TSTP Solution File: SYN059^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN059^5 : 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 : n011.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 11:40:55 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cH,type,
cH: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cJ,type,
cJ: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cF,type,
cF: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cG @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cF @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cF @ eigen__2 )
=> ( cH @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( sP2
=> ~ ( cG @ eigen__4 ) )
=> ~ ( ( cH @ eigen__0 )
=> ~ ( cJ @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( cF @ X1 )
=> ( cH @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> ~ ( cG @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ~ ( ( cF @ X1 )
=> ~ ( cG @ X2 ) )
=> ~ ( ( cH @ X1 )
=> ~ ( cJ @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP1
=> ( cJ @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cJ @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cF @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cH @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cJ @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cG @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( cH @ eigen__0 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( sP2
=> ~ ( cG @ X1 ) )
=> ~ ( ( cH @ eigen__0 )
=> ~ ( cJ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( cG @ X1 )
=> ( cJ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cPELL29,conjecture,
( ~ ( ~ ! [X1: $i] :
~ ( cF @ X1 )
=> ! [X1: $i] :
~ ( cG @ X1 ) )
=> ~ ( ( ~ ( sP5
=> ~ sP16 )
=> sP7 )
=> ~ ( sP7
=> sP16 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ! [X1: $i] :
~ ( cF @ X1 )
=> ! [X1: $i] :
~ ( cG @ X1 ) )
=> ~ ( ( ~ ( sP5
=> ~ sP16 )
=> sP7 )
=> ~ ( sP7
=> sP16 ) ) ),
inference(assume_negation,[status(cth)],[cPELL29]) ).
thf(h1,assumption,
~ ( ~ ! [X1: $i] :
~ ( cF @ X1 )
=> ! [X1: $i] :
~ ( cG @ X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ~ ( sP5
=> ~ sP16 )
=> sP7 )
=> ~ ( sP7
=> sP16 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
~ ( cF @ X1 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
~ ( cG @ X1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
cG @ eigen__1,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP5
=> ~ sP16 )
=> sP7 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP7
=> sP16 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP5
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h11,assumption,
sP5,
introduced(assumption,[]) ).
thf(h12,assumption,
sP16,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ~ ( sP10
=> ~ ( cG @ X1 ) )
=> ~ ( sP11
=> ~ ( cJ @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP10
=> ~ sP1 )
=> ~ ( sP11
=> ~ sP12 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP10
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h16,assumption,
( sP11
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP10,
introduced(assumption,[]) ).
thf(h18,assumption,
sP1,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP3
| ~ sP10
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h19,h17,h18,h15,h16,h14,h13,h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,h11,h17,h19]) ).
thf(4,plain,
( ~ sP16
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP1
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h17,h18,h15,h16,h14,h13,h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0])],[4,5,h12,h18,h20]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h18,h15,h16,h14,h13,h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h16,3,6,h19,h20]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h13,h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,7,h17,h18]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h13,h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,8,h15,h16]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,9,h14]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h10,10,h13]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,11,h11,h12]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,12,h9,h10]) ).
thf(h21,assumption,
sP7,
introduced(assumption,[]) ).
thf(h22,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP13
=> sP9 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP13,
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(14,plain,
( sP14
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP4
| sP6
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP6
| ~ sP2
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h21,h22,h8,h6,h5,h3,h4,h1,h2,h0])],[14,15,16,17,18,h5,h21,h24,h25]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h24,h25])],[h23,19,h24,h25]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h21,h22,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__4)],[h22,20,h23]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h8,21,h21,h22]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h2,13,22,h7,h8]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h4,23,h6]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,24,h5]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,25,h3,h4]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,26,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ! [X1: $i] :
~ ( cF @ X1 )
=> ! [X1: $i] :
~ ( cG @ X1 ) )
=> ~ ( ( ~ ( sP5
=> ~ sP16 )
=> sP7 )
=> ~ ( sP7
=> sP16 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN059^5 : 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
% 0.13/0.33 % Computer : n011.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 13:57:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 24
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------