TSTP Solution File: SEU853^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU853^5 : 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 : n019.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 14:10:32 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% 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__4,type,
eigen__4: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__4 )
=> ( eigen__2 @ eigen__4 ) ) ),
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 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ~ ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ sP6
=> ( eigen__1 @ eigen__4 ) )
=> ~ ( ( eigen__2 @ eigen__4 )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__2 @ X1 ) )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__2 @ X1 )
=> ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP9
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP6
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cGAZING_THM35_pme,conjecture,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) ) )
= ( ! [X4: a] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ( X2 @ X4 ) )
=> ~ ( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) ) )
= ( ! [X4: a] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ( X2 @ X4 ) )
=> ~ ( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cGAZING_THM35_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o,X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( ! [X3: a] :
( ( eigen__0 @ X3 )
=> ( X1 @ X3 ) ) )
= ( ! [X3: a] :
( ~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( eigen__0 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a] :
( ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) )
=> ( sP14
= ( ! [X2: a] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( X1 @ X2 ) )
=> ( eigen__1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( sP5
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( sP14 = sP12 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP5
=> ~ ! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP14 != sP12,
introduced(assumption,[]) ).
thf(h6,assumption,
sP5,
introduced(assumption,[]) ).
thf(h7,assumption,
! [X1: a] :
( ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP14,
introduced(assumption,[]) ).
thf(h9,assumption,
sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ~ ( ~ ( sP10
=> ~ sP11 )
=> sP2 )
=> ~ ( sP11
=> sP10 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP10
=> ~ sP11 )
=> sP2 ),
introduced(assumption,[]) ).
thf(h14,assumption,
( sP11
=> sP10 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP10
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
sP10,
introduced(assumption,[]) ).
thf(h18,assumption,
sP11,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h19,h17,h18,h15,h16,h13,h14,h12,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[h18,h19]) ).
thf(2,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| ~ sP10
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h17,h18,h15,h16,h13,h14,h12,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0])],[2,3,h8,h16,h17]) ).
thf(5,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h12,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h17])],[h14,1,4,h19,h17]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h12,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,5,h17,h18]) ).
thf(7,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h13,6,h15,h16]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,7,h13,h14]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h9,8,h12]) ).
thf(h20,assumption,
~ ( sP4
=> sP8 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP4,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(10,plain,
( sP13
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| ~ sP4
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP15
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| sP6
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP6
| ~ sP4
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h10,h11,h6,h7,h4,h5,h3,h2,h1,h0])],[10,11,12,13,14,15,16,h6,h21,h22,h11]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h10,h11,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,17,h21,h22]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__4)],[h10,18,h20]) ).
thf(20,plain,
$false,
inference(tab_be,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h8,h9]),tab_be(discharge,[h10,h11])],[h5,9,19,h8,h9,h10,h11]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,20,h6,h7]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,21,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,22,h3]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,23,h2]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,24,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o,X3: a > $o] :
( ~ ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ( ! [X4: a] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) ) )
= ( ! [X4: a] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ( X2 @ X4 ) )
=> ~ ( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU853^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n019.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 : Sun Jun 19 13:39:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 21
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------