TSTP Solution File: SEU747^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU747^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -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 : 600s
% DateTime : Tue Jul 19 14:00:46 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_binunion,type,
binunion: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ~ ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ~ ( in @ eigen__3 @ eigen__1 )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__3 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP5
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_binunionE,definition,
binunionE = sP3 ).
thf(binunionTEcontra,conjecture,
( sP3
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binunionTEcontra]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
in @ eigen__1 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( ~ ( in @ X1 @ eigen__2 )
=> ~ ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
in @ eigen__2 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( ~ ( in @ X1 @ eigen__2 )
=> ~ ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( in @ eigen__3 @ eigen__0 )
=> ( ~ sP5
=> ( ~ sP1
=> ~ sP6 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
in @ eigen__3 @ eigen__0,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ sP5
=> ( ~ sP1
=> ~ sP6 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ sP1
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| ~ sP6
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP5
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,h1,h13,h15,h16]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,6,h15,h16]) ).
thf(8,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])],[h12,7,h13,h14]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,8,h11,h12]) ).
thf(10,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)],[h9,9,h10]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,10,h8,h9]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,11,h7]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,12,h5,h6]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,13,h4]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,14,h3]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,15,h1,h2]) ).
thf(0,theorem,
( sP3
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X3 )
=> ~ ( in @ X4 @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU747^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n022.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 : 600
% 0.12/0.34 % DateTime : Mon Jun 20 09:06:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 7
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------