TSTP Solution File: LCL865^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL865^1 : 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 : n008.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 14:11:42 EDT 2022
% Result : Theorem 1.59s 1.76s
% Output : Proof 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 145
% Syntax : Number of formulae : 179 ( 94 unt; 12 typ; 32 def)
% Number of atoms : 352 ( 41 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 610 ( 174 ~; 37 |; 0 &; 271 @)
% ( 37 <=>; 89 =>; 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 : 85 ( 82 usr; 83 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 48 ^ 95 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__12,type,
eigen__12: $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__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( eigen__0 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
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] :
( ~ ( ( eigen__0 @ eigen__3 @ eigen__4 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) )
=> ( eigen__0 @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__8 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__12 @ X1 )
=> ~ ( eigen__0 @ eigen__12 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__3 @ eigen__4 )
=> ~ ( eigen__0 @ eigen__3 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( sP3
=> ~ ( eigen__0 @ eigen__5 @ eigen__7 ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__13 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__8 @ X1 )
=> ( eigen__0 @ X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP6
=> ( 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
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__12 @ eigen__8 )
=> ~ ( eigen__0 @ eigen__12 @ X1 ) )
=> ( eigen__0 @ eigen__8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__5 @ X1 )
=> ~ ( eigen__0 @ eigen__5 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ eigen__3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__13 @ X1 )
=> ~ ( eigen__0 @ eigen__13 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__0 @ eigen__12 @ eigen__8 )
=> ~ ( eigen__0 @ eigen__12 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 @ eigen__13 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
~ ! [X2: $i] :
~ ( eigen__0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ eigen__3 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__12 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] : ( eigen__0 @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
~ ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ~ ( sP3
=> ~ ( eigen__0 @ eigen__5 @ X1 ) )
=> ( eigen__0 @ eigen__6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__0 @ eigen__8 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__0 @ eigen__14 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ( sP9
=> ~ sP18 )
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP9
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP28
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP17
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP3
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ~ ( sP9
=> ~ ( eigen__0 @ eigen__13 @ X1 ) )
=> ( eigen__0 @ eigen__14 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
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] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ) ).
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] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
( ~ ( sP23
=> ~ sP1 ) )
!= ( ~ ( ~ ( sP20
=> ~ sP33 )
=> ~ sP1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP23
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP20
=> ~ sP33 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
( sP23
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( sP20
=> ~ sP33 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP23,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
( sP20
=> ~ sP33 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h13,assumption,
sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP25
| ~ sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP23
| sP24 ),
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] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0 @ X1 @ eigen__3 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP19
=> sP36 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP19,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP36,
introduced(assumption,[]) ).
thf(5,plain,
( ~ sP23
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP21
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP6
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| ~ sP19
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0])],[5,6,7,8,9,10,h7,h8,h16,h17]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,11,h16,h17]) ).
thf(13,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)],[h14,12,h15]) ).
thf(14,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)],[h12,13,h14]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,4,14,h11,h12]) ).
thf(h18,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP35,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h23,assumption,
sP3,
introduced(assumption,[]) ).
thf(h24,assumption,
sP26,
introduced(assumption,[]) ).
thf(16,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP14
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP27
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP8
| sP35
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP35
| ~ sP3
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h20,h19,h18,h10,h7,h8,h3,h4,h2,h1,h0])],[16,17,18,19,20,h8,h23,h24,h22]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h19,h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,21,h23,h24]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h19,h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,22,h21,h22]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__7)],[h19,23,h20]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__6)],[h18,24,h19]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h10,25,h18]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,15,26,h9,h10]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h3,27,h7,h8]) ).
thf(h25,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( sP20
=> ~ sP33 ),
introduced(assumption,[]) ).
thf(h28,assumption,
sP20,
introduced(assumption,[]) ).
thf(h29,assumption,
sP33,
introduced(assumption,[]) ).
thf(29,plain,
( ~ sP13
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP34
| sP17
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP17
| ~ sP22
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP5
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP10
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP32
| ~ sP28
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP4
| sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(37,plain,
( ~ sP20
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP33
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h8,h26,h25,h5,h6,h2,h1,h0])],[29,30,31,32,33,34,35,36,37,38,h26,h28,h29,h8]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h8,h26,h25,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,39,h28,h29]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h25,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h27,h8])],[h6,40,h27,h8]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h25,h5,h6,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__8)],[h25,41,h26]) ).
thf(h30,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h31,assumption,
~ sP37,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h33,assumption,
~ sP31,
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h35,assumption,
sP9,
introduced(assumption,[]) ).
thf(h36,assumption,
sP18,
introduced(assumption,[]) ).
thf(43,plain,
( ~ sP1
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP16
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP37
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP30
| sP31
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP31
| ~ sP9
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h8,h35,h36,h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0])],[43,44,45,46,47,h35,h36,h34,h8]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h8,h35,h36,h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,48,h28,h29]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h36,h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h27,h8])],[h6,49,h27,h8]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h33,50,h35,h36]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h32,51,h33,h34]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h30,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__15)],[h31,52,h32]) ).
thf(54,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h30,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__14)],[h30,53,h31]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__13)],[h10,54,h30]) ).
thf(56,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h25]),tab_imp(discharge,[h10])],[h5,42,55,h25,h10]) ).
thf(57,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,28,56,h3,h4,h5,h6]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,57,h2]) ).
thf(59,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[58,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] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[58,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL865^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 00:54:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.59/1.76 % SZS status Theorem
% 1.59/1.76 % Mode: mode213
% 1.59/1.76 % Inferences: 12558
% 1.59/1.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------