TSTP Solution File: SYO314^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO314^5 : 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 : n003.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 19:31:24 EDT 2022
% Result : Theorem 25.91s 26.09s
% Output : Proof 25.91s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_z,type,
z: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i > $o ).
thf(ty_eigen__5,type,
eigen__5: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ z ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP1
=> ~ ( eigen__1 @ X1 ) )
=> ~ ( eigen__0 @ eigen__2 ) )
=> ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__5 @ z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP1
=> ~ ( eigen__1 @ X2 ) )
=> ~ ( eigen__0 @ X1 ) )
=> ( eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ~ sP1
=> ~ ( eigen__1 @ eigen__3 ) )
=> ~ ( eigen__0 @ eigen__2 ) )
=> ( eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ sP1
=> ~ ( eigen__1 @ eigen__3 ) )
=> ~ ( eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ( X1 @ X3 )
=> ( X1 @ X4 ) )
=> ~ ( X2 @ X4 ) )
=> ( X2 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP1
=> ~ ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP9
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( X1 @ z )
=> ~ ( X1 @ X3 ) )
=> ~ ( eigen__0 @ X2 ) )
=> ( eigen__0 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( X2 @ z )
=> ~ ( X2 @ X4 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ~ sP12
=> ~ ( eigen__5 @ eigen__7 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__4 @ X1 )
=> ( eigen__4 @ X2 ) )
=> ~ ( eigen__5 @ X2 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ ( ~ ( sP9
=> ( eigen__4 @ X1 ) )
=> ~ ( eigen__5 @ X1 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__4 @ X2 )
=> ( eigen__4 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP12
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(cSILLYWFF2,conjecture,
( ( ~ sP10 )
= ( ~ sP15 ) ) ).
thf(h0,negated_conjecture,
( ~ sP10 )
!= ( ~ sP15 ),
inference(assume_negation,[status(cth)],[cSILLYWFF2]) ).
thf(h1,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
sP15,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ( eigen__0 @ X3 ) )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ z ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ( eigen__0 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
( ~ ( ~ ( sP8
=> ( eigen__0 @ X1 ) )
=> ~ ( eigen__1 @ X1 ) )
=> sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ~ ( sP8
=> sP20 )
=> ~ sP14 )
=> sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( sP8
=> sP20 )
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP8
=> sP20 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP14,
introduced(assumption,[]) ).
thf(h13,assumption,
sP8,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP6
| sP7
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP11
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP1
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP15
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0])],[1,2,3,4,5,6,7,h13,h14,h12,h10,h2]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,8,h13,h14]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,9,h11,h12]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h7,h6,h5,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,10,h9,h10]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,11,h8]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,12,h7]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,13,h6]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h1,14,h5]) ).
thf(h15,assumption,
~ ! [X1: $i > $o,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( X1 @ z )
=> ~ ( X1 @ X3 ) )
=> ~ ( eigen__4 @ X2 ) )
=> ( eigen__4 @ X3 ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP4
=> ~ ( eigen__5 @ X2 ) )
=> ~ ( eigen__4 @ X1 ) )
=> ( eigen__4 @ X2 ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
~ ! [X1: $i] :
( ~ ( ~ ( ~ sP4
=> ~ ( eigen__5 @ X1 ) )
=> ~ sP9 )
=> ( eigen__4 @ X1 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ~ ( ~ ( ~ sP4
=> ~ sP18 )
=> ~ sP9 )
=> sP2 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ~ sP4
=> ~ sP18 )
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ sP4
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP9,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h24,assumption,
sP18,
introduced(assumption,[]) ).
thf(16,plain,
( ~ sP19
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| sP22
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| sP12
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP17
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP12
| ~ sP9
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP21
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP10
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h18,h17,h16,h15,h3,h4,h0])],[16,17,18,19,20,21,22,h3,h23,h24,h22,h20]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h18,h17,h16,h15,h3,h4,h0]),tab_negimp(discharge,[h23,h24])],[h21,23,h23,h24]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h17,h16,h15,h3,h4,h0]),tab_negimp(discharge,[h21,h22])],[h19,24,h21,h22]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h17,h16,h15,h3,h4,h0]),tab_negimp(discharge,[h19,h20])],[h18,25,h19,h20]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h16,h15,h3,h4,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__7)],[h17,26,h18]) ).
thf(28,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h16,h15,h3,h4,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__6)],[h16,27,h17]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h3,h4,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h15,28,h16]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h4,29,h15]) ).
thf(31,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,15,30,h1,h2,h3,h4]) ).
thf(0,theorem,
( ( ~ sP10 )
= ( ~ sP15 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[31,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO314^5 : 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
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 00:09:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 25.91/26.09 % SZS status Theorem
% 25.91/26.09 % Mode: mode461
% 25.91/26.09 % Inferences: 312
% 25.91/26.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------