TSTP Solution File: SEU660^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU660^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n016.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 : Tue Jul 19 13:55:38 EDT 2022
% Result : Theorem 26.92s 27.35s
% Output : Proof 26.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 73
% Syntax : Number of formulae : 83 ( 16 unt; 9 typ; 8 def)
% Number of atoms : 193 ( 38 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 340 ( 49 ~; 33 |; 0 &; 187 @)
% ( 30 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 40 con; 0-2 aty)
% Number of variables : 59 ( 6 ^ 53 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cartprod,type,
cartprod: $i > $i > $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_kpair,type,
kpair: $i > $i > $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ ( kpair @ eigen__2 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ eigen__0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
=> ( in @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ( in @ X2 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ eigen__4 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( X3
!= ( kpair @ X4 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ( kpair @ eigen__2 @ eigen__3 )
= ( kpair @ X1 @ X2 ) )
=> ( eigen__3 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ( in @ X2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( X1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ ( kpair @ eigen__2 @ eigen__3 ) @ ( cartprod @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( kpair @ eigen__2 @ eigen__3 )
= ( kpair @ eigen__4 @ eigen__5 ) )
=> ( eigen__3 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__5 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
=> ( in @ X4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( ( kpair @ eigen__2 @ eigen__3 )
= ( kpair @ eigen__4 @ X1 ) )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ eigen__0 @ X1 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__3 = eigen__5 )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__3 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP6
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP6
=> ( in @ eigen__3 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( in @ eigen__3 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ eigen__2 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( in @ eigen__5 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ eigen__4 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( in @ eigen__5 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X2 = X4 ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP1
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( in @ ( kpair @ eigen__2 @ X1 ) @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( kpair @ eigen__2 @ eigen__3 )
!= ( kpair @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
!= ( kpair @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( X1
!= ( kpair @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X2 = X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( kpair @ eigen__2 @ eigen__3 )
= ( kpair @ eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( in @ eigen__4 @ eigen__0 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(def_cartprodmempair1,definition,
cartprodmempair1 = sP1 ).
thf(def_setukpairinjR,definition,
setukpairinjR = sP28 ).
thf(cartprodpairmemER,conjecture,
sP23 ).
thf(h1,negated_conjecture,
~ sP23,
inference(assume_negation,[status(cth)],[cartprodpairmemER]) ).
thf(1,plain,
sP11,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP14
| ~ sP15
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP21
| sP18
| ~ sP8
| ~ sP11 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP28
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP19
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP7
| ~ sP29
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
sP12,
inference(eq_sym,[status(thm)],]) ).
thf(12,plain,
( sP20
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP20
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP2
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(15,plain,
( sP30
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP25
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(17,plain,
( ~ sP1
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP26
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP27
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP16
| ~ sP6
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP17
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP17
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP24
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(24,plain,
( sP4
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(25,plain,
( sP13
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(26,plain,
( sP9
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(27,plain,
( sP22
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP22
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP23
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP23
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,h1]) ).
thf(32,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[31,h0]) ).
thf(0,theorem,
sP23,
inference(contra,[status(thm),contra(discharge,[h1])],[31,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU660^2 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jun 19 06:59:08 EDT 2022
% 0.15/0.36 % CPUTime :
% 26.92/27.35 % SZS status Theorem
% 26.92/27.35 % Mode: mode454
% 26.92/27.35 % Inferences: 836
% 26.92/27.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------