TSTP Solution File: SYN057^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN057^5 : 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 : n009.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 03:19:41 EDT 2023
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cJ,type,
cJ: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cF,type,
cF: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cH,type,
cH: $i > $o ).
thf(ty_cI,type,
cI: $i > $o ).
thf(ty_cG,type,
cG: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cJ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cH @ eigen__0 )
=> ( cG @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cF @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cI @ eigen__1 )
=> ~ ( cH @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cF @ X1 )
=> ( cH @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cG @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ~ ( cI @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP7
=> ( cF @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( cI @ X1 )
=> ~ ( cH @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP3
=> ( cH @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cF @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cH @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ! [X1: $i] :
( ( cH @ X1 )
=> ( cG @ X1 ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cI @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( cH @ X1 )
=> ( cG @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP11
=> ( cH @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( cH @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ~ ( ( cJ @ X1 )
=> ~ ( cI @ X1 ) )
=> ( cF @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cPELL27,conjecture,
( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) )
=> ~ sP5 )
=> ~ sP18 )
=> ~ sP13 )
=> ! [X1: $i] :
( ( cJ @ X1 )
=> ~ ( cI @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) )
=> ~ sP5 )
=> ~ sP18 )
=> ~ sP13 )
=> ! [X1: $i] :
( ( cJ @ X1 )
=> ~ ( cI @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cPELL27]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) )
=> ~ sP5 )
=> ~ sP18 )
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( cJ @ X1 )
=> ~ ( cI @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) )
=> ~ sP5 )
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP13,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP18,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP3
=> sP6 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP3,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| ~ sP3
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP15
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| ~ sP1
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| sP7
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP16
| ~ sP11
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| ~ sP14
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP18
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP5
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP13
| sP15
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h10,h11,h8,h6,h4,h13,h14]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,13,h13,h14]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h2,14,h12]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,15,h10,h11]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h7,16,h9]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,17,h7,h8]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,18,h5,h6]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,19,h3,h4]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) )
=> ~ sP5 )
=> ~ sP18 )
=> ~ sP13 )
=> ! [X1: $i] :
( ( cJ @ X1 )
=> ~ ( cI @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN057^5 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 21:09:20 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % Mode: cade22grackle2xfee4
% 0.12/0.39 % Steps: 40
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------