TSTP Solution File: SYN058^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN058^5 : 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 : Thu Jul 21 11:40:54 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_cS,type,
cS: $i > $o ).
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_cF,type,
cF: $i > $o ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(sP1,plain,
( sP1
<=> ( cG @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ( !! @ cQ ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cF @ eigen__6 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cG @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( cF @ eigen__3 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cQ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ eigen__1 )
=> ( !! @ cQ ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cF @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( cF @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( !! @ cQ ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cS @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
~ ( cS @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( cF @ X1 )
=> ( cG @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(cPELL28,conjecture,
( ~ ( ~ ( sP2
=> ~ ( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ) )
=> ~ ( ~ sP13
=> sP14 ) )
=> ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( sP2
=> ~ ( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ) )
=> ~ ( ~ sP13
=> sP14 ) )
=> ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cPELL28]) ).
thf(h1,assumption,
~ ( ~ ( sP2
=> ~ ( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ) )
=> ~ ( ~ sP13
=> sP14 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP2
=> ~ ( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ sP13
=> sP14 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ sP6
=> ( cR @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( cR @ eigen__0 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP13,
introduced(assumption,[]) ).
thf(h13,assumption,
sP14,
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ~ ( sP9
=> ~ ( cF @ eigen__1 ) )
=> ( cG @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP9
=> ~ ( cF @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( cG @ eigen__1 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP9,
introduced(assumption,[]) ).
thf(h18,assumption,
cF @ eigen__1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,h5,h10,h17]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,4,h17,h18]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,5,h15,h16]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h2,6,h14]) ).
thf(h19,assumption,
~ ( ~ ( ( cP @ eigen__3 )
=> ~ sP10 )
=> sP4 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( ( cP @ eigen__3 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h22,assumption,
cP @ eigen__3,
introduced(assumption,[]) ).
thf(h23,assumption,
sP10,
introduced(assumption,[]) ).
thf(8,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| ~ sP10
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h20,h21,h19,h13,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[8,9,h13,h23,h21]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h13,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h22,h23])],[h20,10,h22,h23]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h13,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h20,h21])],[h19,11,h20,h21]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__3)],[h2,12,h19]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h11,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h4,7,13,h12,h13]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,14,h10,h11]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h7,15,h9]) ).
thf(h24,assumption,
~ ( ( cQ @ eigen__4 )
=> ~ sP12 ),
introduced(assumption,[]) ).
thf(h25,assumption,
cQ @ eigen__4,
introduced(assumption,[]) ).
thf(h26,assumption,
sP12,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( ~ ( ( cP @ eigen__5 )
=> ~ ( cF @ eigen__5 ) )
=> ( cG @ eigen__5 ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( ( cP @ eigen__5 )
=> ~ ( cF @ eigen__5 ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( cG @ eigen__5 ),
introduced(assumption,[]) ).
thf(h30,assumption,
cP @ eigen__5,
introduced(assumption,[]) ).
thf(h31,assumption,
cF @ eigen__5,
introduced(assumption,[]) ).
thf(17,plain,
( ~ sP13
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h30,h31,h28,h29,h27,h12,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0])],[17,h26,h12]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h12,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h30,h31])],[h28,18,h30,h31]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h27,h12,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h28,h29])],[h27,19,h28,h29]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__5)],[h2,20,h27]) ).
thf(h32,assumption,
~ ( ~ ( ( cP @ eigen__6 )
=> ~ sP8 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( ( cP @ eigen__6 )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h34,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h35,assumption,
cP @ eigen__6,
introduced(assumption,[]) ).
thf(h36,assumption,
sP8,
introduced(assumption,[]) ).
thf(22,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP3
| ~ sP8
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h35,h36,h33,h34,h32,h13,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0])],[22,23,h13,h36,h34]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h34,h32,h13,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h35,h36])],[h33,24,h35,h36]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h13,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h33,h34])],[h32,25,h33,h34]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h13,h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__6)],[h2,26,h32]) ).
thf(28,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h25,h26,h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h4,21,27,h12,h13]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h24,28,h25,h26]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h24]),tab_negall(eigenvar,eigen__4)],[h8,29,h24]) ).
thf(31,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,16,30,h7,h8]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,31,h5,h6]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,32,h3,h4]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,33,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( sP2
=> ~ ( ! [X1: $i] :
( ~ ( cQ @ X1 )
=> ( cR @ X1 ) )
=> ~ ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cS @ X1 ) ) ) )
=> ~ ( ~ sP13
=> sP14 ) )
=> ! [X1: $i] :
( ~ ( ( cP @ X1 )
=> ~ ( cF @ X1 ) )
=> ( cG @ X1 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN058^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 12 08:11:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % Mode: mode213
% 0.13/0.40 % Inferences: 35
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------