TSTP Solution File: SEU776^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU776^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 17:29:02 EDT 2023
% Result : Theorem 20.93s 21.16s
% Output : Proof 20.93s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ ( kpair @ eigen__2 @ eigen__3 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ( sP1
=> ( in @ ( kpair @ eigen__3 @ eigen__2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X1: $i,X2: $i] : ( in @ ( kpair @ X2 @ X1 ) @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( X3 @ X4 @ X5 )
=> ( in @ ( kpair @ X4 @ X5 ) @ ( dpsetconstr @ X1 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ eigen__3 ) @ eigen__1 )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ eigen__3 ) @ eigen__1 )
=> ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X2 @ X3 @ X4 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( dpsetconstr @ eigen__0 @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ ( kpair @ eigen__3 @ eigen__2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X1: $i,X2: $i] : ( in @ ( kpair @ X2 @ X1 ) @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( X1 @ X2 @ X3 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( dpsetconstr @ eigen__0 @ eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X1 ) @ eigen__1 )
=> ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] : ( in @ ( kpair @ X4 @ X3 ) @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_breln,definition,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).
thf(def_dpsetconstrI,definition,
( dpsetconstrI
= ( ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X2 )
@ ( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( X3 @ X4 @ X5 )
@ ( in @ ( kpair @ X4 @ X5 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X6: $i,X7: $i] : ( X3 @ X6 @ X7 ) ) ) ) ) ) ) ) ).
thf(def_breln1,definition,
( breln1
= ( ^ [X1: $i,X2: $i] : ( breln @ X1 @ X1 @ X2 ) ) ) ).
thf(def_breln1invset,definition,
( breln1invset
= ( ^ [X1: $i,X2: $i] :
( dpsetconstr @ X1 @ X1
@ ^ [X3: $i,X4: $i] : ( in @ ( kpair @ X4 @ X3 ) @ X2 ) ) ) ) ).
thf(breln1invI,conjecture,
( sP3
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X3 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] : ( in @ ( kpair @ X6 @ X5 ) @ X2 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X3 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] : ( in @ ( kpair @ X6 @ X5 ) @ X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1invI]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X3 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] : ( in @ ( kpair @ X6 @ X5 ) @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( subset @ X1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ ( kpair @ X2 @ X3 ) @ X1 )
=> ( in @ ( kpair @ X3 @ X2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X4: $i,X5: $i] : ( in @ ( kpair @ X5 @ X4 ) @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
=> ( in @ ( kpair @ X2 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] : ( in @ ( kpair @ X4 @ X3 ) @ eigen__1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
subset @ eigen__1 @ ( cartprod @ eigen__0 @ eigen__0 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ eigen__1 )
=> ( in @ ( kpair @ X2 @ X1 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X3: $i,X4: $i] : ( in @ ( kpair @ X4 @ X3 ) @ eigen__1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP12
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__2 @ X1 ) @ eigen__1 )
=> ( in @ ( kpair @ X1 @ eigen__2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ eigen__1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP12,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ ( kpair @ eigen__2 @ X1 ) @ eigen__1 )
=> ( in @ ( kpair @ X1 @ eigen__2 )
@ ( dpsetconstr @ eigen__0 @ eigen__0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ eigen__1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP7
=> sP9 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP7,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP12
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| ~ sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,h1,h8,h11,h13,h14]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,9,h13,h14]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,10,h11,h12]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,11,h10]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,12,h8,h9]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,13,h7]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,14,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,15,h4]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,16,h3]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).
thf(0,theorem,
( sP3
=> ! [X1: $i,X2: $i] :
( ( subset @ X2 @ ( cartprod @ X1 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X3 )
@ ( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] : ( in @ ( kpair @ X6 @ X5 ) @ X2 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU776^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n025.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 : Wed Aug 23 12:58:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 20.93/21.16 % SZS status Theorem
% 20.93/21.16 % Mode: cade22grackle2x798d
% 20.93/21.16 % Steps: 24509
% 20.93/21.16 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------