TSTP Solution File: PUZ110^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PUZ110^5 : 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 : Thu Aug 31 13:21:54 EDT 2023
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $i > $o ).
thf(ty_c1,type,
c1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( eigen__2 @ X1 @ X2 )
=> ~ ( ( eigen__2 @ ( s @ ( s @ X1 ) ) @ X2 )
=> ~ ( eigen__2 @ ( s @ X1 ) @ ( s @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__2 @ eigen__0 @ X1 )
=> ~ ( ( eigen__2 @ ( s @ ( s @ eigen__0 ) ) @ X1 )
=> ~ ( eigen__2 @ ( s @ eigen__0 ) @ ( s @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__2 @ c1 @ c1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP3
=> ( eigen__2 @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__2 @ ( s @ ( s @ eigen__0 ) ) @ eigen__1 )
=> ~ ( eigen__2 @ ( s @ eigen__0 ) @ ( s @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 @ c1 @ c1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 @ ( s @ ( s @ eigen__0 ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP6
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $i > $o] :
( ~ ( ( X1 @ c1 @ c1 )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( ( X1 @ ( s @ ( s @ X2 ) ) @ X3 )
=> ~ ( X1 @ ( s @ X2 ) @ ( s @ X3 ) ) ) ) )
=> ( X1 @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_cCKB6_BLACK,definition,
( cCKB6_BLACK
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X3 @ c1 @ c1 )
& ! [X4: $i,X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X3 @ X4 @ X5 )
@ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
& ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
@ ( X3 @ X1 @ X2 ) ) ) ) ).
thf(cCKB6_L8000,conjecture,
! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ( X3 @ c1 @ c1 )
=> ~ ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ~ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
=> ~ ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: $i > $i > $o] :
( ~ ( ( X3 @ c1 @ c1 )
=> ~ ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ~ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
=> ~ ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ ( s @ ( s @ X1 ) ) @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ( X3 @ c1 @ c1 )
=> ~ ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ~ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
=> ~ ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: $i > $i > $o] :
( ~ ( ( X3 @ c1 @ c1 )
=> ~ ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ~ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
=> ~ ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ ( s @ ( s @ X1 ) ) @ X2 ) ) ),
inference(assume_negation,[status(cth)],[cCKB6_L8000]) ).
thf(h1,assumption,
~ ! [X1: $i] :
( ! [X2: $i > $i > $o] :
( ~ ( ( X2 @ c1 @ c1 )
=> ~ ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ~ ( ( X2 @ ( s @ ( s @ X3 ) ) @ X4 )
=> ~ ( X2 @ ( s @ X3 ) @ ( s @ X4 ) ) ) ) )
=> ( X2 @ eigen__0 @ X1 ) )
=> ! [X2: $i > $i > $o] :
( ~ ( ( X2 @ c1 @ c1 )
=> ~ ! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
=> ~ ( ( X2 @ ( s @ ( s @ X3 ) ) @ X4 )
=> ~ ( X2 @ ( s @ X3 ) @ ( s @ X4 ) ) ) ) )
=> ( X2 @ ( s @ ( s @ eigen__0 ) ) @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP10
=> ! [X1: $i > $i > $o] :
( ~ ( ( X1 @ c1 @ c1 )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( ( X1 @ ( s @ ( s @ X2 ) ) @ X3 )
=> ~ ( X1 @ ( s @ X2 ) @ ( s @ X3 ) ) ) ) )
=> ( X1 @ ( s @ ( s @ eigen__0 ) ) @ eigen__1 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i > $i > $o] :
( ~ ( ( X1 @ c1 @ c1 )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( ( X1 @ ( s @ ( s @ X2 ) ) @ X3 )
=> ~ ( X1 @ ( s @ X2 ) @ ( s @ X3 ) ) ) ) )
=> ( X1 @ ( s @ ( s @ eigen__0 ) ) @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP3
=> sP8 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| ~ sP7
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP5
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| ~ sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,h3,h8,h9,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,8,h8,h9]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,9,h6,h7]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,10,h5]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,11,h3,h4]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ( X3 @ c1 @ c1 )
=> ~ ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ~ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
=> ~ ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ! [X3: $i > $i > $o] :
( ~ ( ( X3 @ c1 @ c1 )
=> ~ ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ~ ( ( X3 @ ( s @ ( s @ X4 ) ) @ X5 )
=> ~ ( X3 @ ( s @ X4 ) @ ( s @ X5 ) ) ) ) )
=> ( X3 @ ( s @ ( s @ X1 ) ) @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ110^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 22:15:48 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: cade22grackle2xfee4
% 0.12/0.36 % Steps: 145
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------