TSTP Solution File: SYN393^4.002 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN393^4.002 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : Thu Jul 21 11:43:23 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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_a1,type,
a1: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_a2,type,
a2: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(sP1,plain,
( sP1
<=> ( ( irel @ eigen__1 @ eigen__5 )
=> ( a2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( irel @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( irel @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( irel @ eigen__0 @ eigen__6 )
=> ~ ( sP4
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP4
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( a2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( irel @ eigen__6 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP10
=> ( a1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP2
=> ( a1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( irel @ eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( a1 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( a1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) )
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( irel @ eigen__0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP3
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( irel @ eigen__6 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( a2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
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(con,conjecture,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
( ( sP8
=> sP13 )
=> ~ ( sP13
=> sP8 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP8
=> sP13 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP13
=> sP8 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP27
=> ~ ( sP15
=> ~ sP22 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP27,
introduced(assumption,[]) ).
thf(h8,assumption,
( sP15
=> ~ sP22 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h11,assumption,
sP18,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h14,assumption,
sP2,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP25
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP12
| ~ sP2
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| ~ sP18
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP16
| ~ sP27
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h7,h8,h6,h4,h5,h2,h1,h0])],[1,2,3,4,5,6,h4,h7,h11,h14,h15]) ).
thf(8,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])],[h13,7,h14,h15]) ).
thf(9,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)],[h12,8,h13]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,9,h11,h12]) ).
thf(h16,assumption,
sP25,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
sP14,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP22
| ~ sP25
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP6
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| ~ sP27
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP18
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP1
| ~ sP14
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h20,h18,h16,h17,h10,h7,h8,h6,h4,h5,h2,h1,h0])],[11,12,13,14,15,16,h4,h7,h16,h19,h20]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,17,h19,h20]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h17,h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h17,18,h18]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h7,h8,h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h10,19,h16,h17]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,10,20,h9,h10]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,21,h7,h8]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,22,h6]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,23,h4,h5]) ).
thf(h21,assumption,
sP13,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP23
=> ~ ( sP20
=> ~ sP4 ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP23,
introduced(assumption,[]) ).
thf(h25,assumption,
( sP20
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h28,assumption,
sP26,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h30,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h31,assumption,
sP3,
introduced(assumption,[]) ).
thf(h32,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(25,plain,
( ~ sP21
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP24
| ~ sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP20
| ~ sP26
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP7
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP5
| ~ sP23
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h32,h30,h28,h29,h26,h24,h25,h23,h21,h22,h3,h1,h0])],[25,26,27,28,29,30,h21,h24,h28,h31,h32]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h28,h29,h26,h24,h25,h23,h21,h22,h3,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,31,h31,h32]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h28,h29,h26,h24,h25,h23,h21,h22,h3,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__7)],[h29,32,h30]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h26,33,h28,h29]) ).
thf(h33,assumption,
sP21,
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h35,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h36,assumption,
sP10,
introduced(assumption,[]) ).
thf(h37,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(35,plain,
( ~ sP4
| ~ sP21
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP5
| ~ sP23
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP26
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP11
| ~ sP10
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h36,h37,h35,h33,h34,h27,h24,h25,h23,h21,h22,h3,h1,h0])],[35,36,37,38,39,40,h21,h24,h33,h36,h37]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h35,h33,h34,h27,h24,h25,h23,h21,h22,h3,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,41,h36,h37]) ).
thf(43,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h33,h34,h27,h24,h25,h23,h21,h22,h3,h1,h0]),tab_negall(discharge,[h35]),tab_negall(eigenvar,eigen__9)],[h34,42,h35]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h24,h25,h23,h21,h22,h3,h1,h0]),tab_negimp(discharge,[h33,h34])],[h27,43,h33,h34]) ).
thf(45,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h24,h25,h23,h21,h22,h3,h1,h0]),tab_imp(discharge,[h26]),tab_imp(discharge,[h27])],[h25,34,44,h26,h27]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,45,h24,h25]) ).
thf(47,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[h22,46,h23]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h3,47,h21,h22]) ).
thf(49,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,24,48,h2,h3]) ).
thf(50,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,49,h1]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[50,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN393^4.002 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 21:30:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % Mode: mode213
% 0.20/0.39 % Inferences: 90
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------