TSTP Solution File: SYO503^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO503^1 : 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 : n021.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 19:33:05 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 67
% Syntax : Number of formulae : 81 ( 24 unt; 7 typ; 2 def)
% Number of atoms : 222 ( 21 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 223 ( 107 ~; 36 |; 0 &; 24 @)
% ( 22 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 28 con; 0-2 aty)
% Number of variables : 5 ( 2 ^ 3 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $o ).
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_b,type,
b: $o ).
thf(ty_g,type,
g: $o > $o ).
thf(ty_f,type,
f: $o > $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] :
( ( f @ X1 )
!= ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $o] :
( ( f @ X1 )
!= ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( p @ f ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> b ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( a = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> eigen__0 ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( f @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( f @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP6
= ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP2 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f @ a ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( f @ sP4 )
= ( g @ sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( f = g ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( a = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o] :
( ( f @ X1 )
= ( g @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( f @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( g @ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( p @ g ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( g @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> a ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( g @ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( g @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(claim,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 )
=> ~ sP20 )
=> ~ sP16 )
=> ~ sP1 )
=> sP17 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 )
=> ~ sP20 )
=> ~ sP16 )
=> ~ sP1 )
=> sP17 ),
inference(assume_negation,[status(cth)],[claim]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 )
=> ~ sP20 )
=> ~ sP16 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 )
=> ~ sP20 )
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 )
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP20,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ( sP19 != sP2 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP5,
introduced(assumption,[]) ).
thf(h12,assumption,
sP19 != sP2,
introduced(assumption,[]) ).
thf(h13,assumption,
sP10,
introduced(assumption,[]) ).
thf(h14,assumption,
sP19,
introduced(assumption,[]) ).
thf(h15,assumption,
sP2,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP13
| ~ sP19
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP16
| sP22
| ~ sP9 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP20
| sP22
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP15
| ~ sP9 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP15
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( sP11
| ~ sP15
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP14
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(9,plain,
( sP12
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP17
| ~ sP12 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h14,h15,h13,h11,h9,h7,h5,h3]) ).
thf(12,plain,
( sP7
| ~ sP2
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP3
| sP19
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| sP18
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP20
| sP18
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP5
| sP6
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP10
| sP6
| ~ sP3 ),
inference(mating_rule,[status(thm)],]) ).
thf(18,plain,
( sP8
| ~ sP6
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP14
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(20,plain,
( sP12
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP1
| sP17
| ~ sP12 ),
inference(mating_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[12,13,14,15,16,17,18,19,20,21,h16,h17,h13,h11,h9,h7,h5,h3]) ).
thf(23,plain,
$false,
inference(tab_be,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_be(discharge,[h14,h15]),tab_be(discharge,[h16,h17])],[h12,11,22,h14,h15,h16,h17]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,23,h12,h13]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,24,h10,h11]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,25,h8,h9]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,26,h6,h7]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,27,h4,h5]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,28,h2,h3]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ( sP19 != sP2 )
=> ~ sP10 )
=> ~ sP5 )
=> ~ sP20 )
=> ~ sP16 )
=> ~ sP1 )
=> sP17 ),
inference(contra,[status(thm),contra(discharge,[h1])],[29,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO503^1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32 % Computer : n021.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Fri Jul 8 22:24:36 EDT 2022
% 0.17/0.32 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % Mode: mode213
% 0.19/0.37 % Inferences: 44
% 0.19/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------