TSTP Solution File: SEV429^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV429^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 18:06:22 EDT 2022
% Result : Timeout 292.95s 292.96s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 32
% Syntax : Number of formulae : 37 ( 10 unt; 2 typ; 1 def)
% Number of atoms : 79 ( 29 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 95 ( 19 ~; 13 |; 0 &; 42 @)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 17 con; 0-2 aty)
% Number of variables : 22 ( 1 ^ 12 !; 0 ?; 22 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_f,type,
f: $i > $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] :
( ( @+[X2: $i] :
( ( f @ X1 )
= ( f @ X2 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ( f @ X1 )
= ( f @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( f @ eigen__8 )
!= ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( @+[X1: $i] :
( ( f @ eigen__8 )
= ( f @ X1 ) ) )
= eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( ( f
@ @+[X2: $i] :
( ( f @ eigen__8 )
= ( f @ X2 ) ) )
= ( f @ X1 ) )
=> ( ( @+[X2: $i] :
( ( f @ eigen__8 )
= ( f @ X2 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( @+[X2: $i] :
( ( f @ X1 )
= ( f @ X2 ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ( f
@ @+[X1: $i] :
( ( f @ eigen__8 )
= ( f @ X1 ) ) )
= ( f @ eigen__8 ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( f
@ @+[X1: $i] :
( ( f @ eigen__8 )
= ( f @ X1 ) ) )
= ( f @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( ( f @ eigen__8 )
= X1 )
=> ( X1
= ( f @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__8 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ( f @ eigen__8 )
= ( f
@ @+[X1: $i] :
( ( f @ eigen__8 )
= ( f @ X1 ) ) ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $i] :
~ ! [X2: $i] :
( ( X1 @ ( f @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( f @ eigen__8 )
= ( f @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( f @ eigen__8 )
= ( f
@ @+[X1: $i] :
( ( f @ eigen__8 )
= ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(invexists,conjecture,
~ sP12 ).
thf(h1,negated_conjecture,
sP12,
inference(assume_negation,[status(cth)],[invexists]) ).
thf(1,plain,
( ~ sP6
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP13
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| ~ sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| ~ sP14
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP14
| sP2 ),
inference(choice_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( sP5
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(12,plain,
sP10,
inference(eq_sym,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(finj,axiom,
sP1 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,finj,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
~ sP12,
inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV429^1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n019.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 : Tue Jun 28 08:42:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 292.95/292.96 % SZS status Theorem
% 292.95/292.96 % Mode: mode469
% 292.95/292.96 % Inferences: 22250
% 292.95/292.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------