TSTP Solution File: LCL956^18 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL956^18 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : Sun Jul 17 14:12:11 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__3,type,
eigen__3: mworld ).
thf(ty_big_q,type,
big_q: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__3 @ X1 )
=> ( p @ X1 ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__3 @ X1 )
=> ( big_q @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mrel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eiw_di @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mworld] :
( ( mrel @ eigen__3 @ X1 )
=> ( big_q @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( big_q @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP2
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__3 )
=> ( ! [X2: mworld] :
( ( mrel @ eigen__3 @ X2 )
=> ( p @ X2 ) )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__3 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP3
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ eigen__3 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(x2109,conjecture,
~ ( ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[x2109]) ).
thf(h1,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( sP13
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) )
=> ~ ( sP13
=> sP5 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( sP13
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) )
=> ~ ( sP13
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( sP13
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
( sP13
=> sP5 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP3
=> ( sP13
=> ~ sP8 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP3,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP13
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP13,
introduced(assumption,[]) ).
thf(h12,assumption,
sP8,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h14,assumption,
sP5,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h16,assumption,
sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP2
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h13,h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h1,h0])],[1,2,h11,h16,h17]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h13,h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,3,h16,h17]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[h13,4,h15]) ).
thf(6,plain,
( ~ sP5
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP12
| ~ sP3
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h1,h0])],[6,7,h9,h12,h14]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h4,h5,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[h7,5,8,h13,h14]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,9,h11,h12]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,10,h9,h10]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,11,h8]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,12,h6,h7]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,13,h4,h5]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,14,h3]) ).
thf(h18,assumption,
~ ( ( mrel @ mactual @ eigen__3 )
=> ( ~ ( sP14
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__3 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__3 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) )
=> ~ sP11 ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
mrel @ mactual @ eigen__3,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ~ ( sP14
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__3 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__3 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP14
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__3 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__3 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP11,
introduced(assumption,[]) ).
thf(h23,assumption,
sP14,
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__3 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__3 @ X2 )
=> ( big_q @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( sP4
=> ~ sP7 ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP4,
introduced(assumption,[]) ).
thf(h27,assumption,
sP7,
introduced(assumption,[]) ).
thf(16,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| ~ sP4
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| ~ sP14
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h26,h27,h25,h23,h24,h21,h22,h19,h20,h18,h2,h0])],[16,17,18,h23,h26,h27,h22]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h25,h23,h24,h21,h22,h19,h20,h18,h2,h0]),tab_negimp(discharge,[h26,h27])],[h25,19,h26,h27]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h18,h2,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__4)],[h24,20,h25]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h18,h2,h0]),tab_negimp(discharge,[h23,h24])],[h21,21,h23,h24]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,22,h21,h22]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,23,h19,h20]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__3)],[h2,24,h18]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,15,25,h1,h2]) ).
thf(0,theorem,
~ ( ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) )
=> ~ ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ~ ( ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( p @ X3 ) )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( big_q @ X2 @ X3 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL956^18 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 15:16:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 7
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------