TSTP Solution File: SYO042^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO042^2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 19:29:47 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 60
% Syntax : Number of formulae : 84 ( 36 unt; 6 typ; 2 def)
% Number of atoms : 214 ( 32 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 160 ( 76 ~; 32 |; 0 &; 15 @)
% ( 18 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 24 con; 0-2 aty)
% Number of variables : 7 ( 4 ^ 3 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_p,type,
p: ( $o > $o ) > $o ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $o ).
thf(ty_y,type,
y: $o ).
thf(ty_g,type,
g: $o > $o ).
thf(ty_x,type,
x: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $o] :
( ( g @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $o] :
( ( g @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( p @ g ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( g
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( g @ eigen__1 )
= ( ~ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> y ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP5 = sP6 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( g @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP8
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( x = sP5 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( g @ x ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> x ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( p
@ ^ [X1: $o] : ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( g @ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP6 = sP2 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o] :
( ( g @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP2 = sP12 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( g @ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(4,conjecture,
( ~ ( ~ ( ~ ( ( sP12 != sP6 )
=> ( sP11 != sP6 ) )
=> ( sP18 != sP12 ) )
=> ~ sP1 )
=> sP13 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ( sP12 != sP6 )
=> ( sP11 != sP6 ) )
=> ( sP18 != sP12 ) )
=> ~ sP1 )
=> sP13 ),
inference(assume_negation,[status(cth)],[4]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ( sP12 != sP6 )
=> ( sP11 != sP6 ) )
=> ( sP18 != sP12 ) )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ( sP12 != sP6 )
=> ( sP11 != sP6 ) )
=> ( sP18 != sP12 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ( sP12 != sP6 )
=> ( sP11 != sP6 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP18 = sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP12 != sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
sP11 = sP6,
introduced(assumption,[]) ).
thf(h10,assumption,
sP12,
introduced(assumption,[]) ).
thf(h11,assumption,
sP6,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h14,assumption,
sP11,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h16,assumption,
sP18,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h10,h14,h11,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h11,h11]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h12,h14,h11,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h11,h11]) ).
thf(3,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h11,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h16,h10]),tab_bq(discharge,[h17,h12])],[h7,1,2,h16,h10,h17,h12]) ).
thf('4_001',plain,
( sP15
| sP6
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP17
| ~ sP2
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP18
| sP8
| ~ sP15 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP11
| ~ sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( sP9
| ~ sP8
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP9
| sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP16
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(11,plain,
( sP3
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP13
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h10,h15,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[4,5,6,7,8,9,10,11,12,h15,h13,h16,h10,h5,h3]) ).
thf(14,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h12,h15,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h10,h12]) ).
thf(15,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h15,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h16,h10]),tab_bq(discharge,[h17,h12])],[h7,13,14,h16,h10,h17,h12]) ).
thf(16,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h14,h11]),tab_bq(discharge,[h15,h13])],[h9,3,15,h14,h11,h15,h13]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h10,h14,h11,h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h10,h12]) ).
thf(18,plain,
( sP10
| sP12
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP7
| ~ sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP11
| sP14
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP14
| sP18
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(22,plain,
( sP4
| ~ sP14
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP4
| sP14
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP16
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(25,plain,
( sP3
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP1
| sP13
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h12,h14,h11,h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[18,19,20,21,22,23,24,25,26,h14,h11,h17,h12,h5,h3]) ).
thf(28,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h11,h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h16,h10]),tab_bq(discharge,[h17,h12])],[h7,17,27,h16,h10,h17,h12]) ).
thf(29,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h10,h15,h13,h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h13,h13]) ).
thf(30,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h12,h15,h13,h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h13,h13]) ).
thf(31,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h15,h13,h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h16,h10]),tab_bq(discharge,[h17,h12])],[h7,29,30,h16,h10,h17,h12]) ).
thf(32,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h12,h13,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h14,h11]),tab_bq(discharge,[h15,h13])],[h9,28,31,h14,h11,h15,h13]) ).
thf(33,plain,
$false,
inference(tab_be,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h8,16,32,h10,h11,h12,h13]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,33,h8,h9]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,34,h6,h7]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,35,h4,h5]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,36,h2,h3]) ).
thf(38,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[37,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ( sP12 != sP6 )
=> ( sP11 != sP6 ) )
=> ( sP18 != sP12 ) )
=> ~ sP1 )
=> sP13 ),
inference(contra,[status(thm),contra(discharge,[h1])],[37,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO042^2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Fri Jul 8 19:44:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % Mode: mode213
% 0.20/0.39 % Inferences: 52
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------