TSTP Solution File: LCL872^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL872^1 : 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 : n007.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 14:11:45 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 119
% Syntax : Number of formulae : 139 ( 65 unt; 13 typ; 34 def)
% Number of atoms : 323 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 598 ( 148 ~; 29 |; 0 &; 291 @)
% ( 29 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 76 usr; 73 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 152 ( 53 ^ 99 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_j,type,
j: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_i,type,
i: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_k,type,
k: $i > $i > $o ).
thf(ty_l,type,
l: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( l @ eigen__2 @ X1 )
=> ( l @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: $i] :
~ ( ( j @ eigen__6 @ X1 )
=> ~ ( l @ eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(sP1,plain,
( sP1
<=> ( k @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( i @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( j @ X1 @ X2 )
=> ~ ( l @ eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( l @ eigen__2 @ X1 )
=> ( l @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( l @ eigen__7 @ eigen__14 )
=> ~ ( eigen__5 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( k @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( l @ X1 @ X2 )
=> ( l @ eigen__2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( j @ eigen__6 @ X1 )
=> ~ ( l @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( i @ eigen__4 @ eigen__6 )
=> ~ ( k @ eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( j @ eigen__6 @ eigen__14 )
=> ~ ( l @ eigen__7 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( i @ eigen__0 @ eigen__1 )
=> ~ ! [X1: $i] :
( ( j @ eigen__1 @ X1 )
=> ~ ( l @ eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( j @ eigen__6 @ eigen__14 )
=> ( eigen__5 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( j @ eigen__6 @ X1 )
=> ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ~ ( ( i @ eigen__4 @ X1 )
=> ~ ( k @ eigen__4 @ X2 ) )
=> ~ ! [X3: $i] :
( ( j @ X1 @ X3 )
=> ~ ( l @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( l @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( i @ eigen__0 @ X2 )
=> ~ ! [X3: $i] :
( ( j @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X2: $i] :
( ( k @ eigen__0 @ X2 )
=> ~ ! [X3: $i] :
( ( l @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP1
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( k @ eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( i @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( j @ eigen__6 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( j @ eigen__1 @ X1 )
=> ~ ( l @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( l @ eigen__7 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP2
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP13
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__5 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( l @ eigen__7 @ X1 )
=> ~ ( eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( i @ X1 @ X2 )
=> ~ ( k @ X1 @ X3 ) )
=> ~ ! [X4: $i] :
( ( j @ X2 @ X4 )
=> ~ ( l @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( i @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( j @ X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X3: $i] :
( ( k @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( l @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP7
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ~ ( ( i @ eigen__4 @ eigen__6 )
=> ~ ( k @ eigen__4 @ X1 ) )
=> ~ ! [X2: $i] :
( ( j @ eigen__6 @ X2 )
=> ~ ( l @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( i @ eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
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(def_confluence,definition,
( confluence
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o,X3: $i > $i > $o,X4: $i > $i > $o] :
! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X1 @ X5 @ X6 )
=> ~ ( X3 @ X5 @ X7 ) )
=> ~ ! [X8: $i] :
( ( X2 @ X6 @ X8 )
=> ~ ( X4 @ X7 @ X8 ) ) ) ) ) ).
thf(conj,conjecture,
( ( ! [X1: $i,X2: $i > $o] :
( ~ ~ ~ ! [X3: $i] :
( ( i @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( j @ X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X3: $i] :
( ( k @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( l @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
= sP25 ) ).
thf(h1,negated_conjecture,
sP26 != sP25,
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
sP26,
introduced(assumption,[]) ).
thf(h3,assumption,
sP25,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( i @ eigen__0 @ X1 )
=> ~ ( k @ eigen__0 @ X2 ) )
=> ~ ! [X3: $i] :
( ( j @ X1 @ X3 )
=> ~ ( l @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ~ ( sP17
=> ~ ( k @ eigen__0 @ X1 ) )
=> ~ ! [X2: $i] :
( ( j @ eigen__1 @ X2 )
=> ~ ( l @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP17
=> ~ sP1 )
=> ~ sP19 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP17
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP19,
introduced(assumption,[]) ).
thf(h11,assumption,
sP17,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP22
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP22
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP3
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(4,plain,
( ~ sP5
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| ~ sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP26
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP21
| sP2
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| ~ sP17
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2,h11,h12,h10]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,11,h11,h12]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,12,h9,h10]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,13,h8]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,15,h6]) ).
thf(h13,assumption,
~ ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( i @ eigen__4 @ X2 )
=> ~ ! [X3: $i] :
( ( j @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X2: $i] :
( ( k @ eigen__4 @ X2 )
=> ~ ! [X3: $i] :
( ( l @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ! [X1: $i] :
( ( i @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( j @ X1 @ X2 )
=> ( eigen__5 @ X2 ) ) )
=> ! [X1: $i] :
( ( k @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( l @ X1 @ X2 )
=> ~ ( eigen__5 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( i @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( j @ X1 @ X2 )
=> ( eigen__5 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( k @ eigen__4 @ X1 )
=> ~ ! [X2: $i] :
( ( l @ X1 @ X2 )
=> ~ ( eigen__5 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP29
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP29,
introduced(assumption,[]) ).
thf(h19,assumption,
sP11,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP16
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP16,
introduced(assumption,[]) ).
thf(h22,assumption,
sP24,
introduced(assumption,[]) ).
thf(17,plain,
( ~ sP24
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP4
| ~ sP20
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP11
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP10
| ~ sP18
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP8
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP8
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP6
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(24,plain,
( ~ sP25
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP12
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP28
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP27
| sP7
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP7
| ~ sP29
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h13,h4,h5,h1,h0])],[17,18,19,20,21,22,23,24,25,26,27,28,h18,h19,h21,h22,h5]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h17,h15,h16,h14,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,29,h21,h22]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h13,h4,h5,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__7)],[h16,30,h20]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,31,h18,h19]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h13,h4,h5,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__6)],[h15,32,h17]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,33,h15,h16]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__5)],[h13,34,h14]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h4,35,h13]) ).
thf(37,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,16,36,h2,h3,h4,h5]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
( ( ! [X1: $i,X2: $i > $o] :
( ~ ~ ~ ! [X3: $i] :
( ( i @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( j @ X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ! [X3: $i] :
( ( k @ X1 @ X3 )
=> ~ ! [X4: $i] :
( ( l @ X3 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
= sP25 ),
inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL872^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 00:28:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % Mode: mode213
% 0.12/0.39 % Inferences: 107
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------