TSTP Solution File: SYN374^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYN374^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 : 300s
% DateTime : Fri Sep 1 03:20:42 EDT 2023
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 54
% Syntax : Number of formulae : 71 ( 32 unt; 8 typ; 2 def)
% Number of atoms : 138 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 102 ( 42 ~; 20 |; 0 &; 24 @)
% ( 15 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 24 con; 0-2 aty)
% Number of variables : 11 ( 2 ^; 9 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__4 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
( ( cP @ eigen__1 )
!= ( cP @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
~ ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( cP @ eigen__4 )
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cP @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( sP1
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] : ( cP @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( sP3
= ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cP @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP3 = sP1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( cP @ X1 )
= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP1 = sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP3 = sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cX2125,conjecture,
( ~ sP12
= ( ~ sP2 = sP7 ) ) ).
thf(h1,negated_conjecture,
( ~ sP12
!= ( ~ sP2 = sP7 ) ),
inference(assume_negation,[status(cth)],[cX2125]) ).
thf(h2,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h3,assumption,
( ~ sP2 = sP7 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP12,
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ sP2 != sP7 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h8,assumption,
sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
sP2,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| ~ sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h11,h7,h8,h6,h2,h3,h1,h0])],[1,2,3,4,h6,h11,h12]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h8,5,h12]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h7,6,h11]) ).
thf(8,plain,
( ~ sP2
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h6,h2,h3,h1,h0])],[8,9,h9,h10]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h3,7,10,h7,h8,h9,h10]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h2,11,h6]) ).
thf(h13,assumption,
cP @ eigen__3,
introduced(assumption,[]) ).
thf(13,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP13
| ~ sP1
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP6
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(16,plain,
( ~ sP12
| ~ sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP7
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h7,h8,h4,h5,h1,h0])],[13,14,15,16,17,h4,h8]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h4,h5,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h7,18,h13]) ).
thf(h14,assumption,
~ ( cP @ eigen__7 ),
introduced(assumption,[]) ).
thf(20,plain,
( ~ sP2
| ~ sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP15
| sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP4
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(23,plain,
( ~ sP12
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP2
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h9,h10,h4,h5,h1,h0])],[20,21,22,23,24,h4,h9]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h4,h5,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__7)],[h10,25,h14]) ).
thf(27,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h4,h5,h1,h0]),tab_bq(discharge,[h7,h8]),tab_bq(discharge,[h9,h10])],[h5,19,26,h7,h8,h9,h10]) ).
thf(28,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,12,27,h2,h3,h4,h5]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
( ~ sP12
= ( ~ sP2 = sP7 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[28,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN374^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.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 : 300
% 0.13/0.34 % DateTime : Sat Aug 26 17:38:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % Mode: cade22grackle2xfee4
% 0.20/0.44 % Steps: 204
% 0.20/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------