TSTP Solution File: SET587^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET587^5 : 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 : n018.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 04:54:07 EDT 2022
% Result : Theorem 0.13s 0.37s
% 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 ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ~ ( sP1
=> ( eigen__1 @ eigen__2 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP1
=> ( eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5
=> ( eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> $false ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( ^ [X1: a] : sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(cBOOL_PROP_45_pme,conjecture,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] : sP8 ) )
= ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] : sP8 ) )
= ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_45_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o] :
( ( ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] : sP8 ) )
= ( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP10 != sP3,
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h8,assumption,
sP1,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP6
| ~ sP1
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP6
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
~ sP8,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h3,h4,h2,h1,h0])],[1,2,3,4,5,h3,h8,h9]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,6,h8,h9]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h4,7,h7]) ).
thf(h10,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h11,assumption,
( ~ sP7 )
!= sP8,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h13,assumption,
sP8,
introduced(assumption,[]) ).
thf(h14,assumption,
sP7,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h16,assumption,
sP5,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(9,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| ~ sP5
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h12,h13,h11,h10,h5,h6,h2,h1,h0])],[9,10,h16,h17,h6]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h12,11,h16,h17]) ).
thf(h18,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h19,assumption,
sP9,
introduced(assumption,[]) ).
thf(13,plain,
$false,
inference(tab_false,[status(thm),assumptions([h18,h14,h15,h11,h10,h5,h6,h2,h1,h0])],[h15]) ).
thf(14,plain,
$false,
inference(tab_false,[status(thm),assumptions([h19,h14,h15,h11,h10,h5,h6,h2,h1,h0])],[h15]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h14,h15,h11,h10,h5,h6,h2,h1,h0]),tab_imp(discharge,[h18]),tab_imp(discharge,[h19])],[h14,13,14,h18,h19]) ).
thf(16,plain,
$false,
inference(tab_be,[status(thm),assumptions([h11,h10,h5,h6,h2,h1,h0]),tab_be(discharge,[h12,h13]),tab_be(discharge,[h14,h15])],[h11,12,15,h12,h13,h14,h15]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__4)],[h10,16,h11]) ).
thf(18,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_fe(discharge,[h10])],[h5,17,h10]) ).
thf(19,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,8,18,h3,h4,h5,h6]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,19,h2]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,20,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] : sP8 ) )
= ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET587^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 01:24:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 27
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------