TSTP Solution File: SEU486^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU486^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 : 300s
% DateTime : Thu Aug 31 17:17:48 EDT 2023
% Result : Theorem 0.20s 0.72s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 92
% Syntax : Number of formulae : 105 ( 45 unt; 6 typ; 31 def)
% Number of atoms : 308 ( 78 equ; 4 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1579 ( 341 ~; 29 |; 12 &; 809 @)
% ( 24 <=>; 364 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 59 con; 0-2 aty)
% Number of variables : 470 ( 77 ^; 388 !; 5 ?; 470 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__17,type,
eigen__17: $i > $i > $o ).
thf(ty_eigen__18,type,
eigen__18: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(sP1,plain,
( sP1
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__1 != eigen__3 )
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> ( eigen__18 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 != eigen__2 )
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__17 @ X1 @ X2 )
=> ~ ( eigen__17 @ X2 @ X3 ) )
=> ( eigen__17 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__17 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__18 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__18 @ X1 @ X2 )
=> ~ ( eigen__18 @ X2 @ X3 ) )
=> ( eigen__18 @ X1 @ X3 ) )
=> ~ sP6 )
=> ( eigen__18 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__18 @ X1 @ X2 )
=> ~ ( eigen__18 @ X2 @ X3 ) )
=> ( eigen__18 @ X1 @ X3 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( sP2
=> ~ sP4 )
=> ~ ! [X1: $i] :
( ( ( eigen__3 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
=> ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__17 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__18 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i] :
( ~ ( ( ( eigen__1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__1 @ X2 ) ) )
=> ~ ( ( eigen__1 != X1 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__1 @ X1 ) ) ) )
=> ~ ! [X3: $i] :
( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP2
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__18 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP5
=> ( eigen__17 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ~ ( ( ( eigen__1 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) )
=> ~ sP4 )
=> ~ ! [X2: $i] :
( ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ( ( eigen__2 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP1
=> ( eigen__17 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( ( eigen__3 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
=> ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__17 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__17 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) )
=> ~ ( ( X1 != X2 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X2 ) ) ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X3 @ X4 )
@ ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_inv,definition,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_idem,definition,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ ( X1 @ X2 ) )
= ( X1 @ X2 ) ) ) ) ).
thf(def_infl,definition,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).
thf(def_mono,definition,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( subrel @ X2 @ X3 )
@ ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irrefl,definition,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 @ X2 ) ) ) ) ).
thf(def_rc,definition,
( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_symm,definition,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X2 ) )
@ ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( (~) @ ( X1 @ X3 @ X2 ) ) ) ) ) ).
thf(def_sc,definition,
( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
| ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_trans,definition,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_tc,definition,
( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( trans @ X4 )
& ( subrel @ X1 @ X4 ) )
@ ( X4 @ X2 @ X3 ) ) ) ) ).
thf(def_trc,definition,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).
thf(def_trsc,definition,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: $i > $i > $o] :
( ( refl @ X1 )
& ( antisymm @ X1 )
& ( trans @ X1 ) ) ) ) ).
thf(def_so,definition,
( so
= ( ^ [X1: $i > $i > $o] :
( ( asymm @ X1 )
& ( trans @ X1 ) ) ) ) ).
thf(def_total,definition,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 @ X2 @ X3 )
| ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_term,definition,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ? [X3: $i] : ( X2 @ X3 )
@ ? [X3: $i] :
( ( X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X2 @ X4 )
@ ( (~) @ ( X1 @ X3 @ X4 ) ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( tc @ X1 @ X3 @ X4 )
@ ( X2 @ X4 ) )
@ ( X2 @ X3 ) )
@ ! [X3: $i] : ( X2 @ X3 ) ) ) ) ).
thf(def_innf,definition,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
( (~)
@ ? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_nfof,definition,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( trc @ X1 @ X3 @ X2 )
& ( innf @ X1 @ X2 ) ) ) ) ).
thf(def_norm,definition,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] : ( nfof @ X1 @ X3 @ X2 ) ) ) ).
thf(def_join,definition,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
? [X4: $i] :
( ( trc @ X1 @ X2 @ X4 )
& ( trc @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_lconfl,definition,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X4 )
& ( X1 @ X2 @ X3 ) )
@ ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_sconfl,definition,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X4 )
& ( trc @ X1 @ X2 @ X3 ) )
@ ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_confl,definition,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( trc @ X1 @ X2 @ X4 )
& ( trc @ X1 @ X2 @ X3 ) )
@ ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_cr,definition,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( trsc @ X1 @ X2 @ X3 )
@ ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(confluence_implies_local_confluence,conjecture,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[confluence_implies_local_confluence]) ).
thf(h2,assumption,
~ ( sP24
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP24,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X2 )
=> ~ ( eigen__0 @ eigen__1 @ X1 ) )
=> ~ ! [X3: $i] :
( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ sP1 )
=> ~ ! [X2: $i] :
( ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ( ( eigen__2 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__2 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP20
=> ~ sP1 )
=> ~ sP21 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP20
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP21,
introduced(assumption,[]) ).
thf(h10,assumption,
sP20,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP15
| ~ sP2
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP15
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| ~ sP20
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP16
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP8
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP7
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP12
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).
thf(10,plain,
( sP2
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP19
| ~ sP1
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP22
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( sP5
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP17
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP17
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP14
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__17]) ).
thf(18,plain,
( sP4
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP18
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP13
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP24
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h3,h10,h11,h9]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,22,h10,h11]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,23,h8,h9]) ).
thf(25,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,24,h7]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,25,h6]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,26,h5]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,27,h3,h4]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,28,h2]) ).
thf(30,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[29,h0]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[29,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU486^1 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n012.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 : 300
% 0.13/0.34 % DateTime : Wed Aug 23 15:56:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.72 % SZS status Theorem
% 0.20/0.72 % Mode: cade22grackle2xfee4
% 0.20/0.72 % Steps: 6360
% 0.20/0.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------