%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL705^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -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 01:02:28 PM UTC 2026
% Result : Theorem 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 92
% Syntax : Number of formulae : 110 ( 60 unt; 0 typ; 33 def)
% Number of atoms : 263 ( 54 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 517 ( 136 ~; 27 |; 0 &; 230 @)
% ( 23 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 63 usr; 63 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 142 ( 49 ^; 93 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
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__19,type,
eigen__19: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> ( eigen__10 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__1 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( eigen__10 = eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__1 @ eigen__19 )
=> ( eigen__2 @ eigen__19 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__1 @ eigen__19 )
=> ~ ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__19 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__10 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__10 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__3 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__10 = eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__2 @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP1
=> ( eigen__10 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__1 @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( eigen__10 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP20
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
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] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ! [X2: $i,X3: $i > $o] :
~ ( ~ ~ ( ~ ~ ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ! [X2: $i,X3: $i > $o] :
~ ( ( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ ( sP9
=> ! [X1: $i,X2: $i > $o] :
~ ( ( ~ ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ~ ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP9,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i > $o] :
~ ( ( ~ ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ~ ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o] :
~ ( ( ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eigen__0 @ eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ( ~ sP8
=> sP14 )
=> ~ ( sP14
=> ~ sP8 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ sP8
=> sP14 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP14
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP23
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP23,
introduced(assumption,[]) ).
thf(h13,assumption,
sP18,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> sP19 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP15
| sP13
| ~ sP11
| ~ sP21 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP17
| ~ sP1
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| ~ sP23
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| ~ sP3
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP10
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP10
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP12
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(11,plain,
( ~ sP9
| ~ sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP18
| sP19
| ~ sP13 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h3,h12,h13,h15,h16]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,13,h15,h16]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h6,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h10,14,h14]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,15,h12,h13]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h6,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h9,16,h11]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,17,h9,h10]) ).
thf(h17,assumption,
sP14,
introduced(assumption,[]) ).
thf(h18,assumption,
sP8,
introduced(assumption,[]) ).
thf(19,plain,
( ~ sP8
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP22
| ~ sP20
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP5
| ~ sP20
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP6
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP12
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19]) ).
thf(25,plain,
( ~ sP9
| ~ sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h8,h6,h5,h3,h4,h2,h1,h0])],[19,20,21,22,23,24,25,h3,h17,h18]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h8,26,h17,h18]) ).
thf(28,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,18,27,h7,h8]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,28,h6]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,29,h5]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,30,h3,h4]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,31,h2]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[32,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) )
=> ! [X2: $i,X3: $i > $o] :
~ ( ~ ~ ( ~ ~ ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[32,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL705^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 15:24:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.22/0.53 % SZS status Theorem
% 0.22/0.53 % Mode: mode213
% 0.22/0.53 % Inferences: 1776
% 0.22/0.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------