TSTP Solution File: SEU668^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU668^2 : 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 : n020.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 13:56:05 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 94
% Syntax : Number of formulae : 111 ( 28 unt; 11 typ; 6 def)
% Number of atoms : 301 ( 61 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 740 ( 129 ~; 34 |; 0 &; 415 @)
% ( 32 <=>; 130 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 44 con; 0-2 aty)
% Number of variables : 129 ( 19 ^ 110 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $i > $o ).
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_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $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__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( in @ X1 @ eigen__1 )
=> ~ ( eigen__2 @ eigen__5 @ X1 ) )
=> ( ( kpair @ eigen__3 @ eigen__4 )
!= ( kpair @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ~ ( ( in @ X2 @ eigen__1 )
=> ~ ( eigen__2 @ X1 @ X2 ) )
=> ( ( kpair @ eigen__3 @ eigen__4 )
!= ( kpair @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( in @ ( kpair @ eigen__3 @ eigen__4 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__1 )
=> ~ ( eigen__2 @ X2 @ X3 ) )
=> ( X1
!= ( kpair @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__4 = eigen__6 )
=> ( eigen__6 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( ( kpair @ eigen__3 @ eigen__4 )
= ( kpair @ X1 @ X2 ) )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ eigen__3 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__1 )
=> ~ ( eigen__2 @ X3 @ X4 ) )
=> ( X2
!= ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ~ ( ( in @ X3 @ eigen__1 )
=> ~ ( eigen__2 @ X2 @ X3 ) )
=> ( X1
!= ( kpair @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( eigen__4 = X1 )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__6 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( ( kpair @ eigen__3 @ eigen__4 )
= ( kpair @ eigen__5 @ X1 ) )
=> ( eigen__4 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__3 = X1 )
=> ( X1 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X2 = X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( ( kpair @ eigen__3 @ eigen__4 )
= ( kpair @ eigen__5 @ X1 ) )
=> ( eigen__3 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ( ( kpair @ eigen__3 @ eigen__4 )
= ( kpair @ X1 @ X2 ) )
=> ( eigen__4 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__3 = eigen__5 )
=> ( eigen__5 = eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ( kpair @ eigen__3 @ eigen__4 )
= ( kpair @ eigen__5 @ eigen__6 ) )
=> ( eigen__3 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( kpair @ eigen__3 @ eigen__4 )
= ( kpair @ eigen__5 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP17
=> ( eigen__4 = eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__2 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP1
=> ~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ~ ( ( in @ X2 @ eigen__1 )
=> ~ ( eigen__2 @ X1 @ X2 ) )
=> ( ( kpair @ eigen__3 @ eigen__4 )
!= ( kpair @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 ) @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__3 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__5 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( in @ eigen__6 @ eigen__1 )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__2 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ~ ( ( in @ X2 @ eigen__1 )
=> ~ ( eigen__2 @ X1 @ X2 ) )
=> ( ( kpair @ eigen__3 @ eigen__4 )
!= ( kpair @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( in @ eigen__5 @ eigen__0 )
=> ! [X1: $i] :
( ~ ( ( in @ X1 @ eigen__1 )
=> ~ ( eigen__2 @ eigen__5 @ X1 ) )
=> ( ( kpair @ eigen__3 @ eigen__4 )
!= ( kpair @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__4 = eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP25
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ~ ( ( in @ X1 @ eigen__1 )
=> ~ ( eigen__2 @ eigen__5 @ X1 ) )
=> ( ( kpair @ eigen__3 @ eigen__4 )
!= ( kpair @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ eigen__3 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( eigen__3 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(def_dsetconstrER,definition,
dsetconstrER = sP5 ).
thf(def_setukpairinjL,definition,
setukpairinjL = sP16 ).
thf(def_setukpairinjR,definition,
setukpairinjR = sP11 ).
thf(def_dpsetconstr,definition,
( dpsetconstr
= ( ^ [X1: $i,X2: $i,X3: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ~ ( ( in @ X6 @ X2 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X4
!= ( kpair @ X5 @ X6 ) ) ) ) ) ) ) ).
thf(dpsetconstrERa,conjecture,
( sP5
=> ( sP16
=> ( sP11
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ( sP16
=> ( sP11
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[dpsetconstrERa]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP16
=> ( sP11
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP16,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP11
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $i > $i > $o,X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ X1 )
@ ^ [X5: $i] :
~ ! [X6: $i] :
( ( in @ X6 @ eigen__0 )
=> ! [X7: $i] :
( ~ ( ( in @ X7 @ X1 )
=> ~ ( X2 @ X6 @ X7 ) )
=> ( X5
!= ( kpair @ X6 @ X7 ) ) ) ) ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i > $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( in @ ( kpair @ X2 @ X3 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X4: $i] :
~ ! [X5: $i] :
( ( in @ X5 @ eigen__0 )
=> ! [X6: $i] :
( ~ ( ( in @ X6 @ eigen__1 )
=> ~ ( X1 @ X5 @ X6 ) )
=> ( X4
!= ( kpair @ X5 @ X6 ) ) ) ) ) )
=> ( X1 @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( in @ ( kpair @ X1 @ X2 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ~ ( ( in @ X5 @ eigen__1 )
=> ~ ( eigen__2 @ X4 @ X5 ) )
=> ( X3
!= ( kpair @ X4 @ X5 ) ) ) ) ) )
=> ( eigen__2 @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ( in @ eigen__3 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__1 )
=> ~ ( eigen__2 @ X3 @ X4 ) )
=> ( X2
!= ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ( eigen__2 @ eigen__3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
in @ eigen__3 @ eigen__0,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( in @ ( kpair @ eigen__3 @ X1 )
@ ( dsetconstr @ ( cartprod @ eigen__0 @ eigen__1 )
@ ^ [X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ~ ( ( in @ X4 @ eigen__1 )
=> ~ ( eigen__2 @ X3 @ X4 ) )
=> ( X2
!= ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ( eigen__2 @ eigen__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( ( in @ eigen__4 @ eigen__1 )
=> ( sP1
=> sP26 ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
in @ eigen__4 @ eigen__1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP1
=> sP26 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP19
| sP26
| ~ sP23
| ~ sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| ~ sP29
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP24
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP14
| ~ sP22
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP24
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP11
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP9
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| ~ sP17
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP32
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP12
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP15
| ~ sP17
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
sP24,
inference(eq_sym,[status(thm)],]) ).
thf(19,plain,
( sP25
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP30
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP30
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP31
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(23,plain,
( sP28
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP27
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(25,plain,
( ~ sP5
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP21
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP6
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP20
| ~ sP1
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h11,h10,h9,h8,h6,h7,h4,h5,h2,h3,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,h2,h4,h6,h17,h18]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,29,h17,h18]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,30,h15,h16]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h13,31,h14]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,32,h12,h13]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h10,33,h11]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h9,34,h10]) ).
thf(36,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h8,35,h9]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h7,36,h8]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,37,h6,h7]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,38,h4,h5]) ).
thf(40,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,39,h2,h3]) ).
thf(41,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[40,h0]) ).
thf(0,theorem,
( sP5
=> ( sP16
=> ( sP11
=> ! [X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 )
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X6: $i] :
~ ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ! [X8: $i] :
( ~ ( ( in @ X8 @ X2 )
=> ~ ( X3 @ X7 @ X8 ) )
=> ( X6
!= ( kpair @ X7 @ X8 ) ) ) ) ) )
=> ( X3 @ X4 @ X5 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[40,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU668^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 03:36:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 22
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------