TSTP Solution File: SEU515^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU515^2 : 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 : n015.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 13:52:41 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% 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: $o ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ eigen__1 ) )
= ( ( eigen__2 != eigen__0 )
=> sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= ( ( X3 != X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__0 @ X1 ) )
= ( ( X2 != eigen__0 )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__1 ) )
= ( ( X1 != eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP4
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(def_setadjoinAx,definition,
setadjoinAx = sP3 ).
thf(setadjoinE,conjecture,
( sP3
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP3
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
inference(assume_negation,[status(cth)],[setadjoinE]) ).
thf(h1,assumption,
sP3,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = eigen__0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__1 ) )
=> ! [X2: $o] :
( ( ( X1 = eigen__0 )
=> X2 )
=> ( ( ( in @ X1 @ eigen__1 )
=> X2 )
=> X2 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP8
=> ! [X1: $o] :
( ( sP4
=> X1 )
=> ( ( sP1
=> X1 )
=> X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $o] :
( ( sP4
=> X1 )
=> ( ( sP1
=> X1 )
=> X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( sP4
=> sP5 )
=> ( ( sP1
=> sP5 )
=> sP5 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( sP4
=> sP5 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( sP1
=> sP5 )
=> sP5 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h12,assumption,
sP5,
introduced(assumption,[]) ).
thf(h13,assumption,
( sP1
=> sP5 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP4
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h13,h14,h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[1,2,3,4,5,h1,h6,h11,h15]) ).
thf(7,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h14,h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[h12,h14]) ).
thf(8,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h12])],[h13,6,7,h15,h12]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h10,8,h13,h14]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h13,h14,h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[h12,h14]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h13,h14,h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[h12,h14]) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h12])],[h13,10,11,h15,h12]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h10,12,h13,h14]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,9,13,h11,h12]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,14,h9,h10]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,15,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,16,h6,h7]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,17,h5]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,18,h4]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,19,h3]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).
thf(0,theorem,
( sP3
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU515^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 22:47:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 % Mode: mode213
% 0.19/0.52 % Inferences: 2254
% 0.19/0.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------