TSTP Solution File: ALG249^3 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG249^3 : 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 : n026.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 4.75s 4.95s
% Output : Proof 4.75s
% 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_comp,type,
comp: subst > subst > 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 > $o ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_var,type,
var: term > $o ).
thf(ty_eigen__3,type,
eigen__3: subst ).
thf(ty_sh,type,
sh: subst ).
thf(ty_eigen__4,type,
eigen__4: term ).
thf(sP1,plain,
( sP1
<=> ( ( sub @ eigen__4 @ ( comp @ sh @ ( push @ eigen__2 @ eigen__3 ) ) )
= ( sub @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
= ( sub @ X1 @ ( comp @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( comp @ sh @ ( push @ eigen__2 @ eigen__3 ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: term] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__1 @ ( sub @ eigen__4 @ sh ) )
= ( eigen__0 @ ( sub @ ( sub @ eigen__4 @ sh ) @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ ( sub @ ( sub @ eigen__4 @ sh ) @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( sub @ ( sub @ eigen__4 @ sh ) @ ( push @ eigen__2 @ eigen__3 ) )
= ( sub @ eigen__4 @ ( comp @ sh @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: term,X2: subst] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( var @ eigen__4 )
=> ( eigen__0 @ ( sub @ eigen__4 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( var @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 @ ( sub @ eigen__4 @ sh ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: subst,X2: subst] :
( ( sub @ ( sub @ eigen__4 @ X1 ) @ X2 )
= ( sub @ eigen__4 @ ( comp @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> $false ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( sub @ eigen__4 @ ( comp @ sh @ ( push @ eigen__2 @ eigen__3 ) ) )
= ( sub @ ( sub @ eigen__4 @ sh ) @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: subst] :
( ( sub @ ( sub @ eigen__4 @ sh ) @ X1 )
= ( sub @ eigen__4 @ ( comp @ sh @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ ( sub @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: subst] :
( ( comp @ sh @ ( push @ eigen__2 @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( sub @ eigen__4 @ eigen__3 )
= ( sub @ ( sub @ eigen__4 @ sh ) @ ( push @ eigen__2 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_axclos,definition,
axclos = sP2 ).
thf(def_axshiftcons,definition,
axshiftcons = sP8 ).
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_lem2v2,definition,
( pushprop_lem2v2
= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ! [X5: term] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( var @ X5 )
@ ( X1 @ ( sub @ X5 @ X4 ) ) )
@ ! [X5: term] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( var @ X5 )
@ ( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X2 @ X5 )
@ ( X2 @ ( sub @ X5 @ sh ) ) ) ) ) ) ) ) ).
thf(def_pushprop_lem2v2_lthm,definition,
( pushprop_lem2v2_lthm
= ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axclos
@ ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axshiftcons
@ pushprop_lem2v2 ) ) ) ).
thf(thm,conjecture,
( sP2
=> ( sP8
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ X4 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X2 @ X5 )
=> ( X2 @ ( sub @ X5 @ sh ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> ( sP8
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ X4 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X2 @ X5 )
=> ( X2 @ ( sub @ X5 @ sh ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP8
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ X4 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X2 @ X5 )
=> ( X2 @ ( sub @ X5 @ sh ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP8,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ X4 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X2 @ X5 )
=> ( X2 @ ( sub @ X5 @ sh ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( X1 @ X4 )
= ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( eigen__0 @ ( sub @ X4 @ X3 ) ) )
=> ! [X4: term] :
( ( var @ X4 )
=> ( ( X1 @ X4 )
=> ( X1 @ ( sub @ X4 @ sh ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: term,X2: subst] :
( ! [X3: term] :
( ( eigen__1 @ X3 )
= ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) )
=> ( ! [X3: term] :
( ( var @ X3 )
=> ( eigen__0 @ ( sub @ X3 @ X2 ) ) )
=> ! [X3: term] :
( ( var @ X3 )
=> ( ( eigen__1 @ X3 )
=> ( eigen__1 @ ( sub @ X3 @ sh ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: subst] :
( ! [X2: term] :
( ( eigen__1 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( eigen__0 @ ( sub @ X2 @ X1 ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( ( eigen__1 @ X2 )
=> ( eigen__1 @ ( sub @ X2 @ sh ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP4
=> ( sP19
=> ! [X1: term] :
( ( var @ X1 )
=> ( ( eigen__1 @ X1 )
=> ( eigen__1 @ ( sub @ X1 @ sh ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP4,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP19
=> ! [X1: term] :
( ( var @ X1 )
=> ( ( eigen__1 @ X1 )
=> ( eigen__1 @ ( sub @ X1 @ sh ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP19,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: term] :
( ( var @ X1 )
=> ( ( eigen__1 @ X1 )
=> ( eigen__1 @ ( sub @ X1 @ sh ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP10
=> ( ( eigen__1 @ eigen__4 )
=> sP11 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP10,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ( eigen__1 @ eigen__4 )
=> sP11 ),
introduced(assumption,[]) ).
thf(h16,assumption,
eigen__1 @ eigen__4,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( sP1
| ~ sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP18
| ~ sP1
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP14 ),
inference(symeq,[status(thm)],]) ).
thf(4,plain,
( ~ sP15
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP16
| sP6
| ~ sP18 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP11
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
~ sP13,
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP12
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| ~ sP10
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP19
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP2
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1,h3,h9,h11,h14,h17]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h10,h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,15,h16,h17]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,16,h14,h15]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,17,h13]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,18,h11,h12]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,19,h9,h10]) ).
thf(21,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)],[h7,20,h8]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,21,h7]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,22,h6]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,23,h5]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,24,h3,h4]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,25,h1,h2]) ).
thf(0,theorem,
( sP2
=> ( sP8
=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ X4 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X2 @ X5 )
=> ( X2 @ ( sub @ X5 @ sh ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG249^3 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:07:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.75/4.95 % SZS status Theorem
% 4.75/4.95 % Mode: cade22sinegrackle2x6978
% 4.75/4.95 % Steps: 68121
% 4.75/4.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------