TSTP Solution File: LCL863^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL863^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : Sun Jul 17 14:11:41 EDT 2022
% Result : Theorem 19.29s 19.66s
% Output : Proof 19.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 166
% Syntax : Number of formulae : 200 ( 88 unt; 12 typ; 32 def)
% Number of atoms : 420 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 763 ( 210 ~; 49 |; 0 &; 341 @)
% ( 47 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 92 usr; 93 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 156 ( 48 ^ 108 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( eigen__0 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X1 @ X3 ) )
=> ( eigen__0 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ X1 )
=> ~ ( eigen__0 @ eigen__6 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( eigen__0 @ eigen__4 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__4 @ eigen__5 ) )
=> ( eigen__0 @ eigen__3 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ eigen__6 @ eigen__7 )
=> ~ ( eigen__0 @ eigen__6 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__8 @ eigen__13 )
=> ( eigen__0 @ eigen__13 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ eigen__3 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__8 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ eigen__15 @ eigen__14 )
=> ~ ( eigen__0 @ eigen__14 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ eigen__4 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__8 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__15 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ( eigen__0 @ eigen__3 @ eigen__4 )
=> ~ ( eigen__0 @ eigen__3 @ eigen__3 ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ( eigen__0 @ eigen__8 @ eigen__13 )
=> ~ ( eigen__0 @ eigen__13 @ eigen__8 ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ eigen__7 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP11
=> ~ ( eigen__0 @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP4
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ ( sP13
=> ~ ( eigen__0 @ eigen__14 @ X1 ) )
=> ( eigen__0 @ eigen__15 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__0 @ X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP9
=> ( eigen__0 @ eigen__15 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__14 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__0 @ eigen__14 @ eigen__15 )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( eigen__0 @ eigen__8 @ eigen__13 )
=> ~ ( eigen__0 @ eigen__13 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__14 @ X1 )
=> ( eigen__0 @ X1 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__0 @ eigen__13 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__0 @ eigen__3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__0 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ eigen__7 )
=> ~ ( eigen__0 @ eigen__6 @ X1 ) )
=> ( eigen__0 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__8 @ eigen__13 )
=> ~ ( eigen__0 @ eigen__13 @ X1 ) )
=> ( eigen__0 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ~ ( sP11
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] : ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ~ ( sP23
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__0 @ eigen__8 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__0 @ eigen__15 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( eigen__0 @ eigen__6 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__15 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__15 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP23
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__8 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__8 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( eigen__0 @ eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__0 @ eigen__14 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( ~ ( ~ ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(conj,conjecture,
! [X1: $i > $i > $o] :
( ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) )
= ( ~ ( ~ ( ! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) )
= ( ~ ( ~ ( ! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
( ~ ( sP35
=> ~ sP1 ) )
!= ( ~ ( ~ ( sP39
=> ~ sP8 )
=> ~ sP34 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP35
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP39
=> ~ sP8 )
=> ~ sP34 ),
introduced(assumption,[]) ).
thf(h5,assumption,
( sP35
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( sP39
=> ~ sP8 )
=> ~ sP34 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP35,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
( sP39
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP34,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP39,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h13,assumption,
sP37,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP37
| ~ sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP35
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h11,h9,h7,h8,h3,h4,h2,h1,h0])],[1,2,h7,h13]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__1)],[h11,3,h13]) ).
thf(h14,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__3 @ X2 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ~ ( sP23
=> ~ ( eigen__0 @ eigen__4 @ X1 ) )
=> ( eigen__0 @ eigen__3 @ X1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( ~ ( sP23
=> ~ sP29 )
=> sP46 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP23
=> ~ sP29 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP46,
introduced(assumption,[]) ).
thf(h19,assumption,
sP23,
introduced(assumption,[]) ).
thf(h20,assumption,
sP29,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP35
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP38
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP44
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP44
| ~ sP23
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP33
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP3
| sP17
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP17
| ~ sP11
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h17,h18,h16,h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0])],[5,6,7,8,9,10,11,12,13,14,15,h7,h8,h19,h20,h18]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,16,h19,h20]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,17,h17,h18]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h15,18,h16]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h14,19,h15]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h12,20,h14]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,4,21,h11,h12]) ).
thf(h21,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__0 @ X1 @ eigen__6 ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( sP32
=> sP16 ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP32,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(23,plain,
( ~ sP35
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP2
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP30
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP18
| sP4
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP4
| ~ sP32
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h22,h21,h10,h7,h8,h3,h4,h2,h1,h0])],[23,24,25,26,27,28,h7,h8,h23,h24]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h21,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,29,h23,h24]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__7)],[h21,30,h22]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__6)],[h10,31,h21]) ).
thf(33,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,22,32,h9,h10]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h3,33,h7,h8]) ).
thf(h25,assumption,
~ sP35,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( sP39
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP34,
introduced(assumption,[]) ).
thf(h30,assumption,
sP39,
introduced(assumption,[]) ).
thf(h31,assumption,
sP8,
introduced(assumption,[]) ).
thf(35,plain,
( ~ sP31
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP15
| sP25
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP25
| ~ sP40
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP45
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP20
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP5
| ~ sP40
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP7
| sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(42,plain,
( ~ sP39
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP8
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP34
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h30,h31,h28,h29,h27,h25,h5,h6,h2,h1,h0])],[35,36,37,38,39,40,41,42,43,44,h27,h30,h31,h29]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h25,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h28,45,h30,h31]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h25,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h6,46,h28,h29]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h5,h6,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__8)],[h25,47,h27]) ).
thf(h32,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__14 @ X1 )
=> ~ ( eigen__0 @ eigen__14 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ ! [X1: $i] :
( ~ ( sP47
=> ~ ( eigen__0 @ eigen__14 @ X1 ) )
=> ( eigen__0 @ eigen__15 @ X1 ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ~ ( sP47
=> ~ sP22 )
=> sP41 ),
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( sP47
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ sP41,
introduced(assumption,[]) ).
thf(h37,assumption,
sP47,
introduced(assumption,[]) ).
thf(h38,assumption,
sP22,
introduced(assumption,[]) ).
thf(49,plain,
( ~ sP26
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP24
| ~ sP47
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP34
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP8
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP43
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP19
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP21
| sP9
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP9
| ~ sP13
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h30,h31,h28,h29,h37,h38,h35,h36,h34,h33,h32,h26,h5,h6,h2,h1,h0])],[49,50,51,52,53,54,55,56,h37,h38,h36,h31,h29]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h37,h38,h35,h36,h34,h33,h32,h26,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h28,57,h30,h31]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h37,h38,h35,h36,h34,h33,h32,h26,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h6,58,h28,h29]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h34,h33,h32,h26,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h37,h38])],[h35,59,h37,h38]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h33,h32,h26,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h34,60,h35,h36]) ).
thf(62,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h33,h32,h26,h5,h6,h2,h1,h0]),tab_negall(discharge,[h34]),tab_negall(eigenvar,eigen__16)],[h33,61,h34]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h32,h26,h5,h6,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__15)],[h32,62,h33]) ).
thf(64,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h5,h6,h2,h1,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__14)],[h26,63,h32]) ).
thf(65,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h25]),tab_imp(discharge,[h26])],[h5,48,64,h25,h26]) ).
thf(66,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,34,65,h3,h4,h5,h6]) ).
thf(67,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,66,h2]) ).
thf(68,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[67,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) )
= ( ~ ( ~ ( ! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[67,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL863^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.10/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32 % Computer : n013.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Mon Jul 4 10:18:29 EDT 2022
% 0.10/0.32 % CPUTime :
% 19.29/19.66 % SZS status Theorem
% 19.29/19.66 % Mode: mode515
% 19.29/19.66 % Inferences: 66040
% 19.29/19.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------