TSTP Solution File: SET611^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET611^5 : 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 : n023.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 15:17:49 EDT 2023
% Result : Theorem 0.14s 0.35s
% Output : Proof 0.14s
% 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 ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__2 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ~ ( ( eigen__0 @ eigen__3 )
=> ( eigen__1 @ eigen__3 ) ) )
= ( eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ eigen__2 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP7
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) )
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cBOOL_PROP_84_pme,conjecture,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
= ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= X1 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
= ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= X1 ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_84_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o] :
( ( ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ~ ( X1 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
= ( ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= eigen__0 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP12 != sP2,
introduced(assumption,[]) ).
thf(h3,assumption,
sP12,
introduced(assumption,[]) ).
thf(h4,assumption,
sP2,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP8 != sP9 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h10,assumption,
sP9,
introduced(assumption,[]) ).
thf(h11,assumption,
sP8,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h13,h9,h10,h8,h7,h3,h4,h2,h1,h0])],[h10,h10]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h13])],[h9,1,h10,h13]) ).
thf(3,plain,
( ~ sP5
| ~ sP9
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| ~ sP9
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h8,h7,h3,h4,h2,h1,h0])],[3,4,5,6,h3,h11,h12]) ).
thf(8,plain,
$false,
inference(tab_be,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,2,7,h9,h10,h11,h12]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,8,h8]) ).
thf(10,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_fe(discharge,[h7])],[h4,9,h7]) ).
thf(h14,assumption,
~ ! [X1: a] :
( ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) )
= $false ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP7
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP7,
introduced(assumption,[]) ).
thf(h17,assumption,
sP10,
introduced(assumption,[]) ).
thf(11,plain,
( sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP6
| ~ sP11
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h14,h5,h6,h2,h1,h0])],[11,12,13,14,h16,h17,h6]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,15,h16,h17]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__3)],[h14,16,h15]) ).
thf(18,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_fe(discharge,[h14])],[h5,17,h14]) ).
thf(19,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,10,18,h3,h4,h5,h6]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,19,h2]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,20,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
= ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET611^5 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.30 % Computer : n023.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Aug 26 13:48:56 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.14/0.35 % SZS status Theorem
% 0.14/0.35 % Mode: cade22grackle2xfee4
% 0.14/0.35 % Steps: 30
% 0.14/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------