TSTP Solution File: SEV290^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV290^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 18:05:44 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 19 ( 10 unt; 2 typ; 3 def)
% Number of atoms : 39 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 121 ( 43 ~; 3 |; 0 &; 41 @)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 34 ( 14 ^ 20 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: ( $i > $o ) > $o ).
thf(ty_c0,type,
c0: ( $i > $o ) > $o ).
thf(h0,assumption,
! [X1: ( ( $i > $o ) > $o ) > $o,X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: ( $i > $o ) > $o] :
~ ( $false
=> ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ X1 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( $i > $o ) > $o] :
( $false
=> ! [X2: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X2 @ X1 )
=> ~ ! [X3: ( $i > $o ) > $o] :
( ( X2 @ X3 )
=> ( X2
@ ^ [X4: $i > $o] :
~ ! [X5: $i] :
( ( X4 @ X5 )
=> ~ ( X3
@ ^ [X6: $i] :
~ ( ( X6 != X5 )
=> ~ ( X4 @ X6 ) ) ) ) ) ) )
=> ( X2 @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( $false
=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X1 @ eigen__0 )
=> ~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1
@ ^ [X3: $i > $o] :
~ ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ( X2
@ ^ [X5: $i] :
~ ( ( X5 != X4 )
=> ~ ( X3 @ X5 ) ) ) ) ) ) )
=> ( X1 @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( ( $i > $o ) > $o ) > $o] :
~ ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3 @ X2 )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i > $o] :
~ ! [X6: $i] :
( ( X5 @ X6 )
=> ~ ( X4
@ ^ [X7: $i] :
~ ( ( X7 != X6 )
=> ~ ( X5 @ X7 ) ) ) ) ) ) )
=> ( X3 @ c0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(def_cSUCC,definition,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ( X1
@ ^ [X4: $i] :
~ ( ( X4 != X3 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ).
thf(def_c_less__eq_,definition,
( c_less__eq_
= ( ^ [X1: ( $i > $o ) > $o,X2: ( $i > $o ) > $o] :
! [X3: ( ( $i > $o ) > $o ) > $o] :
( ~ ( ( X3 @ X1 )
=> ~ ! [X4: ( $i > $o ) > $o] :
( ( X3 @ X4 )
=> ( X3 @ ( cSUCC @ X4 ) ) ) )
=> ( X3 @ X2 ) ) ) ) ).
thf(cBLEDSOE1,conjecture,
~ sP3 ).
thf(h1,negated_conjecture,
sP3,
inference(assume_negation,[status(cth)],[cBLEDSOE1]) ).
thf(1,plain,
~ sP4,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP1
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(4,plain,
( ~ sP3
| ~ sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h1]) ).
thf(6,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[5,h0]) ).
thf(0,theorem,
~ sP3,
inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV290^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.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 : Mon Jun 20 14:24:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % Mode: mode213
% 0.20/0.37 % Inferences: 47
% 0.20/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------