TSTP Solution File: SEV398^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV398^5 : 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 : n024.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 19:34:27 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cF,type,
cF: ( a > $o ) > a > $o ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_cG,type,
cG: ( a > $o ) > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(sP1,plain,
( sP1
<=> ( cF @ ( cG @ ( cF @ eigen__0 ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: a] :
( ( cF @ eigen__0 @ X1 )
=> ( cF @ ( cG @ ( cF @ eigen__0 ) ) @ X1 ) )
=> ~ ! [X1: a] :
( ( cF @ eigen__0 @ X1 )
=> ( cG @ ( cF @ ( cF @ eigen__0 ) ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cF @ eigen__0 @ eigen__1 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( cF @ eigen__0 @ X1 )
=> ( cF @ ( cG @ ( cF @ eigen__0 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( cF @ eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( cF @ ( cG @ ( cF @ eigen__0 ) ) @ X1 )
=> ( cF @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( cF @ ( cG @ eigen__0 ) @ X1 ) )
=> ~ ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( cG @ ( cF @ eigen__0 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( cG @ ( cF @ eigen__0 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> ( cF @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a > $o] :
~ ( ! [X2: a] :
( ( X1 @ X2 )
=> ( cF @ ( cG @ X1 ) @ X2 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( cG @ ( cF @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cF @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( cF @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(cTHM67A_pme,conjecture,
( ~ ( sP13
=> ~ sP10 )
=> ! [X1: a > $o,X2: a] :
( ( cF @ ( cG @ ( cF @ X1 ) ) @ X2 )
= ( cF @ X1 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP13
=> ~ sP10 )
=> ! [X1: a > $o,X2: a] :
( ( cF @ ( cG @ ( cF @ X1 ) ) @ X2 )
= ( cF @ X1 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[cTHM67A_pme]) ).
thf(h1,assumption,
~ ( sP13
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o,X2: a] :
( ( cF @ ( cG @ ( cF @ X1 ) ) @ X2 )
= ( cF @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP13,
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( cF @ ( cG @ ( cF @ eigen__0 ) ) @ X1 )
= ( cF @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP1 != sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP11,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP1
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| ~ sP8
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h3,h4,h7,h8]) ).
thf(9,plain,
( ~ sP3
| ~ sP11
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h6,h5,h3,h4,h1,h2,h0])],[9,10,11,12,h4,h9,h10]) ).
thf(14,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h6,8,13,h7,h8,h9,h10]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,14,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,15,h5]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).
thf(0,theorem,
( ~ ( sP13
=> ~ sP10 )
=> ! [X1: a > $o,X2: a] :
( ( cF @ ( cG @ ( cF @ X1 ) ) @ X2 )
= ( cF @ X1 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV398^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.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 : Thu Aug 24 04:01:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.64 % SZS status Theorem
% 0.19/0.64 % Mode: cade22grackle2xfee4
% 0.19/0.64 % Steps: 2867
% 0.19/0.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------