TSTP Solution File: SYO315^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO315^5 : 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 : n025.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 04:46:16 EDT 2023
% Result : Theorem 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_z,type,
z: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ z ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP1
=> ~ ( eigen__1 @ X1 ) )
=> ~ sP2 )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP1
=> ~ ( eigen__1 @ X2 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ sP1
=> ~ ( eigen__1 @ eigen__3 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP5
=> ( eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP1
=> ~ ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( X2 @ z )
=> ~ ( X2 @ X4 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( X1 @ z )
=> ~ ( X1 @ X3 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( eigen__0 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cSILLYWFF,conjecture,
( ~ ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) )
=> ~ sP9 ) ).
thf(h0,negated_conjecture,
~ ( ~ ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) )
=> ~ sP9 ),
inference(assume_negation,[status(cth)],[cSILLYWFF]) ).
thf(h1,assumption,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ( eigen__0 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ z ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__0 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ~ ( ~ ( sP2
=> ( eigen__0 @ X1 ) )
=> ~ ( eigen__1 @ X1 ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( sP2
=> sP10 )
=> ~ sP8 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP2
=> sP10 )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP2
=> sP10 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP8,
introduced(assumption,[]) ).
thf(h11,assumption,
sP2,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP7
| sP1
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h6,h5,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,h11,h12,h10,h8,h2]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,8,h11,h12]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,9,h9,h10]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,10,h7,h8]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,11,h6]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,12,h5]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,13,h4]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,14,h3]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,15,h1,h2]) ).
thf(0,theorem,
( ~ ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) )
=> ~ sP9 ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO315^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.31 % Computer : n025.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 03:32:07 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.37 % SZS status Theorem
% 0.16/0.37 % Mode: cade22grackle2xfee4
% 0.16/0.37 % Steps: 84
% 0.16/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------