TSTP Solution File: SYO382^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO382^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Thu Jul 21 19:31:45 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 74
% Syntax : Number of formulae : 108 ( 53 unt; 12 typ; 1 def)
% Number of atoms : 178 ( 1 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 241 ( 108 ~; 18 |; 0 &; 52 @)
% ( 20 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 32 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 17 ( 1 ^ 16 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_cS,type,
cS: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $i > $o ).
thf(ty_eigen__7,type,
eigen__7: $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__5,type,
eigen__5: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cQ,type,
cQ: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( cQ @ X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( cQ @ X1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__11 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
~ ( cQ @ X1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
~ ! [X2: $i] : ( cP @ X2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cS @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ eigen__3 @ eigen__4 )
=> ~ ( cQ @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cS @ eigen__1 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cQ @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cQ @ eigen__11 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP3
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( cS @ X1 )
=> ~ ! [X2: $i] :
~ ( cQ @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( !! @ cS ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cS @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( cP @ eigen__11 @ X1 )
=> ~ ( cQ @ eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( cP @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP6
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] : ( cP @ X1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( cP @ eigen__3 @ X1 )
=> ~ ( cQ @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] : ( cP @ X1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(cTHM407,conjecture,
( ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 )
=> ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 ) ) ).
thf(h1,negated_conjecture,
~ ( ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 )
=> ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 ) ),
inference(assume_negation,[status(cth)],[cTHM407]) ).
thf(h2,assumption,
( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ sP5
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP5,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP13,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ sP5
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h15,assumption,
sP12,
introduced(assumption,[]) ).
thf(h16,assumption,
sP20,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h14,h15,h12,h13,h10,h11,h8,h6,h4,h2,h3,h1,h0])],[1,h8,h16]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__0)],[h14,2,h16]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,3,h14,h15]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,4,h12,h13]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,5,h10,h11]) ).
thf(h17,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h18,assumption,
sP14,
introduced(assumption,[]) ).
thf(h19,assumption,
sP2,
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: $i] : ( cP @ X1 @ eigen__2 ),
introduced(assumption,[]) ).
thf(7,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| ~ sP14
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h14,h15,h12,h13,h10,h11,h18,h19,h17,h9,h6,h4,h2,h3,h1,h0])],[7,8,h18,h19,h15]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h18,h19,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__2)],[h14,9,h20]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h18,h19,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,10,h14,h15]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h18,h19,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,11,h12,h13]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,12,h10,h11]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h9,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,13,h18,h19]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__1)],[h9,14,h17]) ).
thf(16,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h6,6,15,h8,h9]) ).
thf(h21,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h23,assumption,
sP16,
introduced(assumption,[]) ).
thf(h24,assumption,
sP9,
introduced(assumption,[]) ).
thf(h25,assumption,
! [X1: $i] : ( cP @ X1 @ eigen__5 ),
introduced(assumption,[]) ).
thf(17,plain,
( ~ sP1
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP19
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP7
| ~ sP16
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h14,h15,h12,h13,h10,h11,h23,h24,h22,h21,h7,h4,h2,h3,h1,h0])],[17,18,19,h23,h24,h13]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h23,h24,h22,h21,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__5)],[h14,20,h25]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h23,h24,h22,h21,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,21,h14,h15]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h23,h24,h22,h21,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,22,h12,h13]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h22,h21,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,23,h10,h11]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h21,h7,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,24,h23,h24]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__4)],[h21,25,h22]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__3)],[h7,26,h21]) ).
thf(28,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h4,16,27,h6,h7]) ).
thf(h26,assumption,
~ ( cS @ eigen__6 ),
introduced(assumption,[]) ).
thf(h27,assumption,
sP18,
introduced(assumption,[]) ).
thf(29,plain,
( ~ sP18
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP1
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP15
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP11
| ~ sP3
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP4
| sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(34,plain,
( ~ sP17
| ~ sP6
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP12
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h27,h14,h15,h12,h13,h10,h11,h26,h5,h2,h3,h1,h0])],[29,30,31,32,33,34,35,36,h27,h15,h13,h11]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h26,h5,h2,h3,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__7)],[h14,37,h27]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h26,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,38,h14,h15]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h26,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,39,h12,h13]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h3,40,h10,h11]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__6)],[h5,41,h26]) ).
thf(43,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h2,28,42,h4,h5]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,43,h2,h3]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[44,h0]) ).
thf(0,theorem,
( ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 )
=> ( ~ ( ~ ( ~ sP5
=> ~ sP12 )
=> ~ sP1 )
=> ~ sP13 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[44,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO382^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 16:15:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % Mode: mode213
% 0.13/0.40 % Inferences: 150
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------