TSTP Solution File: SEU708^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU708^2 : 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 : n032.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 13:58:11 EDT 2022
% Result : Theorem 0.15s 0.37s
% Output : Proof 0.15s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_singleton,type,
singleton: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( ~ sP1
=> ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( sP1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X1 != eigen__3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( singleton
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( singleton @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( setunion @ X1 )
= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( singleton
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( sP1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( in @ eigen__3 @ eigen__0 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ sP1
=> ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP1
=> ( X3 != X1 ) )
=> ~ ( ~ sP1
=> ( X3 != X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP1
=> ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( sP1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X1 != eigen__3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( singleton
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP1
=> ( X3 != X1 ) )
=> ~ ( ~ sP1
=> ( X3 != X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( singleton
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ sP1
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != X1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( sP1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != eigen__3 ) ) ) ) )
=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != eigen__3 ) ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP15
=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( sP1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X1 != eigen__3 ) ) ) ) )
= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( sP1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X1 != eigen__3 ) ) ) ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( in @ eigen__2 @ eigen__0 )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP6
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ sP1
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(def_iffalseProp1,definition,
iffalseProp1 = sP2 ).
thf(def_ifSingleton,definition,
ifSingleton = sP7 ).
thf(def_if,definition,
( if
= ( ^ [X1: $i,X2: $o,X3: $i,X4: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ).
thf(def_theeq,definition,
theeq = sP5 ).
thf(iffalse,conjecture,
( sP2
=> ( sP7
=> ( sP5
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
= X4 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> ( sP7
=> ( sP5
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
= X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[iffalse]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP7
=> ( sP5
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
= X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP5
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
= X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP5,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
= X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ X1
=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
= X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ sP1
=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP1
=> ( X3 != X1 ) )
=> ~ ( ~ sP1
=> ( X3 != X2 ) ) ) ) )
= X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP21
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ sP1
=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != X1 ) ) ) ) )
= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP21,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ sP1
=> ( ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP1
=> ( X2 != X1 ) ) ) ) )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP17
=> ( ~ sP1
=> sP19 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP17,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ sP1
=> sP19 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP20
| ~ sP21
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| ~ sP17
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP23
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| ~ sP17
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP1
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP14
| ~ sP21
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP22
| ~ sP6
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP18
| ~ sP15
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h1,h3,h5,h10,h13,h15,h16]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,18,h15,h16]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,19,h13,h14]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,20,h12]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,21,h10,h11]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,22,h9]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,23,h8]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,24,h7]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,25,h5,h6]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,26,h3,h4]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,27,h1,h2]) ).
thf(0,theorem,
( sP2
=> ( sP7
=> ( sP5
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
= X4 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU708^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Sun Jun 19 16:53:03 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.37 % SZS status Theorem
% 0.15/0.37 % Mode: mode213
% 0.15/0.37 % Inferences: 14
% 0.15/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------