TSTP Solution File: SET594^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET594^5 : 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 : n003.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 : Thu Aug 31 15:17:40 EDT 2023
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( eigen__0 @ eigen__3 )
=> ~ sP1 )
=> ~ ( ( eigen__0 @ eigen__3 )
=> ~ ( eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
= ( eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__3 )
=> ~ ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP6
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ^ [X1: a] :
( ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(cBOOL_PROP_53_pme,conjecture,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ( ^ [X4: a] :
( ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) ) )
= X1 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ( ^ [X4: a] :
( ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) ) )
= X1 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_53_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ( ( eigen__0 @ X3 )
=> ~ ( X1 @ X3 ) )
=> ~ ( ( eigen__0 @ X3 )
=> ~ ( X2 @ X3 ) ) ) )
= eigen__0 )
=> ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ( ( ^ [X2: a] :
( ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X2 ) )
=> ~ ( ( eigen__0 @ X2 )
=> ~ ( X1 @ X2 ) ) ) )
= eigen__0 )
=> ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( ~ ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP9
=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP9,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP6
=> ( ~ sP1
=> sP7 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ sP1
=> sP7 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,h4,h7,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,8,h7,h8]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,9,h6]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ( ^ [X4: a] :
( ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) )
=> ~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) ) )
= X1 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET594^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.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 15:50:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % Mode: cade22grackle2xfee4
% 0.20/0.39 % Steps: 15
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------