TSTP Solution File: SWV447^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWV447^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : Wed Jul 20 21:25:10 EDT 2022
% Result : Theorem 2.00s 2.19s
% Output : Proof 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 36
% Syntax : Number of formulae : 41 ( 11 unt; 4 typ; 1 def)
% Number of atoms : 72 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 167 ( 20 ~; 14 |; 0 &; 109 @)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 19 con; 0-2 aty)
% Number of variables : 37 ( 20 ^ 17 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nil,type,
nil: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_map,type,
map: ( $i > $i ) > $i > $i ).
thf(ty_cons,type,
cons: $i > $i > $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
( ( map
@ ^ [X2: $i] : X2
@ ( cons @ X1 @ nil ) )
!= ( cons @ X1 @ nil ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $i] :
( ( map @ X1 @ nil )
= nil ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i > $o] :
( ( X2 @ X1 )
=> ! [X3: $i] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( map
@ ^ [X3: $i] : X3
@ ( cons @ X1 @ X2 ) )
= ( cons @ X1
@ ( map
@ ^ [X3: $i] : X3
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( map
@ ^ [X1: $i] : X1
@ nil )
= nil ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( ( map
@ ^ [X1: $i] : X1
@ ( cons @ eigen__0 @ nil ) )
= ( cons @ eigen__0
@ ( map
@ ^ [X1: $i] : X1
@ nil ) ) )
=> ( ( cons @ eigen__0
@ ( map
@ ^ [X1: $i] : X1
@ nil ) )
!= ( cons @ eigen__0 @ nil ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cons @ eigen__0
@ ( map
@ ^ [X1: $i] : X1
@ nil ) )
= ( cons @ eigen__0 @ nil ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o] :
( ( X1
@ ( map
@ ^ [X2: $i] : X2
@ ( cons @ eigen__0 @ nil ) ) )
=> ! [X2: $i] :
( ( ( map
@ ^ [X3: $i] : X3
@ ( cons @ eigen__0 @ nil ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $i,X2: $i,X3: $i] :
( ( map @ X1 @ ( cons @ X2 @ X3 ) )
= ( cons @ ( X1 @ X2 ) @ ( map @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( map
@ ^ [X2: $i] : X2
@ ( cons @ X1 @ nil ) )
= ( cons @ X1 @ nil ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( map
@ ^ [X1: $i] : X1
@ ( cons @ eigen__0 @ nil ) )
= ( cons @ eigen__0
@ ( map
@ ^ [X1: $i] : X1
@ nil ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( map
@ ^ [X1: $i] : X1
@ ( cons @ eigen__0 @ nil ) )
!= ( cons @ eigen__0 @ nil ) )
=> ! [X1: $i] :
( ( ( map
@ ^ [X2: $i] : X2
@ ( cons @ eigen__0 @ nil ) )
= X1 )
=> ( X1
!= ( cons @ eigen__0 @ nil ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( ( map
@ ^ [X2: $i] : X2
@ ( cons @ eigen__0 @ nil ) )
= X1 )
=> ( X1
!= ( cons @ eigen__0 @ nil ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( map
@ ^ [X1: $i] : X1
@ ( cons @ eigen__0 @ nil ) )
= ( cons @ eigen__0 @ nil ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( map
@ ^ [X2: $i] : X2
@ ( cons @ eigen__0 @ X1 ) )
= ( cons @ eigen__0
@ ( map
@ ^ [X2: $i] : X2
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(test,conjecture,
sP9 ).
thf(h1,negated_conjecture,
~ sP9,
inference(assume_negation,[status(cth)],[test]) ).
thf(1,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
sP11,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP6
| ~ sP11
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| ~ sP10
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP14
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
sP2,
inference(eq_ind,[status(thm)],]) ).
thf(13,plain,
( sP9
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(ax2,axiom,
sP8 ).
thf(ax1,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,ax2,ax1,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
sP9,
inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV447^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.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 : Tue Jun 14 18:21:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.19 % SZS status Theorem
% 2.00/2.19 % Mode: mode506
% 2.00/2.19 % Inferences: 8183
% 2.00/2.19 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------