TSTP Solution File: SET611^3 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET611^3 : 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 : n021.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 04:54:24 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% 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 > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( ( eigen__0 @ eigen__2 )
=> ~ sP1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ~ ( sP6
=> ( eigen__1 @ eigen__4 ) ) )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ eigen__2 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> $false ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: $i] :
~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) )
= ( ^ [X1: $i] : sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP6
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
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] : sP9 ) ) ).
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 > $o,X2: $i > $o] :
( ( ( ^ [X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( ^ [X3: $i] : sP9 ) )
= ( ( ^ [X3: $i] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= X1 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o] :
( ( ( ^ [X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( ^ [X3: $i] : sP9 ) )
= ( ( ^ [X3: $i] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= X1 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
~ ! [X1: $i > $o] :
( ( ( ^ [X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ~ ( X1 @ X2 ) ) )
= ( ^ [X2: $i] : sP9 ) )
= ( ( ^ [X2: $i] :
~ ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= eigen__0 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP11 != sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
sP11,
introduced(assumption,[]) ).
thf(h4,assumption,
sP4,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ ( sP13
=> sP1 ) )
!= sP13,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP13
=> sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP13,
introduced(assumption,[]) ).
thf(h11,assumption,
( sP13
=> sP1 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h13,h9,h10,h8,h7,h3,h4,h2,h1,h0])],[h10,h10]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h13])],[h9,1,h10,h13]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h11,h12,h8,h7,h3,h4,h2,h1,h0])],[h12,h12]) ).
thf(4,plain,
( ~ sP8
| ~ sP13
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
~ sP9,
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h11,h12,h8,h7,h3,h4,h2,h1,h0])],[4,5,6,7,8,h3,h14,h12]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h12,h8,h7,h3,h4,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h14])],[h11,3,9,h12,h14]) ).
thf(11,plain,
$false,
inference(tab_be,[status(thm),assumptions([h8,h7,h3,h4,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,2,10,h9,h10,h11,h12]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[h7,11,h8]) ).
thf(13,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_fe(discharge,[h7])],[h4,12,h7]) ).
thf(h15,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h16,assumption,
( ~ ( sP6
=> ~ sP10 ) )
!= sP9,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP6
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP9,
introduced(assumption,[]) ).
thf(h19,assumption,
( sP6
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h21,assumption,
sP6,
introduced(assumption,[]) ).
thf(h22,assumption,
sP10,
introduced(assumption,[]) ).
thf(14,plain,
( sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP7
| ~ sP12
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP4
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h17,h18,h16,h15,h5,h6,h2,h1,h0])],[14,15,16,17,h21,h22,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h15,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h17,18,h21,h22]) ).
thf(h23,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h24,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(20,plain,
$false,
inference(tab_false,[status(thm),assumptions([h23,h19,h20,h16,h15,h5,h6,h2,h1,h0])],[h20]) ).
thf(21,plain,
$false,
inference(tab_false,[status(thm),assumptions([h24,h19,h20,h16,h15,h5,h6,h2,h1,h0])],[h20]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h20,h16,h15,h5,h6,h2,h1,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h24])],[h19,20,21,h23,h24]) ).
thf(23,plain,
$false,
inference(tab_be,[status(thm),assumptions([h16,h15,h5,h6,h2,h1,h0]),tab_be(discharge,[h17,h18]),tab_be(discharge,[h19,h20])],[h16,19,22,h17,h18,h19,h20]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h5,h6,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__4)],[h15,23,h16]) ).
thf(25,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_fe(discharge,[h15])],[h5,24,h15]) ).
thf(26,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,13,25,h3,h4,h5,h6]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,26,h2]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,27,h1]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o] :
( ( ( ^ [X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
= ( ^ [X3: $i] : sP9 ) )
= ( ( ^ [X3: $i] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= X1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET611^3 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 19:28:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 68
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------