TSTP Solution File: NUM824^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM824^5 : 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 : n026.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 : Mon Jul 18 13:56:54 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i > $i ).
thf(ty_cEVEN,type,
cEVEN: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_c0,type,
c0: $i ).
thf(ty_cODD,type,
cODD: $i > $o ).
thf(ty_cN,type,
cN: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cEVEN @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cODD @ eigen__0 )
=> ( cN @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( cN @ c0 )
=> ~ ! [X1: $i] :
( ( cN @ X1 )
=> ( cN @ ( cS @ X1 ) ) ) )
=> ~ ! [X1: $i] :
( ( cN @ X1 )
=> ( cN @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ~ ( ( X1 @ c0 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ ( cS @ X3 ) ) ) )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ( X1 @ ( cS @ X3 ) ) ) )
=> ~ ( ! [X3: $i] :
( ( cEVEN @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( cODD @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cODD @ X1 )
=> ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( cN @ c0 )
=> ~ ! [X1: $i] :
( ( cN @ X1 )
=> ( cN @ ( cS @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP3
=> ~ ( ! [X1: $i] :
( ( cEVEN @ X1 )
=> ( cN @ X1 ) )
=> ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cODD @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( cEVEN @ X1 )
=> ( cN @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( cN @ X1 )
=> ( cN @ ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP1
=> ( cN @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cN @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP9
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o] :
( ~ ( ~ ( ( cN @ c0 )
=> ~ ! [X2: $i] :
( ( cN @ X2 )
=> ( X1 @ ( cS @ X2 ) ) ) )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ( cN @ ( cS @ X2 ) ) ) )
=> ~ ( sP9
=> ~ ! [X2: $i] :
( ( cODD @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cN @ c0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM623_pme,conjecture,
( ~ ( ~ ( sP4
=> ~ sP15 )
=> ~ sP10 )
=> ! [X1: $i] :
( ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) )
=> ( cN @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP4
=> ~ sP15 )
=> ~ sP10 )
=> ! [X1: $i] :
( ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) )
=> ( cN @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM623_pme]) ).
thf(h1,assumption,
~ ( ~ ( sP4
=> ~ sP15 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) )
=> ( cN @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP4
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP10,
introduced(assumption,[]) ).
thf(h5,assumption,
sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
sP15,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ~ sP1
=> sP8 )
=> sP12 ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP1
=> sP8 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
sP8,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP11
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP13
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| sP3
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| sP6
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| ~ sP15
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,h5,h6,h4,h10,h9]) ).
thf(10,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| ~ sP8
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP4
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP7
| sP3
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| sP6
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| ~ sP15
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[10,11,12,13,14,15,16,17,h5,h6,h4,h11,h9]) ).
thf(19,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,9,18,h10,h11]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,19,h8,h9]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h2,20,h7]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,21,h5,h6]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,22,h3,h4]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,23,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP4
=> ~ sP15 )
=> ~ sP10 )
=> ! [X1: $i] :
( ( ~ ( cEVEN @ X1 )
=> ( cODD @ X1 ) )
=> ( cN @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM824^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 02:29:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % Mode: mode213
% 0.13/0.40 % Inferences: 104
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------