TSTP Solution File: SET017^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET017^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 04:49:46 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( ( ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__1 ) ) )
= ( ^ [X1: $i] :
( ( X1 != eigen__0 )
=> ( X1 = eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ sP5
=> sP6 )
= ( ~ sP5
=> ( eigen__1 = eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP5
=> ( eigen__1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ~ sP3
=> ( eigen__2 = eigen__1 ) )
= ( ~ sP3
=> sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP3
=> ( eigen__2 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP5
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( ( X1 != eigen__0 )
=> ( X1 = eigen__1 ) )
= ( ( X1 != eigen__0 )
=> ( X1 = eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP3
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP5
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
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] : $false ) ) ).
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] :
( ( 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,X3: $i] :
( ( ( ^ [X4: $i] :
( ( X4 != X1 )
=> ( X4 = X2 ) ) )
= ( ^ [X4: $i] :
( ( X4 != X1 )
=> ( X4 = X3 ) ) ) )
=> ( X2 = X3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( ( ^ [X4: $i] :
( ( X4 != X1 )
=> ( X4 = X2 ) ) )
= ( ^ [X4: $i] :
( ( X4 != X1 )
=> ( X4 = X3 ) ) ) )
=> ( X2 = X3 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i,X2: $i] :
( ( ( ^ [X3: $i] :
( ( X3 != eigen__0 )
=> ( X3 = X1 ) ) )
= ( ^ [X3: $i] :
( ( X3 != eigen__0 )
=> ( X3 = X2 ) ) ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( ( ^ [X2: $i] :
( ( X2 != eigen__0 )
=> ( X2 = eigen__1 ) ) )
= ( ^ [X2: $i] :
( ( X2 != eigen__0 )
=> ( X2 = X1 ) ) ) )
=> ( eigen__1 = X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP1
=> sP13 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP13
| ~ sP18
| ~ sP7 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
sP6,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP15
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP5
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP20
| ~ sP5
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP19
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP3
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| ~ sP15
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP11
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP16
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP1
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP14
| ~ sP12
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP2
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP17
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
sP17,
inference(eq_sym,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h4,h5]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,20,h4,h5]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,21,h3]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,22,h2]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,23,h1]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ( ( ^ [X4: $i] :
( ( X4 != X1 )
=> ( X4 = X2 ) ) )
= ( ^ [X4: $i] :
( ( X4 != X1 )
=> ( X4 = X3 ) ) ) )
=> ( X2 = X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET017^1 : TPTP v8.1.0. Released v3.6.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.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 : Sun Jul 10 18:16:22 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: 32
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------