%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN045^4 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 : 300s
% DateTime : Thu Oct 9 03:17:39 PM UTC 2025
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_p,type,
p: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_q,type,
q: $i > $o ).
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_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_r,type,
r: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(sP1,plain,
( sP1
<=> ( irel @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( irel @ eigen__1 @ eigen__5 )
=> ~ ( ( q @ eigen__5 )
=> ~ ( r @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( r @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( irel @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( q @ eigen__5 )
=> ~ ( r @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( irel @ eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( p @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( r @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP4
=> ( p @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( irel @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( q @ eigen__3 )
=> ~ ( r @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( p @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( q @ X2 )
=> ~ ( r @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( irel @ eigen__6 @ eigen__8 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( r @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( q @ X2 ) ) )
=> ~ ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP13
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( irel @ eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ( ( q @ X1 )
=> ~ ( r @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP6
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( irel @ eigen__1 @ eigen__2 )
=> ( p @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP11
=> ( p @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( r @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP1
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP21
=> ( q @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( q @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( irel @ eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP9
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP20
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( irel @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( p @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP31
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( q @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
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,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
iand = mand ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
ivalid = !! ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(pel13,conjecture,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( q @ X3 )
=> ~ ( r @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( q @ X3 )
=> ~ ( r @ X3 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( q @ X3 )
=> ~ ( r @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( q @ X3 )
=> ~ ( r @ X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[pel13]) ).
thf(h1,assumption,
( ( sP16
=> sP19 )
=> ~ ( sP19
=> sP16 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP16
=> sP19 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP19
=> sP16 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP16,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP9
=> ~ ( ( ~ sP6
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) )
=> ~ ( ~ sP6
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP9,
introduced(assumption,[]) ).
thf(h8,assumption,
( ( ~ sP6
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) )
=> ~ ( ~ sP6
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ sP6
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( q @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ sP6
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( r @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( q @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h14,assumption,
sP34,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP1
=> sP30 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(1,plain,
( sP12
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP6
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP24
| ~ sP34
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP22
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP28
| ~ sP1
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP16
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP32
| ~ sP9
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP23
| sP6
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h9,h7,h8,h6,h4,h5,h2,h1,h0])],[1,2,3,4,5,6,7,8,h4,h7,h14,h15,h17,h18]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h9,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,9,h17,h18]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__3)],[h12,10,h16]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h9,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,11,h14,h15]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h11,12,h13]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,13,h11,h12]) ).
thf(h19,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( r @ X1 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h21,assumption,
sP4,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP7
=> sP26 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP7,
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(15,plain,
( sP5
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP10
| ~ sP4
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP16
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP32
| ~ sP9
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP23
| sP6
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP22
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP2
| ~ sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h11,h19,h10,h7,h8,h6,h4,h5,h2,h1,h0])],[15,16,17,18,19,20,21,22,h4,h7,h21,h22,h24,h25]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h11,h19,h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,23,h24,h25]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h11,h19,h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__5)],[h19,24,h23]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h11,h19,h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,25,h21,h22]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h19,h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__4)],[h11,26,h20]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h11,h19])],[h10,27,h11,h19]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,14,28,h9,h10]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,29,h7,h8]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,30,h6]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,31,h4,h5]) ).
thf(h26,assumption,
sP19,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( sP31
=> ( ~ sP13
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( q @ X1 )
=> ~ ( r @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
sP31,
introduced(assumption,[]) ).
thf(h30,assumption,
~ ( ~ sP13
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( q @ X1 )
=> ~ ( r @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h32,assumption,
~ ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ~ ( ( q @ X1 )
=> ~ ( r @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h34,assumption,
sP11,
introduced(assumption,[]) ).
thf(h35,assumption,
~ sP35,
introduced(assumption,[]) ).
thf(h36,assumption,
~ ( sP21
=> ~ ( sP37
=> ~ sP3 ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
sP21,
introduced(assumption,[]) ).
thf(h38,assumption,
( sP37
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h39,assumption,
~ sP37,
introduced(assumption,[]) ).
thf(h40,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(33,plain,
( ~ sP15
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP29
| ~ sP21
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP20
| sP13
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP33
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP19
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP36
| ~ sP31
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP13
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP25
| ~ sP11
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h39,h37,h38,h36,h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h3,h1,h0])],[33,34,35,36,37,38,39,40,h26,h29,h34,h35,h37,h39]) ).
thf(42,plain,
( ~ sP18
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP17
| ~ sP21
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP8
| sP13
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP33
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP19
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP36
| ~ sP31
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP13
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP25
| ~ sP11
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h40,h37,h38,h36,h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h3,h1,h0])],[42,43,44,45,46,47,48,49,h26,h29,h34,h35,h37,h40]) ).
thf(51,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h37,h38,h36,h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h3,h1,h0]),tab_imp(discharge,[h39]),tab_imp(discharge,[h40])],[h38,41,50,h39,h40]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h3,h1,h0]),tab_negimp(discharge,[h37,h38])],[h36,51,h37,h38]) ).
thf(53,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h34,h35,h33,h31,h32,h29,h30,h28,h26,h27,h3,h1,h0]),tab_negall(discharge,[h36]),tab_negall(eigenvar,eigen__8)],[h32,52,h36]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h31,h32,h29,h30,h28,h26,h27,h3,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,53,h34,h35]) ).
thf(55,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h31,h32,h29,h30,h28,h26,h27,h3,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__7)],[h31,54,h33]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h29,h30,h28,h26,h27,h3,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,55,h31,h32]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h26,h27,h3,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,56,h29,h30]) ).
thf(58,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h26,h27,h3,h1,h0]),tab_negall(discharge,[h28]),tab_negall(eigenvar,eigen__6)],[h27,57,h28]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h3,58,h26,h27]) ).
thf(60,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,32,59,h2,h3]) ).
thf(61,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,60,h1]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( q @ X3 )
=> ~ ( r @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( q @ X3 )
=> ~ ( r @ X3 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[61,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN045^4 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n016.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 : 300
% 0.12/0.34 % DateTime : Wed Oct 8 15:14:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % Mode: mode213
% 0.19/0.51 % Inferences: 1399
% 0.19/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------