ [X1: $o] : ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__1 @ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ~ eigen__11 )
= ( ~ ( ~ sP2
=> ~ ( ~ sP18
=> sP3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP5
= ( ~ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__8 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( ^ [X1: $o] : sP13 )
= ( ^ [X1: $o] :
~ ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP18
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP6 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__14 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP6 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> eigen__14 ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP18
=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP6 = sP29 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $o] :
( sP13
= ( ~ ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $o] :
( ( ~ sP13 )
= ( ~ ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( eigen__2 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> eigen__8 ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP25
= ( ~ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__1 @ eigen__2 )
= ( ~ sP35 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP2
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__1
= ( ^ [X1: $o] : ~ sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP18
=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP22
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__1
= ( ^ [X1: $o] : sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__1
= ( ^ [X1: $o] :
~ ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP2
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__0
@ ^ [X1: $o] :
~ ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X2: $o] : ~ X2 )
= ( ~ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $o] :
( ( sP29 = X1 )
=> ( X1 = sP29 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP13
= ( ~ ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__6 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> eigen__2 ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $o] :
( ( eigen__1 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> eigen__11 ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ sP2
=> ~ ( ~ sP18
=> ( ( eigen__0
@ ^ [X1: $o] : ~ X1 )
= ( ~ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__0
@ ^ [X1: $o] : ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $o] :
( ( sP36 = X1 )
=> ( X1 = sP36 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( eigen__1 @ sP51 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(def_t,definition,
( t
= ( ^ [X1: ( $o > $o ) > $o,X2: $o] :
~ ( ~ ( X1
@ ^ [X3: $o] : sP13 )
=> ~ ( ~ ( X1
@ ^ [X3: $o] : ~ sP13 )
=> ( ( X1
@ ^ [X3: $o] : ~ X3 )
= ( ~ X2 ) ) ) ) ) ) ).
thf(choiceoo1,conjecture,
! [X1: ( $o > $o ) > $o] :
( ~ ! [X2: $o > $o] :
~ ( X1 @ X2 )
=> ( X1
@ ^ [X2: $o] :
~ ( ~ ( X1
@ ^ [X3: $o] : sP13 )
=> ~ ( ~ ( X1
@ ^ [X3: $o] : ~ sP13 )
=> ( ( X1
@ ^ [X3: $o] : ~ X3 )
= ( ~ X2 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: ( $o > $o ) > $o] :
( ~ ! [X2: $o > $o] :
~ ( X1 @ X2 )
=> ( X1
@ ^ [X2: $o] :
~ ( ~ ( X1
@ ^ [X3: $o] : sP13 )
=> ~ ( ~ ( X1
@ ^ [X3: $o] : ~ sP13 )
=> ( ( X1
@ ^ [X3: $o] : ~ X3 )
= ( ~ X2 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[choiceoo1]) ).
thf(h2,assumption,
~ ( ~ ! [X1: $o > $o] :
~ ( eigen__0 @ X1 )
=> sP48 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $o > $o] :
~ ( eigen__0 @ X1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP48,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP14
| sP29
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| ~ sP14
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP49
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP27
| ~ sP29
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP38
| sP49 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP34
| sP51
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP22
| ~ sP36
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP22
| sP36
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP43
| ~ sP22
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP56
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP38
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP19
| sP5
| ~ sP31 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP5
| sP25
| ~ sP27 ),
inference(mating_rule,[status(thm)],]) ).
thf(14,plain,
( sP3
| ~ sP55
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP24
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP46
| sP2
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP3
| ~ sP55
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP24
| sP18
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP46
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP28
| ~ sP6
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP57
| sP25
| ~ sP34 ),
inference(mating_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP19
| sP25
| ~ sP26 ),
inference(mating_rule,[status(thm)],]) ).
thf(23,plain,
( sP54
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP30
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP40
| sP2
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP21
| ~ sP5
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP21
| sP5
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP52
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(29,plain,
( sP20
| sP53
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP20
| ~ sP53
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP4
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(32,plain,
~ sP13,
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP19
| sP57
| ~ sP28 ),
inference(mating_rule,[status(thm)],]) ).
thf(34,plain,
( sP37
| ~ sP25
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP12
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(36,plain,
( sP50
| sP13
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP32
| ~ sP50 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(38,plain,
( sP8
| sP13
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP33
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(40,plain,
( sP16
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP15
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP17
| sP19
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP10
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(44,plain,
( sP41
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP23
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP11
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP1
| sP55
| ~ sP16 ),
inference(mating_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP55
| sP48
| ~ sP15 ),
inference(mating_rule,[status(thm)],]) ).
thf(49,plain,
( sP44
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP1
| sP18
| ~ sP41 ),
inference(mating_rule,[status(thm)],]) ).
thf(51,plain,
( sP47
| sP55
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP2
| sP48
| ~ sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(53,plain,
( sP42
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP35
| sP2
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP18
| sP48
| ~ sP11 ),
inference(mating_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP47
| sP55
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP1
| sP2
| ~ sP44 ),
inference(mating_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP42
| sP18
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP35
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP39
| ~ sP57
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP39
| sP57
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
sP38,
inference(eq_sym,[status(thm)],]) ).
thf(63,plain,
( sP7
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(64,plain,
( sP45
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP1
| sP48
| ~ sP45 ),
inference(mating_rule,[status(thm)],]) ).
thf(66,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,h5,h4]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h3,66,h5]) ).
thf(68,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,67,h3,h4]) ).
thf(69,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,68,h2]) ).
thf(70,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[69,h0]) ).
thf(0,theorem,
! [X1: ( $o > $o ) > $o] :
( ~ ! [X2: $o > $o] :
~ ( X1 @ X2 )
=> ( X1
@ ^ [X2: $o] :
~ ( ~ ( X1
@ ^ [X3: $o] : sP13 )
=> ~ ( ~ ( X1
@ ^ [X3: $o] : ~ sP13 )
=> ( ( X1
@ ^ [X3: $o] : ~ X3 )
= ( ~ X2 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[69,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO515^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n004.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 09:33:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % Mode: mode213
% 0.20/0.37 % Inferences: 198
% 0.20/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------