TSTP Solution File: SEU527^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU527^2 : 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 : n029.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 13:52:50 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 = eigen__1 )
=> ~ ! [X1: $o] :
( ( ( eigen__0 = eigen__1 )
=> X1 )
=> ( ( ( in @ eigen__0 @ emptyset )
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( in @ eigen__0 @ emptyset )
=> ~ ! [X1: $o] :
( ( ( eigen__0 = eigen__1 )
=> X1 )
=> ( ( ( in @ eigen__0 @ emptyset )
=> X1 )
=> X1 ) ) )
=> ~ ! [X1: $o] :
( ( ( eigen__0 = eigen__1 )
=> X1 )
=> ( ( ( in @ eigen__0 @ emptyset )
=> X1 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( in @ eigen__0 @ emptyset )
=> ! [X1: $o] : X1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP2
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o] : X1 ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( in @ X1 @ ( setadjoin @ eigen__1 @ emptyset ) )
=> ! [X2: $o] :
( ( ( X1 = eigen__1 )
=> X2 )
=> ( ( ( in @ X1 @ emptyset )
=> X2 )
=> X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o] :
( ( ( eigen__0 = eigen__1 )
=> X1 )
=> ( ( ( in @ eigen__0 @ emptyset )
=> X1 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__0 @ emptyset )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ eigen__1 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = eigen__1 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( in @ eigen__0 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(def_emptysetE,definition,
emptysetE = sP14 ).
thf(def_setadjoinE,definition,
setadjoinE = sP10 ).
thf(uniqinunit,conjecture,
( sP14
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP14
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[uniqinunit]) ).
thf(h1,assumption,
sP14,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i] :
( ( in @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( eigen__0 = X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| ~ sP15
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP9
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| ~ sP2
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP9
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP12
| ~ sP1
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1,h3,h7,h8]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,13,h7,h8]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,14,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,15,h5]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,16,h3,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2]) ).
thf(0,theorem,
( sP14
=> ( sP10
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU527^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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 18:58:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % Mode: mode213
% 0.12/0.37 % Inferences: 54
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------