TSTP Solution File: ALG248^3 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG248^3 : 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 : n011.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 16:33:40 EDT 2023
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% 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 > $o ).
thf(ty_eigen__2,type,
eigen__2: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_eigen__0,type,
eigen__0: term > $o ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_one,type,
one: term ).
thf(ty_eigen__3,type,
eigen__3: subst ).
thf(sP1,plain,
( sP1
<=> ! [X1: term] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__1 @ one )
= ( eigen__0 @ ( sub @ one @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: subst] :
( ( sub @ one @ ( push @ eigen__2 @ X1 ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__2
= ( sub @ one @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 @ one ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ ( sub @ one @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( sub @ one @ ( push @ eigen__2 @ eigen__3 ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(def_axvarcons,definition,
axvarcons = sP9 ).
thf(def_pushprop_p_and_p_prime,definition,
( pushprop_p_and_p_prime
= ( ^ [X1: term,X2: subst,X3: term > $o,X4: term > $o] :
! [X5: term] :
( ( X4 @ X5 )
<=> ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) ).
thf(def_pushprop_lem1v2,definition,
( pushprop_lem1v2
= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
@ ( X2 @ one ) ) ) ) ) ).
thf(def_pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axvarcons
@ pushprop_lem1v2 ) ) ).
thf(thm,conjecture,
( sP9
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( X2 @ one ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP9
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( X2 @ one ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP9,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( X2 @ one ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: term > $o,X2: term,X3: subst] :
( ( eigen__0 @ X2 )
=> ( ! [X4: term] :
( ( X1 @ X4 )
= ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) )
=> ( X1 @ one ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: term,X2: subst] :
( ( eigen__0 @ X1 )
=> ( ! [X3: term] :
( ( eigen__1 @ X3 )
= ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) )
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: subst] :
( sP5
=> ( ! [X2: term] :
( ( eigen__1 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) )
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP5
=> ( sP1
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> sP6 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP7
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP4 ),
inference(symeq,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,h1,h7,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,7,h9,h10]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,8,h7,h8]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,9,h6]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,10,h5]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,11,h4]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,12,h3]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,13,h1,h2]) ).
thf(0,theorem,
( sP9
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( X2 @ one ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG248^3 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.10/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n011.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 : Mon Aug 28 03:13:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % Mode: cade22sinegrackle2x6978
% 0.19/0.41 % Steps: 29
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------