TSTP Solution File: QUA002^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : QUA002^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : 300s
% DateTime : Thu Aug 31 13:31:53 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 34
% Syntax : Number of formulae : 41 ( 18 unt; 4 typ; 8 def)
% Number of atoms : 114 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 111 ( 34 ~; 16 |; 4 &; 29 @)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 21 con; 0-2 aty)
% Number of variables : 42 ( 28 ^; 10 !; 4 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_sup,type,
sup: ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
( ( ( X1 != eigen__0 )
=> ( X1 = eigen__1 ) )
!= ( ( X1 != eigen__1 )
=> ( X1 = eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( ( X1 != eigen__0 )
=> ( X1 = eigen__1 ) )
= ( ( X1 != eigen__1 )
=> ( X1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__2 != eigen__1 )
=> ( eigen__2 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__1 ) ) )
= ( ^ [X1: $i] :
( ( X1 != eigen__1 )
=> ( X1 = eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( eigen__2 != eigen__0 )
=> ( eigen__2 = eigen__1 ) )
= sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( sup
@ ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__1 ) ) )
= ( sup
@ ^ [X1: $i] :
( ( X1 != eigen__1 )
=> ( X1 = eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__2 != eigen__0 )
=> ( eigen__2 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_supset,definition,
( supset
= ( ^ [X1: ( $i > $o ) > $o,X2: $i] :
? [X3: $i > $o] :
( ( X1 @ X3 )
& ( ( sup @ X3 )
= X2 ) ) ) ) ).
thf(def_unionset,definition,
( unionset
= ( ^ [X1: ( $i > $o ) > $o,X2: $i] :
? [X3: $i > $o] :
( ( X1 @ X3 )
& ( X3 @ X2 ) ) ) ) ).
thf(def_addition,definition,
( addition
= ( ^ [X1: $i,X2: $i] : ( sup @ ( union @ ( singleton @ X1 ) @ ( singleton @ X2 ) ) ) ) ) ).
thf(def_crossmult,definition,
( crossmult
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
? [X4: $i,X5: $i] :
( ( X1 @ X4 )
& ( X2 @ X5 )
& ( X3
= ( multiplication @ X4 @ X5 ) ) ) ) ) ).
thf(addition_comm,conjecture,
! [X1: $i,X2: $i] :
( ( sup
@ ^ [X3: $i] :
( ( X3 != X1 )
=> ( X3 = X2 ) ) )
= ( sup
@ ^ [X3: $i] :
( ( X3 != X2 )
=> ( X3 = X1 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( sup
@ ^ [X3: $i] :
( ( X3 != X1 )
=> ( X3 = X2 ) ) )
= ( sup
@ ^ [X3: $i] :
( ( X3 != X2 )
=> ( X3 = X1 ) ) ) ),
inference(assume_negation,[status(cth)],[addition_comm]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( sup
@ ^ [X2: $i] :
( ( X2 != eigen__0 )
=> ( X2 = X1 ) ) )
= ( sup
@ ^ [X2: $i] :
( ( X2 != X1 )
=> ( X2 = eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(1,plain,
( sP2
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP6
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP7
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP8
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP4
| ~ sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP4
| sP6
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP1
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(10,plain,
( sP3
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h3]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,12,h3]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,13,h2]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( sup
@ ^ [X3: $i] :
( ( X3 != X1 )
=> ( X3 = X2 ) ) )
= ( sup
@ ^ [X3: $i] :
( ( X3 != X2 )
=> ( X3 = X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : QUA002^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n028.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 : 300
% 0.13/0.34 % DateTime : Sat Aug 26 16:55:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 % SZS status Theorem
% 0.19/0.63 % Mode: cade22grackle2xfee4
% 0.19/0.63 % Steps: 2107
% 0.19/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------