TSTP Solution File: SYO276^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO276^5 : 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 : n029.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 19:31:13 EDT 2022
% Result : Theorem 1.98s 2.22s
% Output : Proof 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 51 ( 11 unt; 7 typ; 2 def)
% Number of atoms : 96 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 123 ( 28 ~; 20 |; 0 &; 38 @)
% ( 18 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 25 con; 0-2 aty)
% Number of variables : 17 ( 2 ^ 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_s,type,
s: $i > $i ).
thf(ty_n,type,
n: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_cO,type,
cO: $i ).
thf(ty_m,type,
m: $i ).
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] :
~ ! [X2: $i] :
( ( X2 = X1 )
=> ( ( s @ X2 )
= ( s @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( X1 = eigen__1 )
=> ( ( s @ X1 )
= ( s @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i > $i > $o] :
( ~ ( ( X1 @ cO @ cO )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( s @ X2 ) @ ( s @ X3 ) ) ) )
=> ( X1 @ n @ m ) )
=> ~ ( cP @ n ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__2 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( m = n ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cO = cO ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cP @ n ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( X2 = X1 )
=> ( ( s @ X2 )
= ( s @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( s @ eigen__2 )
= ( s @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP4
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( n = m ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( m = X1 )
=> ( X1 = m ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cP @ m ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP1
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP2
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP3
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP8
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $i > $o] :
( ~ ( ( X1 @ cO @ cO )
=> ~ ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( s @ X2 ) @ ( s @ X3 ) ) ) )
=> ( X1 @ n @ m ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( X1 = eigen__1 )
=> ( ( s @ X1 )
= ( s @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(cBLEDSOE_FENG_SV_I2,conjecture,
sP12 ).
thf(h1,negated_conjecture,
~ sP12,
inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_SV_I2]) ).
thf(1,plain,
( sP7
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP13
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP13
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP18
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(5,plain,
( sP6
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(6,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP4
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP16
| sP8
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP15
| ~ sP3
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP14
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
sP14,
inference(eq_sym,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP11
| ~ sP9 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( sP1
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP1
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP12
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,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,h1]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
sP12,
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO276^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n029.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 : Fri Jul 8 22:02:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.22 % SZS status Theorem
% 1.98/2.22 % Mode: mode506
% 1.98/2.22 % Inferences: 60231
% 1.98/2.22 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------