%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL866^1 : 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 : n007.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 01:02:48 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__12,type,
eigen__12: $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 > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ eigen__1 @ eigen__2 )
=> ( eigen__0 @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__9 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ eigen__7 )
=> ~ ( eigen__0 @ eigen__6 @ X1 ) )
=> ( eigen__0 @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ eigen__10 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__6 @ eigen__7 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ( eigen__0 @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__11 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__11 @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__5 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__12 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP7
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__6 @ X1 )
=> ~ ( eigen__0 @ eigen__6 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__0 @ eigen__2 @ eigen__1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__0 @ eigen__4 @ eigen__5 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ eigen__1 )
=> ~ ( eigen__0 @ eigen__2 @ X1 ) )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__9 @ X1 )
=> ( eigen__0 @ X1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP11
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0 @ eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP25
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP3
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ~ ( sP11
=> ~ ( eigen__0 @ eigen__11 @ X1 ) )
=> ( eigen__0 @ eigen__12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ~ ( eigen__0 @ eigen__2 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X1 @ X3 ) )
=> ( eigen__0 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__11 @ X1 )
=> ~ ( eigen__0 @ eigen__11 @ X2 ) )
=> ( eigen__0 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP17
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
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 )
=> ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) )
= ( ~ ( ~ ( ! [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 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ~ ( ! [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 ) ) ) )
= ( ~ ( ~ ( ! [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 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
( ( ~ ( sP10
=> ~ sP32 ) )
!= ( ~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP10 )
=> ~ sP32 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP10
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP10 )
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( sP10
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP10 )
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP10,
introduced(assumption,[]) ).
thf(h7,assumption,
sP32,
introduced(assumption,[]) ).
thf(h8,assumption,
( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ~ ( sP23
=> ~ ( eigen__0 @ eigen__2 @ X1 ) )
=> ( eigen__0 @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP23
=> ~ sP1 )
=> sP27 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP23
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h17,assumption,
sP23,
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP21
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| ~ sP23
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP31
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP19
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP34
| sP17
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP17
| ~ sP22
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP32
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h13,h12,h10,h8,h6,h7,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h6,h7,h17,h18,h16]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h13,h12,h10,h8,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,9,h17,h18]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h12,h10,h8,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,10,h15,h16]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h12,h10,h8,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,11,h14]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h8,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,12,h13]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h10,13,h12]) ).
thf(h19,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h21,assumption,
sP26,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(15,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP8
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP18
| ~ sP26
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h19,h11,h8,h6,h7,h2,h3,h1,h0])],[15,16,17,h6,h21,h22]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h19,h11,h8,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,18,h21,h22]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h11,h8,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,19,h20]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h8,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__4)],[h11,20,h19]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h6,h7,h2,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,14,21,h10,h11]) ).
thf(h23,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h28,assumption,
sP20,
introduced(assumption,[]) ).
thf(h29,assumption,
sP4,
introduced(assumption,[]) ).
thf(23,plain,
( ~ sP32
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP16
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP5
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP15
| sP7
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP7
| ~ sP20
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h28,h29,h26,h27,h25,h24,h23,h9,h6,h7,h2,h3,h1,h0])],[23,24,25,26,27,h7,h28,h29,h27]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h25,h24,h23,h9,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h26,28,h28,h29]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h24,h23,h9,h6,h7,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,29,h26,h27]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h23,h9,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__8)],[h24,30,h25]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h9,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__7)],[h23,31,h24]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h7,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[h9,32,h23]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h3,22,33,h8,h9]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h2,34,h6,h7]) ).
thf(h30,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h31,assumption,
~ sP29,
introduced(assumption,[]) ).
thf(h32,assumption,
sP3,
introduced(assumption,[]) ).
thf(h33,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h34,assumption,
~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h35,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(36,plain,
( ~ sP10
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP24
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP29
| ~ sP3
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h6,h34,h7,h32,h33,h31,h30,h11,h4,h5,h1,h0])],[36,37,38,h32,h33,h6]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h7,h32,h33,h31,h30,h11,h4,h5,h1,h0]),tab_negimp(discharge,[h35,h6])],[h34,39,h35,h6]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h33,h31,h30,h11,h4,h5,h1,h0]),tab_negimp(discharge,[h34,h7])],[h5,40,h34,h7]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h31,h30,h11,h4,h5,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,41,h32,h33]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h30,h11,h4,h5,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__10)],[h30,42,h31]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h4,h5,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__9)],[h11,43,h30]) ).
thf(h36,assumption,
~ sP33,
introduced(assumption,[]) ).
thf(h37,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h38,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h39,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h40,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h41,assumption,
sP11,
introduced(assumption,[]) ).
thf(h42,assumption,
sP9,
introduced(assumption,[]) ).
thf(45,plain,
( ~ sP32
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP33
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP30
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP28
| sP25
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP25
| ~ sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h6,h34,h7,h41,h42,h39,h40,h38,h37,h36,h9,h4,h5,h1,h0])],[45,46,47,48,49,h41,h42,h40,h7]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h7,h41,h42,h39,h40,h38,h37,h36,h9,h4,h5,h1,h0]),tab_negimp(discharge,[h35,h6])],[h34,50,h35,h6]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h38,h37,h36,h9,h4,h5,h1,h0]),tab_negimp(discharge,[h34,h7])],[h5,51,h34,h7]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h39,h40,h38,h37,h36,h9,h4,h5,h1,h0]),tab_negimp(discharge,[h41,h42])],[h39,52,h41,h42]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h38,h37,h36,h9,h4,h5,h1,h0]),tab_negimp(discharge,[h39,h40])],[h38,53,h39,h40]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h37,h36,h9,h4,h5,h1,h0]),tab_negall(discharge,[h38]),tab_negall(eigenvar,eigen__13)],[h37,54,h38]) ).
thf(56,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h36,h9,h4,h5,h1,h0]),tab_negall(discharge,[h37]),tab_negall(eigenvar,eigen__12)],[h36,55,h37]) ).
thf(57,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h4,h5,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__11)],[h9,56,h36]) ).
thf(58,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h5,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h9])],[h4,44,57,h11,h9]) ).
thf(59,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,35,58,h2,h3,h4,h5]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,59,h1]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ( ~ ( ! [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 ) ) ) )
= ( ~ ( ~ ( ! [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 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[60,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL866^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 19:56:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.43 % SZS status Theorem
% 0.13/0.43 % Mode: mode213
% 0.13/0.43 % Inferences: 20
% 0.13/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------