TSTP Solution File: SYN051^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN051^5 : 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 : n028.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 : Thu Jul 21 11:40:48 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cF,type,
cF: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cF @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cF @ eigen__0 )
=> p ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cF @ eigen__3 )
=> p ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> p ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cF @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( p
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( p
=> ( cF @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( p
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> p ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( sP9
=> ( cF @ X1 ) )
=> ~ ( ( cF @ X1 )
=> sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP7
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP6
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( cF @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cPELL21,conjecture,
( ~ ( ~ ! [X1: $i] :
~ ( sP9
=> ( cF @ X1 ) )
=> ! [X1: $i] :
~ ( ( cF @ X1 )
=> sP9 ) )
=> ~ sP10 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ! [X1: $i] :
~ ( sP9
=> ( cF @ X1 ) )
=> ! [X1: $i] :
~ ( ( cF @ X1 )
=> sP9 ) )
=> ~ sP10 ),
inference(assume_negation,[status(cth)],[cPELL21]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i] :
~ ( sP9
=> ( cF @ X1 ) )
=> ! [X1: $i] :
~ ( ( cF @ X1 )
=> sP9 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP10,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
~ ( sP9
=> ( cF @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
~ ( ( cF @ X1 )
=> sP9 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h7,assumption,
sP5,
introduced(assumption,[]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
sP9,
introduced(assumption,[]) ).
thf(1,plain,
( sP4
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| ~ sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP10
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,h6,h9,h2]) ).
thf(6,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h8,h6,h5,h3,h4,h1,h2,h0])],[h10,h6]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h6,h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,5,6,h9,h10]) ).
thf(8,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h4,7,h8]) ).
thf(h11,assumption,
sP3,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(9,plain,
( sP3
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP11
| ~ sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP13
| ~ sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP10
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h11,h7,h5,h3,h4,h1,h2,h0])],[9,10,11,12,13,14,15,16,h7,h12,h2]) ).
thf(18,plain,
( sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP6
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP13
| ~ sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP10
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h7,h5,h3,h4,h1,h2,h0])],[18,19,20,21,h7,h10,h2]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h11,h7,h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h10])],[h11,17,22,h12,h10]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h4,23,h11]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,8,24,h6,h7]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,25,h5]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,26,h3,h4]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,27,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ! [X1: $i] :
~ ( sP9
=> ( cF @ X1 ) )
=> ! [X1: $i] :
~ ( ( cF @ X1 )
=> sP9 ) )
=> ~ sP10 ),
inference(contra,[status(thm),contra(discharge,[h0])],[28,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN051^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n028.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 : Mon Jul 11 19:28:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 70
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------