TSTP Solution File: SEU584^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU584^2 : 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 : n020.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 17:19:07 EDT 2023
% Result : Theorem 20.14s 20.43s
% Output : Proof 20.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ eigen__2 @ X1 )
=> ( ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
=> ( in @ eigen__2 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ( sP2
=> ( in @ eigen__2 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> ( in @ eigen__2 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__2 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] : ( in @ X1 @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) )
=> ( in @ X1 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(def_setunionI,definition,
( setunionI
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X2 @ X3 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ).
thf(def_binunion,definition,
( binunion
= ( ^ [X1: $i,X2: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_upairset2IR,definition,
upairset2IR = sP6 ).
thf(binunionIR,conjecture,
( sP10
=> ( sP6
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP10
=> ( sP6
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binunionIR]) ).
thf(h1,assumption,
sP10,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP6
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ ( setunion @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP1
=> sP7 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP2
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h3,h8,h9]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,8,h8,h9]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,9,h7]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,10,h6]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,11,h5]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,12,h3,h4]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,13,h1,h2]) ).
thf(0,theorem,
( sP10
=> ( sP6
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU584^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31 % Computer : n020.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 23 21:31:15 EDT 2023
% 0.10/0.31 % CPUTime :
% 20.14/20.43 % SZS status Theorem
% 20.14/20.43 % Mode: cade22grackle2x798d
% 20.14/20.43 % Steps: 832
% 20.14/20.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------