TSTP Solution File: ALG254^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG254^2 : 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 : 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 : Wed Aug 30 16:33:42 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_eigen__1,type,
eigen__1: subst ).
thf(ty_id,type,
id: subst ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(ty_eigen__2,type,
eigen__2: subst ).
thf(ty_eigen__0,type,
eigen__0: subst ).
thf(ty_eigen__3,type,
eigen__3: subst ).
thf(ty_eigen__4,type,
eigen__4: subst ).
thf(sP1,plain,
( sP1
<=> ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( comp @ ( comp @ eigen__2 @ eigen__3 ) @ eigen__4 )
= ( comp @ eigen__2 @ ( comp @ eigen__3 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: subst] :
( ( comp @ ( comp @ eigen__2 @ eigen__3 ) @ X1 )
= ( comp @ eigen__2 @ ( comp @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: subst,X2: subst] :
( ( comp @ ( comp @ eigen__2 @ X1 ) @ X2 )
= ( comp @ eigen__2 @ ( comp @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( comp @ eigen__0 @ id )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( comp @ id @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_axidl,definition,
axidl = sP8 ).
thf(def_axassoc,definition,
axassoc = sP5 ).
thf(def_axidr,definition,
axidr = sP1 ).
thf(def_substmonoid,definition,
( substmonoid
= ( sP5
& sP8
& sP1 ) ) ).
thf(def_substmonoid_lthm,definition,
( substmonoid_lthm
= ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axidl
@ ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axassoc
@ ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axidr
@ substmonoid ) ) ) ) ).
thf(thm,conjecture,
( sP8
=> ( sP5
=> ( sP1
=> ~ ( ~ ( sP5
=> ~ sP8 )
=> ~ sP1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP8
=> ( sP5
=> ( sP1
=> ~ ( ~ ( sP5
=> ~ sP8 )
=> ~ sP1 ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP8,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ( sP1
=> ~ ( ~ ( sP5
=> ~ sP8 )
=> ~ sP1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP1
=> ~ ( ~ ( sP5
=> ~ sP8 )
=> ~ sP1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( sP5
=> ~ sP8 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
( sP5
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h12,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,h3,h13]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,4,h13]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,5,h12]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,6,h11]) ).
thf(h14,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(8,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h10,h7,h5,h6,h3,h4,h1,h2,h0])],[8,h1,h14]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h10,9,h14]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h7,7,10,h9,h10]) ).
thf(h15,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(12,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h8,h5,h6,h3,h4,h1,h2,h0])],[12,h5,h15]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__0)],[h8,13,h15]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,11,14,h7,h8]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,16,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,
( sP8
=> ( sP5
=> ( sP1
=> ~ ( ~ ( sP5
=> ~ sP8 )
=> ~ sP1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : ALG254^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.08/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 03:24:05 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22sinegrackle2x6978
% 0.19/0.43 % Steps: 203
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------