TSTP Solution File: ALG001^5 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG001^5 : 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 : n022.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 16:32:54 EDT 2023
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_b,type,
b: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__3,type,
eigen__3: b > b > b ).
thf(ty_eigen__6,type,
eigen__6: g ).
thf(ty_eigen__1,type,
eigen__1: b > a ).
thf(ty_eigen__2,type,
eigen__2: g > g > g ).
thf(ty_eigen__5,type,
eigen__5: g ).
thf(ty_eigen__4,type,
eigen__4: a > a > a ).
thf(ty_eigen__0,type,
eigen__0: g > b ).
thf(sP1,plain,
( sP1
<=> ! [X1: b,X2: b] :
( ( eigen__1 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__4 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
( ( eigen__1 @ ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ X1 ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) )
= ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) )
= ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: g,X2: g] :
( ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) )
= ( eigen__3 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__1 @ ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) ) )
= ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__1 @ ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ eigen__6 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: g] :
( ( eigen__0 @ ( eigen__2 @ eigen__5 @ X1 ) )
= ( eigen__3 @ ( eigen__0 @ eigen__5 ) @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cTHM133_pme,conjecture,
! [X1: g > b,X2: b > a,X3: g > g > g,X4: b > b > b,X5: a > a > a] :
( ~ ( ! [X6: g,X7: g] :
( ( X1 @ ( X3 @ X6 @ X7 ) )
= ( X4 @ ( X1 @ X6 ) @ ( X1 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ( X2 @ ( X4 @ X6 @ X7 ) )
= ( X5 @ ( X2 @ X6 ) @ ( X2 @ X7 ) ) ) )
=> ! [X6: g,X7: g] :
( ( X2 @ ( X1 @ ( X3 @ X6 @ X7 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X7 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: g > b,X2: b > a,X3: g > g > g,X4: b > b > b,X5: a > a > a] :
( ~ ( ! [X6: g,X7: g] :
( ( X1 @ ( X3 @ X6 @ X7 ) )
= ( X4 @ ( X1 @ X6 ) @ ( X1 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ( X2 @ ( X4 @ X6 @ X7 ) )
= ( X5 @ ( X2 @ X6 ) @ ( X2 @ X7 ) ) ) )
=> ! [X6: g,X7: g] :
( ( X2 @ ( X1 @ ( X3 @ X6 @ X7 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X7 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM133_pme]) ).
thf(h1,assumption,
~ ! [X1: b > a,X2: g > g > g,X3: b > b > b,X4: a > a > a] :
( ~ ( ! [X5: g,X6: g] :
( ( eigen__0 @ ( X2 @ X5 @ X6 ) )
= ( X3 @ ( eigen__0 @ X5 ) @ ( eigen__0 @ X6 ) ) )
=> ~ ! [X5: b,X6: b] :
( ( X1 @ ( X3 @ X5 @ X6 ) )
= ( X4 @ ( X1 @ X5 ) @ ( X1 @ X6 ) ) ) )
=> ! [X5: g,X6: g] :
( ( X1 @ ( eigen__0 @ ( X2 @ X5 @ X6 ) ) )
= ( X4 @ ( X1 @ ( eigen__0 @ X5 ) ) @ ( X1 @ ( eigen__0 @ X6 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: g > g > g,X2: b > b > b,X3: a > a > a] :
( ~ ( ! [X4: g,X5: g] :
( ( eigen__0 @ ( X1 @ X4 @ X5 ) )
= ( X2 @ ( eigen__0 @ X4 ) @ ( eigen__0 @ X5 ) ) )
=> ~ ! [X4: b,X5: b] :
( ( eigen__1 @ ( X2 @ X4 @ X5 ) )
= ( X3 @ ( eigen__1 @ X4 ) @ ( eigen__1 @ X5 ) ) ) )
=> ! [X4: g,X5: g] :
( ( eigen__1 @ ( eigen__0 @ ( X1 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: b > b > b,X2: a > a > a] :
( ~ ( ! [X3: g,X4: g] :
( ( eigen__0 @ ( eigen__2 @ X3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X3 ) @ ( eigen__0 @ X4 ) ) )
=> ~ ! [X3: b,X4: b] :
( ( eigen__1 @ ( X1 @ X3 @ X4 ) )
= ( X2 @ ( eigen__1 @ X3 ) @ ( eigen__1 @ X4 ) ) ) )
=> ! [X3: g,X4: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a > a > a] :
( ~ ( sP6
=> ~ ! [X2: b,X3: b] :
( ( eigen__1 @ ( eigen__3 @ X2 @ X3 ) )
= ( X1 @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) )
=> ! [X2: g,X3: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( sP6
=> ~ sP1 )
=> ! [X1: g,X2: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP6
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: g,X2: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ X1 @ X2 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: g] :
( ( eigen__1 @ ( eigen__0 @ ( eigen__2 @ eigen__5 @ X1 ) ) )
= ( eigen__4 @ ( eigen__1 @ ( eigen__0 @ eigen__5 ) ) @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP4
| ~ sP5
| sP3 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| sP7
| ~ sP8
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(4,plain,
~ sP3,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,h8,h9,h11]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__6)],[h10,9,h11]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__5)],[h7,10,h10]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,11,h8,h9]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,12,h6,h7]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__4)],[h4,13,h5]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,14,h4]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,15,h3]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,16,h2]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,17,h1]) ).
thf(0,theorem,
! [X1: g > b,X2: b > a,X3: g > g > g,X4: b > b > b,X5: a > a > a] :
( ~ ( ! [X6: g,X7: g] :
( ( X1 @ ( X3 @ X6 @ X7 ) )
= ( X4 @ ( X1 @ X6 ) @ ( X1 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ( X2 @ ( X4 @ X6 @ X7 ) )
= ( X5 @ ( X2 @ X6 ) @ ( X2 @ X7 ) ) ) )
=> ! [X6: g,X7: g] :
( ( X2 @ ( X1 @ ( X3 @ X6 @ X7 ) ) )
= ( X5 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X7 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG001^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n022.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 04:51:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % Mode: cade22grackle2xfee4
% 0.20/0.46 % Steps: 1399
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------