TSTP Solution File: ITP210^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP210^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : Sun Jul 17 00:29:33 EDT 2022
% Result : Theorem 23.91s 23.90s
% Output : Proof 23.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 82
% Syntax : Number of formulae : 97 ( 28 unt; 8 typ; 2 def)
% Number of atoms : 235 ( 27 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 328 ( 104 ~; 51 |; 0 &; 108 @)
% ( 26 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 32 con; 0-2 aty)
% Number of variables : 19 ( 13 ^ 6 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_assn,type,
assn: $tType ).
thf(ty_produc3658429121746597890et_nat,type,
produc3658429121746597890et_nat: $tType ).
thf(ty_abs_assn,type,
abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
thf(ty_eigen__1,type,
eigen__1: produc3658429121746597890et_nat ).
thf(ty_y,type,
y: assn ).
thf(ty_eigen__3,type,
eigen__3: produc3658429121746597890et_nat ).
thf(ty_rep_assn,type,
rep_assn: assn > produc3658429121746597890et_nat > $o ).
thf(ty_x,type,
x: assn ).
thf(h0,assumption,
! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: produc3658429121746597890et_nat] :
( ( ~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
!= ( ~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: produc3658429121746597890et_nat] :
( ( ~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
!= ( ~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( x
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) )
=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) )
= x ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( ( rep_assn @ x @ eigen__1 )
=> ~ ( rep_assn @ y @ eigen__1 ) ) )
= ( ~ ( ( rep_assn @ y @ eigen__1 )
=> ~ ( rep_assn @ x @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( rep_assn @ x @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( rep_assn @ y @ eigen__1 )
=> ~ ( rep_assn @ x @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( rep_assn @ y @ eigen__3 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( rep_assn @ y @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( rep_assn @ x @ eigen__1 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( rep_assn @ x @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ~ ( sP4
=> ~ ( rep_assn @ y @ eigen__3 ) ) )
= ( ~ sP6 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( x = x ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( x
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( x
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: produc3658429121746597890et_nat] :
( ( ~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= ( ~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( rep_assn @ y @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( y
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: assn] :
( ( x = X1 )
=> ( X1 = x ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: assn,X2: assn] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP4
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= ( ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ x @ X1 )
=> ~ ( rep_assn @ y @ X1 ) ) )
= ( abs_assn
@ ^ [X1: produc3658429121746597890et_nat] :
~ ( ( rep_assn @ y @ X1 )
=> ~ ( rep_assn @ x @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP13
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( y = y ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(conj_0,conjecture,
( ( ~ ( sP13
=> sP1 ) )
= ( ~ ( sP13
=> sP17 ) ) ) ).
thf(h1,negated_conjecture,
( ~ ( sP13
=> sP1 ) )
!= ( ~ ( sP13
=> sP17 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h2,assumption,
~ ( sP13
=> sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP13
=> sP17 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( sP13
=> sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
( sP13
=> sP17 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP13,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h9,assumption,
sP17,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h8,h6,h7,h2,h3,h1,h0])],[h6,h8]) ).
thf(2,plain,
( ~ sP13
| sP14
| ~ sP12
| ~ sP24 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP14
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP18
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP9
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| ~ sP10
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
sP26,
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| ~ sP7
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP3
| sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP3
| ~ sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP15
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(15,plain,
( sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP17
| sP1
| ~ sP23
| ~ sP26 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(18,plain,
sP12,
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP19
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
sP19,
inference(eq_sym,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h6,h7,h2,h3,h1,h0])],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,h6,h7,h9]) ).
thf(22,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h6,h7,h2,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h3,1,21,h8,h9]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h2,22,h6,h7]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(24,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h11,h8,h4,h5,h1,h0])],[h6,h8]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h4,h5,h1,h0]),tab_negimp(discharge,[h6,h11])],[h5,24,h6,h11]) ).
thf(26,plain,
( sP20
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
sP22,
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP4
| sP16
| ~ sP1
| ~ sP22 ),
inference(mating_rule,[status(thm)],]) ).
thf(29,plain,
( sP6
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP20
| ~ sP4
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP6
| ~ sP16
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP11
| sP20
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP11
| ~ sP20
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP15
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(35,plain,
( sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP13
| sP14
| ~ sP8
| ~ sP24 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP1
| sP17
| ~ sP1
| ~ sP14 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP25
| ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP18
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP19
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
sP19,
inference(eq_sym,[status(thm)],]) ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h11,h10,h4,h5,h1,h0])],[26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,h10,h6,h11]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h4,h5,h1,h0]),tab_negimp(discharge,[h6,h11])],[h5,43,h6,h11]) ).
thf(45,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h5,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h10])],[h4,25,44,h8,h10]) ).
thf(46,plain,
$false,
inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,23,45,h2,h3,h4,h5]) ).
thf(47,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[46,h0]) ).
thf(0,theorem,
( ( ~ ( sP13
=> sP1 ) )
= ( ~ ( sP13
=> sP17 ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[46,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP210^1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jun 3 10:48:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 23.91/23.90 % SZS status Theorem
% 23.91/23.90 % Mode: mode9a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 23.91/23.90 % Inferences: 284
% 23.91/23.90 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------