TSTP Solution File: SEV311^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV311^5 : 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 : n006.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 18:05:50 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 42
% Syntax : Number of formulae : 52 ( 14 unt; 5 typ; 1 def)
% Number of atoms : 115 ( 1 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 245 ( 22 ~; 16 |; 0 &; 126 @)
% ( 15 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 19 con; 0-2 aty)
% Number of variables : 67 ( 10 ^ 57 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_cF,type,
cF: ( a > $o ) > a > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a] :
~ ( ! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: a > $o] :
( ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__2 ) )
=> ( eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( cF @ eigen__1 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cF @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
=> ( eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3
=> ! [X1: a] :
( ( cF
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ( cF @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cF
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__0 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cF
@ ^ [X1: a] :
! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( cF
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ( cF @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a > $o] :
( ! [X2: a] :
( ! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
=> ( X1 @ X2 ) )
=> ! [X2: a] :
( ( cF
@ ^ [X3: a] :
! [X4: a > $o] :
( ! [X5: a] :
( ( cF @ X4 @ X5 )
=> ( X4 @ X5 ) )
=> ( X4 @ X3 ) )
@ X2 )
=> ( cF @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cF @ X1 @ X3 )
=> ( cF @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM521_pme,conjecture,
( sP15
=> ! [X1: a] :
( ( cF
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP15
=> ! [X1: a] :
( ( cF
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM521_pme]) ).
thf(h2,assumption,
sP15,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a] :
( ( cF
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP11
=> ! [X1: a > $o] :
( ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP11,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: a > $o] :
( ! [X2: a] :
( ( cF @ X1 @ X2 )
=> ( X1 @ X2 ) )
=> ( X1 @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP2
=> sP12 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP2,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP1
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP1
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP3
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
( ~ sP15
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| ~ sP3
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| ~ sP11
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP6
| ~ sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,h5,h8,h9]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,13,h8,h9]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,14,h7]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,15,h5,h6]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,16,h4]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
( sP15
=> ! [X1: a] :
( ( cF
@ ^ [X2: a] :
! [X3: a > $o] :
( ! [X4: a] :
( ( cF @ X3 @ X4 )
=> ( X3 @ X4 ) )
=> ( X3 @ X2 ) )
@ X1 )
=> ! [X2: a > $o] :
( ! [X3: a] :
( ( cF @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ( X2 @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV311^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.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 06:10:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 26
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------