TSTP Solution File: SYO506^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO506^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 04:47:19 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% 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_c,type,
c: $o > $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( c @ ~ $false @ X1 @ X2 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( c @ sP2 @ eigen__0 @ eigen__1 )
= ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( c @ sP2 @ eigen__0 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( c @ ~ sP2 @ eigen__0 @ eigen__0 )
= ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( c @ ~ sP2 @ eigen__0 @ eigen__0 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP2
= ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( c @ sP2 @ X1 @ X2 )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( c @ sP2 @ eigen__0 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( c @ ~ sP2 @ eigen__0 @ X1 )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(claim,conjecture,
( ~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP1 )
=> ~ sP9 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP1 )
=> ~ sP9 ),
inference(assume_negation,[status(cth)],[claim]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( c @ ( eigen__0 = X1 ) @ eigen__0 @ X1 )
= X1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| sP2
| sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| sP8
| ~ sP3
| ~ sP10 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( sP7
| sP2
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
~ sP2,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP5
| ~ sP11
| sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP8
| ~ sP5
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,h6,h4,h2]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,11,h6]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,12,h5]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,13,h3,h4]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,14,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ! [X1: $i,X2: $i] :
( ( c @ ( X1 = X2 ) @ X1 @ X2 )
= X2 )
=> ~ sP1 )
=> ~ sP9 ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO506^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 02:43:50 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % Mode: cade22grackle2xfee4
% 0.21/0.41 % Steps: 90
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------