TSTP Solution File: SET612^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET612^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 04:54:26 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(sP1,plain,
( sP1
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(cBOOL_PROP_85_pme,conjecture,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) )
= ( ^ [X4: a] :
~ ( ~ ( ~ ( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ( X1 @ X4 ) )
=> ( X3 @ X4 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) )
= ( ^ [X4: a] :
~ ( ~ ( ~ ( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ( X1 @ X4 ) )
=> ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_85_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
~ ( ( eigen__0 @ X3 )
=> ( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) )
= ( ^ [X3: a] :
~ ( ~ ( ~ ( ( eigen__0 @ X3 )
=> ( X1 @ X3 ) )
=> ~ ( eigen__0 @ X3 ) )
=> ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ( ~ ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) )
= ( ^ [X2: a] :
~ ( ~ ( ~ ( ( eigen__0 @ X2 )
=> ( eigen__1 @ X2 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) )
!= ( ^ [X1: a] :
~ ( ~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: a] :
( ( ~ ( ( 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,
( ~ ( sP3
=> ( ~ sP2
=> sP1 ) ) )
!= ( ~ ( ~ ( ~ ( sP3
=> sP2 )
=> ~ sP3 )
=> sP1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP3
=> ( ~ sP2
=> sP1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( sP3
=> sP2 )
=> ~ sP3 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
( sP3
=> ( ~ sP2
=> sP1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ~ ( ~ ( sP3
=> sP2 )
=> ~ sP3 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP3,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h14,assumption,
( ~ ( sP3
=> sP2 )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
( sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h18,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h16,h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h10,h17]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h18,h16,h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h18,h12]) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h17]),tab_imp(discharge,[h18])],[h16,1,2,h17,h18]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h10,h17]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,3,4,h16,h17]) ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h15,h13]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h7,5,6,h14,h15]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,7,h12,h13]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h6,8,h10,h11]) ).
thf(h19,assumption,
( ~ sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ~ ( sP3
=> sP2 )
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP3
=> sP2 ),
introduced(assumption,[]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h12,h21,h10,h20,h13,h17,h8,h9,h5,h4,h3,h2,h1,h0])],[h10,h17]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h10,h20,h13,h17,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h12])],[h21,10,h10,h12]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h13,h17,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h10])],[h20,11,h21,h10]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h13])],[h9,12,h20,h13]) ).
thf(14,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h12,h21,h10,h20,h13,h18,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h18,h12]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h10,h20,h13,h18,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h12])],[h21,14,h10,h12]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h13,h18,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h10])],[h20,15,h21,h10]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h13])],[h9,16,h20,h13]) ).
thf(18,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h12,h21,h10,h20,h13,h15,h19,h8,h9,h5,h4,h3,h2,h1,h0])],[h15,h13]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h10,h20,h13,h15,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h12])],[h21,18,h10,h12]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h13,h15,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h10])],[h20,19,h21,h10]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h20,h13])],[h9,20,h20,h13]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h19,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h15])],[h19,17,21,h18,h15]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h17]),tab_imp(discharge,[h19])],[h8,13,22,h17,h19]) ).
thf(24,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,9,23,h6,h7,h8,h9]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,24,h5]) ).
thf(26,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h2,h1,h0]),tab_fe(discharge,[h4])],[h3,25,h4]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,26,h3]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,27,h2]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,28,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ( ~ ( X2 @ X4 )
=> ( X3 @ X4 ) ) ) )
= ( ^ [X4: a] :
~ ( ~ ( ~ ( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ( X1 @ X4 ) )
=> ( X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET612^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n023.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jul 11 07:39:55 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.13/0.34 % SZS status Theorem
% 0.13/0.34 % Mode: mode213
% 0.13/0.34 % Inferences: 0
% 0.13/0.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------