TSTP Solution File: SET624^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET624^5 : 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 04:54:35 EDT 2022
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% 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__5,type,
eigen__5: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ eigen__5 )
=> ~ ( ~ ( eigen__1 @ eigen__5 )
=> ( eigen__2 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__3 )
=> ~ ( eigen__2 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ( ~ ( eigen__1 @ X1 )
=> ( eigen__2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__0 @ eigen__3 )
=> ~ ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( eigen__1 @ eigen__5 )
=> ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
=> ~ ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP9
=> ~ ( ~ sP13
=> ( eigen__2 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ sP13
=> ( eigen__2 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cBOOL_PROP_100_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 ) )
=> ~ ! [X4: a] :
( ( 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 ) )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_100_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 ) )
=> ~ ! [X3: a] :
( ( eigen__0 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > $o] :
( ( ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ( ~ ( eigen__1 @ X2 )
=> ( X1 @ X2 ) ) ) )
= ( sP2
=> ~ ! [X2: a] :
( ( eigen__0 @ X2 )
=> ~ ( X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
( ~ sP4 )
!= ( sP2
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h5,assumption,
( sP2
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP2
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP16
=> ~ ( ~ sP11
=> sP6 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP16,
introduced(assumption,[]) ).
thf(h10,assumption,
( ~ sP11
=> sP6 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP11,
introduced(assumption,[]) ).
thf(h12,assumption,
sP6,
introduced(assumption,[]) ).
thf(h13,assumption,
sP2,
introduced(assumption,[]) ).
thf(h14,assumption,
sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h9,h10,h8,h4,h5,h3,h2,h1,h0])],[1,2,h9,h11,h13]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h5,3,h13,h14]) ).
thf(5,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| ~ sP16
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h9,h10,h8,h4,h5,h3,h2,h1,h0])],[5,6,h9,h12,h14]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h9,h10,h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h5,7,h13,h14]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h10,4,8,h11,h12]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,9,h9,h10]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h4,10,h8]) ).
thf(h15,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP9
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP9,
introduced(assumption,[]) ).
thf(h19,assumption,
sP13,
introduced(assumption,[]) ).
thf(12,plain,
( sP15
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| ~ sP9
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h6,h7,h3,h2,h1,h0])],[12,13,14,h6,h18,h19]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h15,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,15,h18,h19]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h15,16,h17]) ).
thf(h20,assumption,
~ ( sP7
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h21,assumption,
sP7,
introduced(assumption,[]) ).
thf(h22,assumption,
sP10,
introduced(assumption,[]) ).
thf(18,plain,
( sP8
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP4
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP1
| ~ sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h20,h16,h6,h7,h3,h2,h1,h0])],[18,19,20,h6,h21,h22]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h16,h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,21,h21,h22]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h6,h7,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h16,22,h20]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h7,17,23,h15,h16]) ).
thf(25,plain,
$false,
inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,11,24,h4,h5,h6,h7]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,25,h3]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,26,h2]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,27,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 ) )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET624^5 : 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
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 9 23:04:12 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % Mode: mode213
% 0.11/0.36 % Inferences: 23
% 0.11/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------