TSTP Solution File: ALG256^2 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG256^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 : Wed Aug 30 16:33:43 EDT 2023
% Result : Theorem 20.29s 20.74s
% Output : Proof 20.29s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_eigen__1,type,
eigen__1: term ).
thf(ty_id,type,
id: subst ).
thf(ty_eigen__2,type,
eigen__2: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_eigen__0,type,
eigen__0: term ).
thf(ty_eigen__3,type,
eigen__3: term ).
thf(ty_ap,type,
ap: term > term > term ).
thf(sP1,plain,
( sP1
<=> ( ( ap @ ( sub @ eigen__0 @ id ) @ eigen__2 )
= ( ap @ ( sub @ eigen__1 @ id ) @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( sub @ eigen__1 @ id )
= ( sub @ eigen__0 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: term,X2: term] :
( ( ( ap @ ( sub @ eigen__1 @ id ) @ X1 )
= ( ap @ ( sub @ eigen__0 @ id ) @ X2 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ap @ ( sub @ eigen__1 @ id ) @ eigen__3 )
= ( ap @ ( sub @ eigen__0 @ id ) @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: term] :
( ( ( ap @ ( sub @ eigen__1 @ id ) @ eigen__3 )
= ( ap @ ( sub @ eigen__0 @ id ) @ X1 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: term,X2: term,X3: term] :
( ( ( ap @ ( sub @ eigen__1 @ id ) @ X2 )
= ( ap @ X1 @ X3 ) )
=> ( ( sub @ eigen__1 @ id )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( sub @ ( sub @ eigen__1 @ id ) @ id )
= ( sub @ eigen__1 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( sub @ eigen__1 @ id )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( sub @ eigen__0 @ id )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( sub @ eigen__0 @ id )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP4
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_axvarid,definition,
axvarid = sP13 ).
thf(def_apinj1,definition,
( apinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X4 ) )
@ ( X1 = X2 ) ) ) ) ).
thf(def_hoasap,definition,
( hoasap
= ( ^ [X1: subst,X2: term,X3: subst,X4: term] : ( ap @ ( sub @ X2 @ X3 ) @ X4 ) ) ) ).
thf(def_hoasapinj1,definition,
( hoasapinj1
= ( ! [X1: term,X2: term,X3: term,X4: term] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( hoasap @ id @ X1 @ id @ X3 )
= ( hoasap @ id @ X2 @ id @ X4 ) )
@ ( X1 = X2 ) ) ) ) ).
thf(def_hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axvarid
@ ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ apinj1
@ hoasapinj1 ) ) ) ).
thf(thm,conjecture,
( sP13
=> ( sP9
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP13
=> ( sP9
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP13,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP9
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP9,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: term,X2: term,X3: term] :
( ( ( ap @ ( sub @ eigen__0 @ id ) @ X2 )
= ( ap @ ( sub @ X1 @ id ) @ X3 ) )
=> ( eigen__0 = X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: term,X2: term] :
( ( ( ap @ ( sub @ eigen__0 @ id ) @ X1 )
= ( ap @ ( sub @ eigen__1 @ id ) @ X2 ) )
=> sP10 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: term] :
( ( ( ap @ ( sub @ eigen__0 @ id ) @ eigen__2 )
= ( ap @ ( sub @ eigen__1 @ id ) @ X1 ) )
=> sP10 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP10 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP12
| ~ sP2
| ~ sP8 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP14
| ~ sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP10
| ~ sP11
| ~ sP12 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP1
| sP4 ),
inference(symeq,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1,h3,h9,h10]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,12,h9,h10]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,13,h8]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,15,h6]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,16,h5]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,17,h3,h4]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,18,h1,h2]) ).
thf(0,theorem,
( sP13
=> ( sP9
=> ! [X1: term,X2: term,X3: term,X4: term] :
( ( ( ap @ ( sub @ X1 @ id ) @ X3 )
= ( ap @ ( sub @ X2 @ id ) @ X4 ) )
=> ( X1 = X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG256^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.08/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 02:52:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.29/20.74 % SZS status Theorem
% 20.29/20.74 % Mode: cade22sinegrackle2xfaf3
% 20.29/20.74 % Steps: 4308
% 20.29/20.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------