TSTP Solution File: SEV017^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV017^5 : 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 : Thu Aug 31 19:32:20 EDT 2023
% Result : Theorem 0.15s 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__0 @ eigen__3 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ~ ( ( eigen__0 @ eigen__3 @ eigen__2 )
=> ~ ( eigen__0 @ eigen__2 @ X1 ) )
=> ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__0 @ eigen__3 @ eigen__2 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ eigen__1 @ eigen__2 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP6
=> ( eigen__0 @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__0 @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__0 @ X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__0 @ eigen__3 @ eigen__1 )
=> ( eigen__0 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP2
=> ( eigen__0 @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0 @ X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cTHM514_pme,conjecture,
! [X1: a > a > $o] :
( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ! [X2: a,X3: a,X4: a] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > $o] :
( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ! [X2: a,X3: a,X4: a] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM514_pme]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ! [X1: a] : ( eigen__0 @ X1 @ X1 )
=> ~ sP4 )
=> ~ sP16 )
=> ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ! [X1: a] : ( eigen__0 @ X1 @ X1 )
=> ~ sP4 )
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a,X2: a,X3: a] :
( ( eigen__0 @ X1 @ X2 )
=> ( ( eigen__0 @ X2 @ X3 )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ! [X1: a] : ( eigen__0 @ X1 @ X1 )
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP16,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a] : ( eigen__0 @ X1 @ X1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP4,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: a,X2: a] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( ( eigen__0 @ X1 @ X2 )
=> ( eigen__0 @ eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: a] :
( sP12
=> ( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__0 @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP12
=> ( sP2
=> sP14 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP12,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP2
=> sP14 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP17
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP6
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP15
| ~ sP2
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| ~ sP12
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP11
| ~ sP13
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h7,h5,h11,h13,h14]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,15,h13,h14]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,16,h11,h12]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,17,h10]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,18,h9]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h3,19,h8]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,20,h6,h7]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,21,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,22,h2,h3]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,23,h1]) ).
thf(0,theorem,
! [X1: a > a > $o] :
( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
=> ~ ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) )
=> ~ ! [X2: a,X3: a,X4: a] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ! [X2: a,X3: a,X4: a] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV017^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.30 % Computer : n021.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Aug 24 03:13:09 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % Mode: cade22grackle2xfee4
% 0.15/0.35 % Steps: 86
% 0.15/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------