TSTP Solution File: SYO223^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO223^5 : 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 : 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 19:30:57 EDT 2022
% Result : Theorem 2.00s 2.22s
% Output : Proof 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 51
% Syntax : Number of formulae : 56 ( 10 unt; 6 typ; 1 def)
% Number of atoms : 125 ( 15 equ; 3 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 147 ( 38 ~; 27 |; 0 &; 41 @)
% ( 21 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 29 con; 0-2 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 12 ( 1 ^ 11 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cS,type,
cS: $i ).
thf(ty_cP,type,
cP: $i ).
thf(ty_cUNIQUE,type,
cUNIQUE: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cJ,type,
cJ: $i ).
thf(ty_cLIKE,type,
cLIKE: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ( !! @ ( (=) @ X1 ) ) )
=> ~ ( cUNIQUE @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ( !! @ ( (=) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cUNIQUE @ eigen__1 )
=> ~ ( cLIKE @ cJ @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = cS ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( cS = X1 )
=> ( X1 = cS ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( !! @ ( (=) @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( cLIKE @ cJ @ cS ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( cJ = cJ ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cLIKE @ cP @ cS )
= ( cLIKE @ cP @ cS ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cS = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
= ( ~ ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cUNIQUE @ cS ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o] :
( ( ( X1 @ cP )
= ( cLIKE @ cP @ cS ) )
=> ( ( X1 @ cJ )
!= ( ~ ! [X2: $i] :
( ( cUNIQUE @ X2 )
=> ~ ( cLIKE @ cJ @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP13
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP1
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP11
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP13
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cLIKE @ cJ @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( cUNIQUE @ X1 )
=> ~ ( cLIKE @ cJ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP10
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(cLING2,conjecture,
sP16 ).
thf(h1,negated_conjecture,
~ sP16,
inference(assume_negation,[status(cth)],[cLING2]) ).
thf(1,plain,
( sP12
| ~ sP8
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP12
| sP8
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| ~ sP13
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP17
| ~ sP11
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
sP5,
inference(eq_sym,[status(thm)],]) ).
thf(10,plain,
sP9,
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP19
| sP8
| ~ sP9
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( sP3
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP20
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(14,plain,
( ~ sP20
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| ~ sP13
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP1
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP1
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP21
| ~ sP10
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
sP10,
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP16
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP16
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,h1]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
sP16,
inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO223^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % 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 17:22:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.22 % SZS status Theorem
% 2.00/2.22 % Mode: mode506
% 2.00/2.22 % Inferences: 38883
% 2.00/2.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------