%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:27:43 PM UTC 2026
% Result : Theorem 224.19s 183.32s
% Output : Proof 224.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 108
% Syntax : Number of formulae : 128 ( 65 unt; 0 typ; 34 def)
% Number of atoms : 322 ( 42 equ; 4 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 550 ( 112 ~; 34 |; 10 &; 290 @)
% ( 30 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 75 con; 0-2 aty)
% Number of variables : 161 ( 73 ^; 81 !; 7 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_k,type,
k: $i > $i > $o ).
thf(ty_eigen__45,type,
eigen__45: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_i,type,
i: $i > $i > $o ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_j,type,
j: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__187,type,
eigen__187: $i ).
thf(ty_l,type,
l: $i > $i > $o ).
thf(ty_eigen__43,type,
eigen__43: $i > $o ).
thf(ty_eigen__44,type,
eigen__44: $i ).
thf(ty_eigen__42,type,
eigen__42: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( l @ eigen__2 @ X1 )
=> ~ ( j @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__187,definition,
( eigen__187
= ( eps__0
@ ^ [X1: $i] :
~ ( ( j @ eigen__44 @ X1 )
=> ~ ( l @ eigen__45 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__187])]) ).
thf(sP1,plain,
( sP1
<=> ( k @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( j @ eigen__1 @ eigen__6 )
=> ~ ( l @ eigen__2 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( j @ eigen__44 @ X1 )
=> ~ ( l @ eigen__45 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( k @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( l @ X1 @ X2 )
=> ~ ( j @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( i @ eigen__42 @ eigen__44 )
=> ~ ( k @ eigen__42 @ eigen__45 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( j @ eigen__44 @ eigen__187 )
=> ( eigen__43 @ eigen__187 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ( i @ eigen__42 @ eigen__44 )
=> ~ ( k @ eigen__42 @ X1 ) )
=> ~ ! [X2: $i] :
( ( j @ eigen__44 @ X2 )
=> ~ ( l @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( l @ eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( k @ eigen__42 @ eigen__45 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( l @ eigen__45 @ eigen__187 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( j @ eigen__44 @ eigen__187 )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__43 @ eigen__187 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( j @ eigen__1 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( j @ eigen__44 @ X1 )
=> ( eigen__43 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( i @ eigen__42 @ eigen__44 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP5
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP10
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [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,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( i @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( j @ eigen__1 @ X1 )
=> ~ ( l @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( l @ eigen__2 @ X1 )
=> ~ ( j @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( i @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( j @ X1 @ X2 )
=> ( j @ eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [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,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i] :
( ~ ( ( i @ eigen__42 @ X1 )
=> ~ ( k @ eigen__42 @ X2 ) )
=> ~ ! [X3: $i] :
( ( j @ X1 @ X3 )
=> ~ ( l @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( l @ eigen__45 @ X1 )
=> ~ ( eigen__43 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP8
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( j @ eigen__44 @ eigen__187 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [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,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP22
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP1
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
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,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
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] : $true ) ) ).
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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X4 )
@ ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( 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] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
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] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
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] :
( ^ [X8: $o,X9: $o] :
( X8
=> X9 )
@ ( ( X1 @ X5 @ X6 )
& ( X3 @ X5 @ X7 ) )
@ ? [X8: $i] :
( ( X2 @ X6 @ X8 )
& ( X4 @ X7 @ X8 ) ) ) ) ) ).
thf(conj,conjecture,
sP28 = sP23 ).
thf(h1,negated_conjecture,
sP28 != sP23,
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
sP28,
introduced(assumption,[]) ).
thf(h3,assumption,
sP23,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP23,
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] :
( ~ ( sP19
=> ~ ( k @ eigen__0 @ X1 ) )
=> ~ ! [X2: $i] :
( ( j @ eigen__1 @ X2 )
=> ~ ( l @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( sP19
=> ~ sP1 )
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP19
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP20,
introduced(assumption,[]) ).
thf(h11,assumption,
sP19,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP13
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP20
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP30
| ~ sP1
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP26
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP26
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP21
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(7,plain,
( ~ sP4
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP22
| ~ sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP29
| sP22
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP18
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP28
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h2,h11,h12,h10]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,12,h11,h12]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,13,h9,h10]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,14,h8]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,15,h7]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,16,h6]) ).
thf(h13,assumption,
~ ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( i @ eigen__42 @ X2 )
=> ~ ! [X3: $i] :
( ( j @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X2: $i] :
( ( k @ eigen__42 @ X2 )
=> ~ ! [X3: $i] :
( ( l @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ! [X1: $i] :
( ( i @ eigen__42 @ X1 )
=> ~ ! [X2: $i] :
( ( j @ X1 @ X2 )
=> ( eigen__43 @ X2 ) ) )
=> ! [X1: $i] :
( ( k @ eigen__42 @ X1 )
=> ~ ! [X2: $i] :
( ( l @ X1 @ X2 )
=> ~ ( eigen__43 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( i @ eigen__42 @ X1 )
=> ~ ! [X2: $i] :
( ( j @ X1 @ X2 )
=> ( eigen__43 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i] :
( ( k @ eigen__42 @ X1 )
=> ~ ! [X2: $i] :
( ( l @ X1 @ X2 )
=> ~ ( eigen__43 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP15
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP15,
introduced(assumption,[]) ).
thf(h19,assumption,
sP14,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP9
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP9,
introduced(assumption,[]) ).
thf(h22,assumption,
sP25,
introduced(assumption,[]) ).
thf(18,plain,
( ~ sP17
| ~ sP10
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP6
| ~ sP27
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP25
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP5
| ~ sP15
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP16
| sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP11
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP11
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP3
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__187]) ).
thf(27,plain,
( ~ sP7
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP24
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP23
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h13,h4,h5,h1,h0])],[18,19,20,21,22,23,24,25,26,27,28,29,h18,h19,h21,h22,h5]) ).
thf(31,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])],[h20,30,h21,h22]) ).
thf(32,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__45)],[h16,31,h20]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,32,h18,h19]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h13,h4,h5,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__44)],[h15,33,h17]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h4,h5,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,34,h15,h16]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__43)],[h13,35,h14]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__42)],[h4,36,h13]) ).
thf(38,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,17,37,h2,h3,h4,h5]) ).
thf(39,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[38,h0]) ).
thf(0,theorem,
sP28 = sP23,
inference(contra,[status(thm),contra(discharge,[h1])],[38,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 15:12:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 224.19/183.32 % SZS status Theorem
% 224.19/183.32 % Mode: cade22grackle2x2d0b
% 224.19/183.32 % Steps: 7074
% 224.19/183.32 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------