TSTP Solution File: SET171^3 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET171^3 : 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 : n003.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 04:51:46 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
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(union_distributes_over_intersection,conjecture,
! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ^ [X4: $i] :
( ~ ( X1 @ X4 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) )
= ( ^ [X4: $i] :
~ ( ( ~ ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ( ~ ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ^ [X4: $i] :
( ~ ( X1 @ X4 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) )
= ( ^ [X4: $i] :
~ ( ( ~ ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ( ~ ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[union_distributes_over_intersection]) ).
thf(h1,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ( ^ [X3: $i] :
( ~ ( eigen__0 @ X3 )
=> ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) )
= ( ^ [X3: $i] :
~ ( ( ~ ( eigen__0 @ X3 )
=> ( X1 @ X3 ) )
=> ~ ( ~ ( eigen__0 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i > $o] :
( ( ^ [X2: $i] :
( ~ ( eigen__0 @ X2 )
=> ~ ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) ) ) )
= ( ^ [X2: $i] :
~ ( ( ~ ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ^ [X1: $i] :
( ~ ( eigen__0 @ X1 )
=> ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ) )
!= ( ^ [X1: $i] :
~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) )
= ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ sP1
=> ~ ( sP3
=> ~ sP2 ) )
!= ( ~ ( ( ~ sP1
=> sP3 )
=> ~ ( ~ sP1
=> sP2 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ sP1
=> ~ ( sP3
=> ~ sP2 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ~ sP1
=> sP3 )
=> ~ ( ~ sP1
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ sP1
=> ~ ( sP3
=> ~ sP2 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ( ~ sP1
=> sP3 )
=> ~ ( ~ sP1
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP3
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ sP1
=> sP3 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h15,h12,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h10,h14]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,1,h14,h15]) ).
thf(h16,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(3,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h16,h13,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h10,h14]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h16])],[h13,3,h14,h16]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h7,2,4,h12,h13]) ).
thf(h17,assumption,
sP3,
introduced(assumption,[]) ).
thf(h18,assumption,
sP2,
introduced(assumption,[]) ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h15,h12,h17,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h17,h15]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h17,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,6,h14,h15]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h16,h13,h17,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h18,h16]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h17,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h16])],[h13,8,h14,h16]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h7,7,9,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h11,10,h17,h18]) ).
thf(12,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h6,5,11,h10,h11]) ).
thf(h19,assumption,
( sP3
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h20,assumption,
( ~ sP1
=> sP3 ),
introduced(assumption,[]) ).
thf(h21,assumption,
( ~ sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(13,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h10,h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h10,h14]) ).
thf(14,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h10,h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h10,h14]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h18])],[h21,13,14,h10,h18]) ).
thf(16,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h17,h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h17,h15]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h17,h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h17,h15]) ).
thf(18,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h18])],[h21,16,17,h10,h18]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h21,h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h17])],[h20,15,18,h10,h17]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h9,19,h20,h21]) ).
thf(21,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h10,h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h10,h14]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h10,h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h18,h16]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h18])],[h21,21,22,h10,h18]) ).
thf(24,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h17,h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h10,h14]) ).
thf(25,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h17,h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h18,h16]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h18])],[h21,24,25,h10,h18]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h20,h21,h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h17])],[h20,23,26,h10,h17]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h9,27,h20,h21]) ).
thf(29,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h19,20,28,h15,h16]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h19])],[h8,29,h14,h19]) ).
thf(31,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,12,30,h6,h7,h8,h9]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,31,h5]) ).
thf(33,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h2,h1,h0]),tab_fe(discharge,[h4])],[h3,32,h4]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,33,h3]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,34,h2]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,35,h1]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ^ [X4: $i] :
( ~ ( X1 @ X4 )
=> ~ ( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) ) )
= ( ^ [X4: $i] :
~ ( ( ~ ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ( ~ ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[36,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET171^3 : TPTP v8.1.0. Released v3.6.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n003.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 : Mon Jul 11 04:11:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 0
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------