TSTP Solution File: SEU746^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU746^2 : 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 14:00:40 EDT 2022
% Result : Theorem 0.12s 0.35s
% 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__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $o ).
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__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ~ ( in @ eigen__4 @ eigen__1 )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( in @ eigen__4 @ eigen__1 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ~ ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ( ~ ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ~ ( in @ X2 @ eigen__1 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( in @ eigen__4 @ ( binunion @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(def_binunionE,definition,
binunionE = sP7 ).
thf(binunionTE,conjecture,
( sP7
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP7
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binunionTE]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ eigen__0 ) )
=> ! [X3: $o,X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ( ( in @ X4 @ ( binunion @ X1 @ X2 ) )
=> ( ( ( in @ X4 @ X1 )
=> X3 )
=> ( ( ( in @ X4 @ X2 )
=> X3 )
=> X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
=> ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ( ( in @ X3 @ eigen__1 )
=> X2 )
=> ( ( ( in @ X3 @ X1 )
=> X2 )
=> X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
in @ eigen__1 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( powerset @ eigen__0 ) )
=> ! [X2: $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ( in @ X3 @ ( binunion @ eigen__1 @ X1 ) )
=> ( ( ( in @ X3 @ eigen__1 )
=> X2 )
=> ( ( ( in @ X3 @ X1 )
=> X2 )
=> X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( in @ eigen__2 @ ( powerset @ eigen__0 ) )
=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X2 @ eigen__1 )
=> X1 )
=> ( ( ( in @ X2 @ eigen__2 )
=> X1 )
=> X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
in @ eigen__2 @ ( powerset @ eigen__0 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( in @ X2 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X2 @ eigen__1 )
=> X1 )
=> ( ( ( in @ X2 @ eigen__2 )
=> X1 )
=> X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( in @ X1 @ ( binunion @ eigen__1 @ eigen__2 ) )
=> ( ( ( in @ X1 @ eigen__1 )
=> sP6 )
=> ( ( ( in @ X1 @ eigen__2 )
=> sP6 )
=> sP6 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ( in @ eigen__4 @ eigen__0 )
=> ( sP9
=> ( ( sP5
=> sP6 )
=> ( ( sP1
=> sP6 )
=> sP6 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
in @ eigen__4 @ eigen__0,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP9
=> ( ( sP5
=> sP6 )
=> ( ( sP1
=> sP6 )
=> sP6 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP9,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ( sP5
=> sP6 )
=> ( ( sP1
=> sP6 )
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
( sP5
=> sP6 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ( sP1
=> sP6 )
=> sP6 ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h19,assumption,
sP6,
introduced(assumption,[]) ).
thf(h20,assumption,
( sP1
=> sP6 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP5
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h20,h21,h18,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,h1,h14,h18,h22]) ).
thf(7,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h19,h20,h21,h18,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[h19,h21]) ).
thf(8,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h21,h18,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h19])],[h20,6,7,h22,h19]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h17,8,h20,h21]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h22,h20,h21,h19,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[h19,h21]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h19,h20,h21,h19,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0])],[h19,h21]) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h21,h19,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_imp(discharge,[h22]),tab_imp(discharge,[h19])],[h20,10,11,h22,h19]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h17,12,h20,h21]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h19])],[h16,9,13,h18,h19]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,14,h16,h17]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,15,h14,h15]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,16,h12,h13]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h10,17,h11]) ).
thf(19,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)],[h9,18,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,19,h8,h9]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,20,h7]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,21,h5,h6]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,22,h4]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,23,h3]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,24,h1,h2]) ).
thf(0,theorem,
( sP7
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ X5 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X5 @ X2 )
=> X4 )
=> ( ( ( in @ X5 @ X3 )
=> X4 )
=> X4 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU746^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 12:01:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 8
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------