TSTP Solution File: QUA004^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : QUA004^1 : 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 : n008.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 13:31:54 EDT 2023
% Result : Theorem 60.43s 60.54s
% Output : Proof 60.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 39 ( 16 unt; 3 typ; 9 def)
% Number of atoms : 103 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 23 ~; 16 |; 4 &; 27 @)
% ( 10 <=>; 9 =>; 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 : 24 ( 22 usr; 22 con; 0-2 aty)
% Number of variables : 35 ( 26 ^; 5 !; 4 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_sup,type,
sup: ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
( ( X1 = eigen__0 )
!= ( ( X1 != eigen__0 )
=> ( X1 = eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
( ( sup
@ ^ [X2: $i] :
( ( X2 != X1 )
=> ( X2 = X1 ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__3 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ sP1
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ^ [X1: $i] : ( X1 = eigen__0 ) )
= ( ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( X1 = eigen__0 )
= ( ( X1 != eigen__0 )
=> ( X1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( sup
@ ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__0 ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( sup
@ ^ [X2: $i] : ( X2 = X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( sup
@ ^ [X2: $i] :
( ( X2 != X1 )
=> ( X2 = X1 ) ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( sup
@ ^ [X1: $i] : ( X1 = eigen__0 ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( sup
@ ^ [X1: $i] : ( X1 = eigen__0 ) )
= ( sup
@ ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
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_idemp,conjecture,
sP8 ).
thf(h1,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[addition_idemp]) ).
thf(1,plain,
( sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP1
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP4
| ~ sP1
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP5
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(6,plain,
( sP3
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP10
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP6
| ~ sP10
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( sP8
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(sup_singleset,axiom,
sP7 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,sup_singleset,h1]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[11,h0]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h1])],[11,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : QUA004^1 : 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 : n008.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 16:42:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 60.43/60.54 % SZS status Theorem
% 60.43/60.54 % Mode: cade22grackle2x34cb
% 60.43/60.54 % Steps: 303
% 60.43/60.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------