TSTP Solution File: SYO901^11 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO901^11 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n026.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 : Fri Sep 1 04:48:33 EDT 2023
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_q,type,
q: mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld,X2: mworld,X3: mworld] :
( ~ ( ( mrel @ X1 @ X3 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( mrel @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__0 @ X1 )
=> ~ ( mrel @ eigen__0 @ eigen__1 ) )
=> ( mrel @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mrel @ eigen__0 @ eigen__1 )
=> ( p @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( mrel @ eigen__0 @ mactual )
=> ~ ( mrel @ eigen__0 @ eigen__2 ) )
=> ( mrel @ mactual @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mrel @ eigen__0 @ mactual )
=> ~ ( mrel @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( mrel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( mrel @ mactual @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: mworld] :
( ~ ( ( mrel @ mactual @ X1 )
=> ~ ( mrel @ mactual @ mactual ) )
=> ( mrel @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( mrel @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ eigen__0 @ X2 )
=> ~ ( mrel @ eigen__0 @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP12
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( mrel @ mactual @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP8
=> ( q @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( p @ eigen__1 )
= ( q @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( mrel @ mactual @ eigen__1 )
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( sP14
=> ~ sP16 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP14
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( q @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( p @ eigen__2 )
= ( q @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: mworld] : ( mrel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP10
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( p @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( mrel @ mactual @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: mworld] :
( ~ ( ( mrel @ eigen__0 @ X1 )
=> ~ sP8 )
=> ( mrel @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ mactual @ X2 )
=> ~ ( mrel @ mactual @ X1 ) )
=> ( mrel @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( mrel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP7
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( q @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( mrel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
? [X3: mworld] :
( ( mrel @ X2 @ X3 )
& ( X1 @ X3 ) ) ) ) ).
thf(con,conjecture,
( sP2
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) )
= ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) )
= ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) )
= ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP14
=> ( sP9 = sP5 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP14,
introduced(assumption,[]) ).
thf(h5,assumption,
sP9 != sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
sP9,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP31
=> sP22 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP31,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP21
| ~ sP14
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| sP21
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP29
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| ~ sP12
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP32
| sP7
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP24
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP3
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| ~ sP30
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| ~ sP31
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP19
| ~ sP27
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(mrel_euclidean,axiom,
sP1 ).
thf(mrel_reflexive,axiom,
sP24 ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h6,h7,h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h1,h4,h6,h11,h12,mrel_euclidean,mrel_reflexive]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h6,h7,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,17,h11,h12]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h7,18,h10]) ).
thf(h13,assumption,
~ ( sP8
=> sP26 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP8,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(20,plain,
( ~ sP15
| ~ sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP6
| sP15
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP28
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP23
| sP26
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP17
| ~ sP8
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP25
| ~ sP10
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP5
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP2
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP13
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP21
| ~ sP14
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP20
| sP21
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP11
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP29
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP1
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP24
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h8,h9,h4,h5,h3,h1,h2,h0])],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,h1,h4,h14,h15,h9,mrel_euclidean,mrel_reflexive]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h8,h9,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,36,h14,h15]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h8,37,h13]) ).
thf(39,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,19,38,h6,h7,h8,h9]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,39,h4,h5]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,40,h3]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,41,h1,h2]) ).
thf(0,theorem,
( sP2
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( p @ X2 ) ) )
= ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( q @ X2 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[42,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO901^11 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 06:15:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % Mode: cade22grackle2xfee4
% 0.21/0.39 % Steps: 319
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------