TSTP Solution File: SET635^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET635^5 : 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 : n008.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 04:54:43 EDT 2022
% Result : Theorem 0.21s 0.37s
% Output : Proof 0.21s
% 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_117_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_117_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
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h12,assumption,
sP3,
introduced(assumption,[]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(h14,assumption,
( sP3
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP3
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h12,h16]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h14,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h13,h17]) ).
thf(3,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])],[h14,1,2,h16,h17]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h12,h18,h15,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0])],[h18,h11]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h12,h13,h10,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h18])],[h15,4,h12,h18]) ).
thf(6,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])],[h7,3,5,h14,h15]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,6,h12,h13]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h6,7,h10,h11]) ).
thf(h19,assumption,
( sP3
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h12,h13,h10,h19,h16,h14,h8,h9,h5,h4,h3,h2,h1,h0])],[h12,h16]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h11,h12,h13,h10,h19,h16,h14,h8,h9,h5,h4,h3,h2,h1,h0])],[h12,h16]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h13,h10,h19,h16,h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h11])],[h19,9,10,h16,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h19,h16,h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,11,h12,h13]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h19])],[h9,12,h10,h19]) ).
thf(14,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h12,h13,h10,h19,h17,h14,h8,h9,h5,h4,h3,h2,h1,h0])],[h12,h16]) ).
thf(15,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h11,h12,h13,h10,h19,h17,h14,h8,h9,h5,h4,h3,h2,h1,h0])],[h13,h17]) ).
thf(16,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h13,h10,h19,h17,h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h11])],[h19,14,15,h16,h11]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h19,h17,h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,16,h12,h13]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h19])],[h9,17,h10,h19]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,13,18,h16,h17]) ).
thf(20,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h12,h13,h10,h19,h18,h8,h9,h5,h4,h3,h2,h1,h0])],[h12,h16]) ).
thf(21,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h11,h12,h13,h10,h19,h18,h8,h9,h5,h4,h3,h2,h1,h0])],[h18,h11]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h12,h13,h10,h19,h18,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h11])],[h19,20,21,h16,h11]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h19,h18,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,22,h12,h13]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h19])],[h9,23,h10,h19]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h18])],[h8,19,24,h14,h18]) ).
thf(26,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,8,25,h6,h7,h8,h9]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,26,h5]) ).
thf(28,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h3,h2,h1,h0]),tab_fe(discharge,[h4])],[h3,27,h4]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,28,h3]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,29,h2]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,30,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])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET635^5 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 04:58:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % Mode: mode213
% 0.21/0.37 % Inferences: 0
% 0.21/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------