TSTP Solution File: SYO170^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO170^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 04:45:43 EDT 2023
% Result : Theorem 0.21s 0.63s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $i ).
thf(ty_e,type,
e: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_ab,type,
ab: $i ).
thf(ty_cP,type,
cP: $i > $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cP @ a @ b @ ab ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ ab @ ab @ X2 )
=> ~ ( cP @ ab @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cP @ ab @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ b @ b @ e ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ( cP @ ab @ X1 @ X3 )
=> ~ ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
= ( cP @ ab @ X4 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cP @ ab @ b @ a )
= ( cP @ a @ e @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] : ( cP @ X1 @ e @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ e @ b @ b )
= ( cP @ ab @ a @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cP @ ab @ e @ ab ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ a @ a @ e ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cP @ ab @ b @ a ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( cP @ ab @ ab @ e )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( cP @ b @ a @ ab )
= sP8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] : ( cP @ e @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ ab @ ab @ e )
=> ~ ( cP @ ab @ b @ X1 ) )
=> ( ( cP @ e @ b @ X2 )
= ( cP @ ab @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ( cP @ a @ X1 @ X3 )
=> ~ ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
= ( cP @ a @ X4 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ a @ b @ X2 )
=> ~ ( cP @ b @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cP @ a @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP1
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ a @ X1 )
=> ~ ( cP @ a @ a @ X2 ) )
=> ( ( cP @ X1 @ a @ X3 )
= ( cP @ ab @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ sP11
=> ( ( cP @ e @ b @ X1 )
= ( cP @ ab @ a @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP17
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ ab @ ab @ X1 )
=> ~ ( cP @ ab @ b @ X2 ) )
=> ( ( cP @ X1 @ b @ X3 )
= ( cP @ ab @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( cP @ a @ e @ a ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cP @ ab @ a @ b ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ( cP @ X1 @ X2 @ X4 )
=> ~ ( cP @ X2 @ X3 @ X5 ) )
=> ( ( cP @ X4 @ X3 @ X6 )
= ( cP @ X1 @ X5 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( cP @ b @ a @ ab ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP23
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ a @ b @ X1 )
=> ~ ( cP @ b @ b @ X2 ) )
=> ( ( cP @ X1 @ b @ X3 )
= ( cP @ a @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP11
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( cP @ ab @ ab @ e ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i] :
( ~ ( sP1
=> ~ ( cP @ b @ b @ X1 ) )
=> ( ( cP @ ab @ b @ X2 )
= ( cP @ a @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( cP @ e @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ( cP @ ab @ a @ X2 )
=> ~ ( cP @ a @ X1 @ X3 ) )
=> ( ( cP @ X2 @ X1 @ X4 )
= ( cP @ ab @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ~ sP17
=> ( ( cP @ ab @ b @ X1 )
= ( cP @ a @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i,X2: $i] :
( ~ ( sP23
=> ~ ( cP @ a @ a @ X1 ) )
=> ( ( cP @ b @ a @ X2 )
= ( cP @ ab @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] : ( cP @ X1 @ X1 @ e ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP26
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ~ sP26
=> ( ( cP @ b @ a @ X1 )
= ( cP @ ab @ e @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(cTHM105,conjecture,
( ~ ( ~ ( ~ ( sP13
=> ~ sP6 )
=> ~ sP35 )
=> ~ sP24 )
=> ( sP1
=> sP25 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( sP13
=> ~ sP6 )
=> ~ sP35 )
=> ~ sP24 )
=> ( sP1
=> sP25 ) ),
inference(assume_negation,[status(cth)],[cTHM105]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( sP13
=> ~ sP6 )
=> ~ sP35 )
=> ~ sP24 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP1
=> sP25 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP13
=> ~ sP6 )
=> ~ sP35 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP24,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP13
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP35,
introduced(assumption,[]) ).
thf(h7,assumption,
sP13,
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP28
| sP11
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| ~ sP29
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| ~ sP31
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP20
| sP17
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP17
| ~ sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP10
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP19
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP36
| sP26
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP26
| ~ sP23
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| sP25
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP33
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP14
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP37
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP30
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP21
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP34
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP18
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP32
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP2
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP4
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP35
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP24
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP27
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP16
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP15
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP35
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP6
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP24
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP35
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP13
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,h7,h8,h6,h4,h9,h10]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,33,h9,h10]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,34,h7,h8]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,35,h5,h6]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,36,h3,h4]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,37,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( sP13
=> ~ sP6 )
=> ~ sP35 )
=> ~ sP24 )
=> ( sP1
=> sP25 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[38,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO170^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 05:30:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.63 % SZS status Theorem
% 0.21/0.63 % Mode: cade22grackle2xfee4
% 0.21/0.63 % Steps: 2882
% 0.21/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------