TSTP Solution File: SYO315^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO315^5 : 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 : 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 : Thu Jul 21 19:31:24 EDT 2022
% Result : Theorem 1.97s 2.29s
% Output : Proof 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 40
% Syntax : Number of formulae : 49 ( 14 unt; 5 typ; 4 def)
% Number of atoms : 117 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 231 ( 79 ~; 19 |; 0 &; 69 @)
% ( 16 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 34 ( 4 ^ 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_z,type,
z: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( eigen__0 @ eigen__2 )
=> ( eigen__0 @ X1 ) )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: $i > $o] :
~ ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ( eigen__0 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__0 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> ( eigen__1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ( eigen__0 @ eigen__2 )
=> ( eigen__0 @ eigen__3 ) )
=> ~ ( eigen__1 @ eigen__3 ) )
=> ( eigen__1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ~ ( eigen__1 @ z )
=> ~ ( eigen__1 @ eigen__3 ) )
=> ( eigen__1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__0 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> ( eigen__1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( eigen__1 @ z )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__1 @ z ) )
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( eigen__1 @ z )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ~ ( ~ ( ( eigen__0 @ eigen__2 )
=> ( eigen__0 @ X1 ) )
=> ~ ( eigen__1 @ X1 ) )
=> ( eigen__1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 @ z ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( X2 @ z )
=> ~ ( X2 @ X4 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP1
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( eigen__0 @ eigen__2 )
=> ( eigen__0 @ eigen__3 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( X1 @ z )
=> ~ ( X1 @ X3 ) )
=> ( eigen__1 @ X2 ) )
=> ~ ( eigen__1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ( eigen__0 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP9
=> ~ ( eigen__1 @ X2 ) )
=> ( eigen__1 @ X1 ) )
=> ~ ( eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP3
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cSILLYWFF,conjecture,
sP11 ).
thf(h2,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[cSILLYWFF]) ).
thf(1,plain,
( ~ sP6
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP12
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP2
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP8
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(12,plain,
( sP5
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(13,plain,
( sP14
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(14,plain,
( sP1
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(15,plain,
( sP11
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP11
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[17,h1]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h2])],[17,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO315^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Fri Jul 8 22:40:06 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.97/2.29 % SZS status Theorem
% 1.97/2.29 % Mode: mode506
% 1.97/2.29 % Inferences: 57972
% 1.97/2.29 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------