TSTP Solution File: SET086^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET086^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 15:15:50 EDT 2023
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> $false ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ( X1 != eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : sP1 ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 = X1 )
| ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) )
| ( ( (~) @ ( X1 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
( (~)
@ ? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) ).
thf(thm,conjecture,
! [X1: $i] :
~ ! [X2: $i] : ( X2 != X1 ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
~ ! [X2: $i] : ( X2 != X1 ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
~ sP1,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,h1]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).
thf(0,theorem,
! [X1: $i] :
~ ! [X2: $i] : ( X2 != X1 ),
inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET086^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n012.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 : 300
% 0.12/0.33 % DateTime : Sat Aug 26 08:18:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % Mode: cade22grackle2xfee4
% 0.19/0.38 % Steps: 3
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------