TSTP Solution File: SYO102^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO102^5 : 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 : n008.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 04:45:13 EDT 2023
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( cP @ eigen__2 @ eigen__2 )
=> ~ sP1 )
=> ( cP @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] : ( cP @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cP @ eigen__2 @ eigen__2 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ( cP @ eigen__2 @ eigen__1 )
=> ~ ( cP @ X1 @ eigen__1 ) )
=> ( cP @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cP @ eigen__2 @ eigen__1 )
=> ~ ( cP @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ eigen__2 @ X1 )
=> ~ ( cP @ X2 @ X1 ) )
=> ( cP @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cP @ eigen__0 @ X1 )
=> ~ ( cP @ X2 @ X1 ) )
=> ( cP @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ~ ( sP3
=> ~ ( cP @ X1 @ eigen__0 ) )
=> ( cP @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cP @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ~ ( ( cP @ eigen__2 @ eigen__2 )
=> ~ ( cP @ X1 @ eigen__2 ) )
=> ( cP @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cP @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cP @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP10
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X3 @ X2 ) )
=> ( cP @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP8
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( cP @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM101,conjecture,
( ~ ( sP5
=> ~ sP18 )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP5
=> ~ sP18 )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[cTHM101]) ).
thf(h1,assumption,
~ ( sP5
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
sP18,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( cP @ eigen__0 @ X1 )
=> ~ ( cP @ X1 @ X2 ) )
=> ( cP @ eigen__0 @ X2 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ~ ( sP13
=> ~ ( cP @ eigen__1 @ X1 ) )
=> ( cP @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP13
=> ~ sP1 )
=> sP15 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP13
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h10,assumption,
sP13,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP16
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP19
| sP8
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| ~ sP20
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP6
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| ~ sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| sP10
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP18
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h3,h4,h10,h11,h9]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h8,17,h10,h11]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,18,h8,h9]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,19,h7]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,20,h6]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,21,h5]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,22,h3,h4]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,23,h1,h2]) ).
thf(0,theorem,
( ~ ( sP5
=> ~ sP18 )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( cP @ X1 @ X2 )
=> ~ ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYO102^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 04:29:47 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % Mode: cade22grackle2xfee4
% 0.18/0.41 % Steps: 73
% 0.18/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------