%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO904^12 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 : Wed Feb 25 09:55:10 AM UTC 2026
% Result : Theorem 130.39s 20.03s
% Output : Refutation 130.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 166
% Number of leaves : 33
% Syntax : Number of formulae : 1081 ( 567 unt; 0 typ; 17 def)
% Number of atoms : 34838 (1085 equ; 0 cnn)
% Maximal formula atoms : 159 ( 32 avg)
% Number of connectives : 90251 (2455 ~;1777 |;5367 &;57730 @)
% ( 17 <=>;10052 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 419 ( 419 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 82 usr; 23 con; 0-3 aty)
% (9510 !!;3343 ??; 0 @@+; 0 @@-)
% Number of variables : 14019 (12686 ^;1331 !; 2 ?;14019 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
v1: mworld > $o ).
thf(func_def_13,type,
v2: mworld > $o ).
thf(func_def_14,type,
v3: mworld > $o ).
thf(func_def_15,type,
v4: mworld > $o ).
thf(func_def_16,type,
v5: mworld > $o ).
thf(func_def_17,type,
v6: mworld > $o ).
thf(func_def_18,type,
v7: mworld > $o ).
thf(func_def_19,type,
v8: mworld > $o ).
thf(func_def_20,type,
v9: mworld > $o ).
thf(func_def_21,type,
v10: mworld > $o ).
thf(func_def_22,type,
v12: mworld > $o ).
thf(func_def_23,type,
v11: mworld > $o ).
thf(func_def_24,type,
v14: mworld > $o ).
thf(func_def_25,type,
v13: mworld > $o ).
thf(func_def_26,type,
v16: mworld > $o ).
thf(func_def_27,type,
v15: mworld > $o ).
thf(func_def_28,type,
v18: mworld > $o ).
thf(func_def_29,type,
v17: mworld > $o ).
thf(func_def_30,type,
v19: mworld > $o ).
thf(func_def_31,type,
v21: mworld > $o ).
thf(func_def_32,type,
v20: mworld > $o ).
thf(func_def_33,type,
v23: mworld > $o ).
thf(func_def_34,type,
v22: mworld > $o ).
thf(func_def_35,type,
v25: mworld > $o ).
thf(func_def_36,type,
v24: mworld > $o ).
thf(func_def_37,type,
v27: mworld > $o ).
thf(func_def_38,type,
v26: mworld > $o ).
thf(func_def_39,type,
v28: mworld > $o ).
thf(func_def_54,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
sK2: mworld ).
thf(func_def_56,type,
sK3: mworld > mworld ).
thf(func_def_57,type,
sK4: mworld > mworld ).
thf(func_def_58,type,
sK5: mworld > mworld ).
thf(func_def_59,type,
sK6: mworld > mworld ).
thf(func_def_60,type,
sK7: mworld > mworld ).
thf(func_def_61,type,
sK8: mworld > mworld ).
thf(func_def_62,type,
sK9: mworld > mworld ).
thf(func_def_63,type,
sK10: mworld > mworld ).
thf(func_def_64,type,
sK11: mworld > mworld ).
thf(func_def_65,type,
sK12: mworld > mworld ).
thf(func_def_66,type,
sK13: mworld > mworld ).
thf(func_def_67,type,
sK14: mworld > mworld ).
thf(func_def_68,type,
sK15: mworld > mworld ).
thf(func_def_69,type,
sK16: mworld > mworld ).
thf(func_def_70,type,
sK17: mworld > mworld ).
thf(func_def_71,type,
sK18: mworld > mworld ).
thf(func_def_72,type,
sK19: mworld > mworld ).
thf(func_def_73,type,
sK20: mworld > mworld ).
thf(func_def_74,type,
sK21: mworld > mworld ).
thf(func_def_75,type,
sK22: mworld > mworld ).
thf(func_def_76,type,
sK23: mworld > mworld ).
thf(func_def_77,type,
sK24: mworld > mworld ).
thf(func_def_78,type,
sK25: mworld > mworld ).
thf(func_def_79,type,
sK26: mworld > mworld ).
thf(func_def_80,type,
sK27: mworld > mworld ).
thf(f4811,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1048,f2396,f2551,f2927,f2990,f3111,f3142,f3401,f3930,f4004,f4079,f4218,f4483,f4484,f4616,f4740,f4745,f4810]) ).
thf(f4810,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[status(thm)],[f4809]) ).
thf(f4809,plain,
( $false
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f4806]) ).
thf(f4806,plain,
( ( $true = $false )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f2702,f4798]) ).
thf(f4798,plain,
( ! [X17: mworld] :
( ( v5 @ X17 )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f4797]) ).
thf(f4797,plain,
( ! [X17: mworld] :
( ( $true
=> ( v5 @ X17 ) )
= $true )
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f4796,f358]) ).
thf(f358,plain,
! [X2: mworld,X1: mworld] :
( ( mrel @ X2 @ X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f357]) ).
thf(f357,plain,
! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] : ( mrel @ Y0 @ X1 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f356]) ).
thf(f356,plain,
! [X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] : ( mrel @ Y0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f355]) ).
thf(f355,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] : ( mrel @ Y1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f226]) ).
thf(f226,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] : ( mrel @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
thf(f93,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( !! @ mworld
@ ^ [Y1: mworld] : ( mrel @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld,X4: mworld] : ( mrel @ X2 @ X4 ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mrel_universal) ).
thf(f4796,plain,
( ! [X16: mworld,X17: mworld] :
( ( ( mrel @ X16 @ X17 )
=> ( v5 @ X17 ) )
= $true )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f4795]) ).
thf(f4795,plain,
( ! [X16: mworld,X17: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v5 @ Y0 ) )
@ X17 ) )
| ~ spl0_14 ),
inference(pi_clausification,[status(thm)],[f4788]) ).
thf(f4788,plain,
( ! [X16: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v5 @ Y0 ) ) )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f4787]) ).
thf(f4787,plain,
( ! [X16: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v5 @ Y0 ) ) ) )
= $true )
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f4786,f358]) ).
thf(f4786,plain,
( ! [X16: mworld,X15: mworld] :
( $true
= ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( v5 @ Y0 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f4785]) ).
thf(f4785,plain,
( ! [X16: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) )
@ X16 )
= $true )
| ~ spl0_14 ),
inference(pi_clausification,[status(thm)],[f4777]) ).
thf(f4777,plain,
( ! [X15: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f4776]) ).
thf(f4776,plain,
( ! [X15: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f4775,f358]) ).
thf(f4775,plain,
( ! [X14: mworld,X15: mworld] :
( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v5 @ Y1 ) ) ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f4774]) ).
thf(f4774,plain,
( ! [X14: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) )
@ X15 )
= $true )
| ~ spl0_14 ),
inference(pi_clausification,[status(thm)],[f2124]) ).
thf(f2124,plain,
( ! [X14: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f2123]) ).
thf(f2123,definition,
( spl0_14
<=> ! [X14: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f2702,plain,
! [X23: mworld] :
( $false
= ( v5 @ ( sK27 @ X23 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f2695]) ).
thf(f2695,plain,
! [X23: mworld] :
( ( ~ ( v5 @ ( sK27 @ X23 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2694]) ).
thf(f2694,plain,
! [X23: mworld] :
( $true
= ( ~ ( v5 @ ( sK27 @ X23 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2693,f358]) ).
thf(f2693,plain,
! [X23: mworld] :
( $true
= ( ~ ( v5 @ ( sK27 @ X23 ) )
& ( mrel @ X23 @ ( sK27 @ X23 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2692]) ).
thf(f2692,plain,
! [X23: mworld] :
( ( ^ [Y0: mworld] :
( ~ ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) )
@ ( sK27 @ X23 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f2643]) ).
thf(f2643,plain,
! [X23: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2639]) ).
thf(f2639,plain,
! [X23: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2632]) ).
thf(f2632,plain,
! [X23: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ mworld @ ( mrel @ Y3 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2631]) ).
thf(f2631,plain,
! [X23: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ mworld @ ( mrel @ Y3 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2630,f358]) ).
thf(f2630,plain,
! [X22: mworld,X23: mworld] :
( $true
= ( ( mrel @ X22 @ X23 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ?? @ mworld @ ( mrel @ Y3 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v5 @ Y0 )
& ( mrel @ X23 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2629]) ).
thf(f2629,plain,
! [X22: mworld,X23: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld @ ( mrel @ Y4 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X23 )
= $true ),
inference(pi_clausification,[status(thm)],[f2534]) ).
thf(f2534,plain,
! [X22: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld @ ( mrel @ Y4 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2527]) ).
thf(f2527,plain,
! [X22: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld @ ( mrel @ Y4 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2526]) ).
thf(f2526,plain,
! [X22: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld @ ( mrel @ Y4 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2525,f358]) ).
thf(f2525,plain,
! [X21: mworld,X22: mworld] :
( $true
= ( ( mrel @ X21 @ X22 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ?? @ mworld @ ( mrel @ Y4 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v5 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2524]) ).
thf(f2524,plain,
! [X21: mworld,X22: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld @ ( mrel @ Y5 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X22 )
= $true ),
inference(pi_clausification,[status(thm)],[f2518]) ).
thf(f2518,plain,
! [X21: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld @ ( mrel @ Y5 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2517]) ).
thf(f2517,plain,
! [X21: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld @ ( mrel @ Y5 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f2490,f2515]) ).
thf(f2515,plain,
! [X21: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2490]) ).
thf(f2490,plain,
! [X21: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld @ ( mrel @ Y5 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2489]) ).
thf(f2489,plain,
! [X21: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld @ ( mrel @ Y5 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2488,f358]) ).
thf(f2488,plain,
! [X21: mworld,X20: mworld] :
( ( ( mrel @ X20 @ X21 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ?? @ mworld @ ( mrel @ Y5 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v5 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v6 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2487]) ).
thf(f2487,plain,
! [X21: mworld,X20: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld @ ( mrel @ Y6 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X21 ) ),
inference(pi_clausification,[status(thm)],[f2482]) ).
thf(f2482,plain,
! [X20: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld @ ( mrel @ Y6 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2481]) ).
thf(f2481,plain,
! [X20: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld @ ( mrel @ Y6 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f2474,f2479]) ).
thf(f2479,plain,
! [X20: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2474]) ).
thf(f2474,plain,
! [X20: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld @ ( mrel @ Y6 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2473]) ).
thf(f2473,plain,
! [X20: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld @ ( mrel @ Y6 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2472,f358]) ).
thf(f2472,plain,
! [X19: mworld,X20: mworld] :
( $true
= ( ( mrel @ X19 @ X20 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ?? @ mworld @ ( mrel @ Y6 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v5 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v6 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v7 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2471]) ).
thf(f2471,plain,
! [X19: mworld,X20: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld @ ( mrel @ Y7 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X20 )
= $true ),
inference(pi_clausification,[status(thm)],[f2466]) ).
thf(f2466,plain,
! [X19: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld @ ( mrel @ Y7 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2465]) ).
thf(f2465,plain,
! [X19: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld @ ( mrel @ Y7 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f2464,f1603]) ).
thf(f1603,plain,
! [X1: mworld] :
( ( ?? @ mworld @ ( mrel @ X1 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1601]) ).
thf(f1601,plain,
! [X1: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld @ ( mrel @ Y25 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X1 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1600]) ).
thf(f1600,plain,
! [X1: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld @ ( mrel @ Y25 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X1 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1599,f358]) ).
thf(f1599,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld @ ( mrel @ Y25 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1598]) ).
thf(f1598,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld @ ( mrel @ Y26 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y25 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1597]) ).
thf(f1597,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld @ ( mrel @ Y26 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y25 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1596]) ).
thf(f1596,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld @ ( mrel @ Y26 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y25 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f353,f1594]) ).
thf(f1594,plain,
( ( ?? @ mworld @ ( mrel @ mactual ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f353]) ).
thf(f353,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld @ ( mrel @ Y26 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y25 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f352]) ).
thf(f352,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] : ( mrel @ Y26 @ Y27 ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] : ( mrel @ Y25 @ Y26 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] : ( mrel @ Y24 @ Y25 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] : ( mrel @ Y23 @ Y24 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] : ( mrel @ Y18 @ Y19 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] : ( mrel @ Y17 @ Y18 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] : ( mrel @ Y16 @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] : ( mrel @ Y15 @ Y16 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] : ( mrel @ Y10 @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] : ( mrel @ Y9 @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] : ( mrel @ Y8 @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] : ( mrel @ Y7 @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] : ( mrel @ Y2 @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] : ( mrel @ Y1 @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] : ( mrel @ Y0 @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ mactual ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f351]) ).
thf(f351,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( $true
& ( mrel @ Y26 @ Y27 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f350]) ).
thf(f350,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( $true
& ( mrel @ Y26 @ Y27 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] : ( mrel @ mactual @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f349]) ).
thf(f349,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ( !! @ mworld
@ ^ [Y26: mworld] :
( ( mrel @ Y25 @ Y26 )
=> ( ?? @ mworld
@ ^ [Y27: mworld] :
( $true
& ( mrel @ Y26 @ Y27 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y26: mworld] :
( $true
& ( mrel @ Y25 @ Y26 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y25: mworld] :
( $true
& ( mrel @ Y24 @ Y25 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y24: mworld] :
( $true
& ( mrel @ Y23 @ Y24 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) )
& ( ?? @ mworld
@ ^ [Y23: mworld] :
( ~ ( v5 @ Y23 )
& ( mrel @ Y22 @ Y23 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v6 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v7 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v8 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( $true
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( $true
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( $true
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( $true
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v13 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v14 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v15 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v16 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( $true
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( $true
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( $true
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( $true
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v21 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v22 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v23 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v24 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( $true
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( $true
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( $true
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( $true
& ( mrel @ mactual @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f295]) ).
thf(f295,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v5 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v5 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v6 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v7 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v7 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v8 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v8 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v13 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v13 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v14 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v14 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v16 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v16 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v21 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v22 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v23 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v23 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
@ ^ [Y0: mworld] : $true ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f243,f207,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f209,f209,f209,f209,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f209,f209,f209,f209,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f209,f209,f209,f209,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f209,f209,f209,f209]) ).
thf(f208,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
thf(f110,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mnot_def) ).
thf(f209,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
thf(f184,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f183]) ).
thf(f183,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mdia_def) ).
thf(f201,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
thf(f178,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f177]) ).
thf(f177,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mbox_def) ).
thf(f198,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
thf(f168,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f167]) ).
thf(f167,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mand_def) ).
thf(f207,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
thf(f94,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mlocal_def) ).
thf(f243,plain,
( ( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [Y0: mworld] : $true ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f116]) ).
thf(f116,plain,
( ( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [Y0: mworld] : $true ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
@ ( mdia
@ ^ [Y0: mworld] : $true ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f115]) ).
thf(f115,plain,
( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [X0: mworld] : $true ) )
@ ( mdia
@ ^ [X1: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X3: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [X4: mworld] : $true ) ) )
@ ( mdia
@ ^ [X5: mworld] : $true ) ) )
@ ( mdia
@ ^ [X6: mworld] : $true ) ) )
@ ( mdia
@ ^ [X7: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [X8: mworld] : $true ) ) )
@ ( mdia
@ ^ [X9: mworld] : $true ) ) )
@ ( mdia
@ ^ [X10: mworld] : $true ) ) )
@ ( mdia
@ ^ [X11: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [X12: mworld] : $true ) ) )
@ ( mdia
@ ^ [X13: mworld] : $true ) ) )
@ ( mdia
@ ^ [X14: mworld] : $true ) ) )
@ ( mdia
@ ^ [X15: mworld] : $true ) ) ),
inference(rectify,[status(thm)],[f60]) ).
thf(f60,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mand
@ ( mbox
@ ( mdia
@ ^ [X2: mworld] : $true ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
@ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
@ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
@ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
@ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
@ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
@ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
@ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
@ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
@ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) )
@ ( mdia
@ ^ [X2: mworld] : $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',alt1) ).
thf(f2464,plain,
! [X19: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld @ ( mrel @ Y7 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X19 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2463]) ).
thf(f2463,plain,
! [X19: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld @ ( mrel @ Y7 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X19 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2462,f358]) ).
thf(f2462,plain,
! [X18: mworld,X19: mworld] :
( $true
= ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ?? @ mworld @ ( mrel @ Y7 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v5 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v6 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v7 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v8 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X19 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2461]) ).
thf(f2461,plain,
! [X18: mworld,X19: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld @ ( mrel @ Y8 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X19 )
= $true ),
inference(pi_clausification,[status(thm)],[f2454]) ).
thf(f2454,plain,
! [X18: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld @ ( mrel @ Y8 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2453]) ).
thf(f2453,plain,
! [X18: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld @ ( mrel @ Y8 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f2452,f1603]) ).
thf(f2452,plain,
! [X18: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld @ ( mrel @ Y8 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X18 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2451]) ).
thf(f2451,plain,
! [X18: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld @ ( mrel @ Y8 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X18 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2450,f358]) ).
thf(f2450,plain,
! [X18: mworld,X17: mworld] :
( $true
= ( ( mrel @ X17 @ X18 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ?? @ mworld @ ( mrel @ Y8 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v5 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v6 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v7 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v8 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X18 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2449]) ).
thf(f2449,plain,
! [X18: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld @ ( mrel @ Y9 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X18 )
= $true ),
inference(pi_clausification,[status(thm)],[f2447]) ).
thf(f2447,plain,
! [X17: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld @ ( mrel @ Y9 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2446]) ).
thf(f2446,plain,
! [X17: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld @ ( mrel @ Y9 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2445,f1603]) ).
thf(f2445,plain,
! [X17: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld @ ( mrel @ Y9 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X17 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2444]) ).
thf(f2444,plain,
! [X17: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld @ ( mrel @ Y9 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X17 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2443,f358]) ).
thf(f2443,plain,
! [X16: mworld,X17: mworld] :
( ( ( mrel @ X16 @ X17 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ?? @ mworld @ ( mrel @ Y9 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v5 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v6 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v7 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v8 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X17 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2442]) ).
thf(f2442,plain,
! [X16: mworld,X17: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld @ ( mrel @ Y10 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X17 ) ),
inference(pi_clausification,[status(thm)],[f2437]) ).
thf(f2437,plain,
! [X16: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld @ ( mrel @ Y10 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2436]) ).
thf(f2436,plain,
! [X16: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld @ ( mrel @ Y10 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2435,f1603]) ).
thf(f2435,plain,
! [X16: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld @ ( mrel @ Y10 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X16 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2434]) ).
thf(f2434,plain,
! [X16: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld @ ( mrel @ Y10 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X16 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2433,f358]) ).
thf(f2433,plain,
! [X16: mworld,X15: mworld] :
( $true
= ( ( mrel @ X15 @ X16 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ?? @ mworld @ ( mrel @ Y10 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v5 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v6 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v7 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v8 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X16 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2432]) ).
thf(f2432,plain,
! [X16: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld @ ( mrel @ Y11 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X16 )
= $true ),
inference(pi_clausification,[status(thm)],[f2294]) ).
thf(f2294,plain,
! [X15: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld @ ( mrel @ Y11 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2288]) ).
thf(f2288,plain,
! [X15: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld @ ( mrel @ Y11 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2287]) ).
thf(f2287,plain,
! [X15: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld @ ( mrel @ Y11 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2286,f358]) ).
thf(f2286,plain,
! [X14: mworld,X15: mworld] :
( $true
= ( ( mrel @ X14 @ X15 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ?? @ mworld @ ( mrel @ Y11 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v5 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v6 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v7 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v8 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2285]) ).
thf(f2285,plain,
! [X14: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld @ ( mrel @ Y12 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X15 )
= $true ),
inference(pi_clausification,[status(thm)],[f2257]) ).
thf(f2257,plain,
! [X14: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld @ ( mrel @ Y12 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2177]) ).
thf(f2177,plain,
! [X14: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld @ ( mrel @ Y12 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2176]) ).
thf(f2176,plain,
! [X14: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld @ ( mrel @ Y12 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2175,f358]) ).
thf(f2175,plain,
! [X14: mworld,X13: mworld] :
( $true
= ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ?? @ mworld @ ( mrel @ Y12 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v5 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v6 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v7 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v8 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v13 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2174]) ).
thf(f2174,plain,
! [X14: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld @ ( mrel @ Y13 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X14 )
= $true ),
inference(pi_clausification,[status(thm)],[f2169]) ).
thf(f2169,plain,
! [X13: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld @ ( mrel @ Y13 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2168]) ).
thf(f2168,plain,
! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld @ ( mrel @ Y13 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f2161,f2166]) ).
thf(f2166,plain,
! [X13: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2161]) ).
thf(f2161,plain,
! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld @ ( mrel @ Y13 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2160]) ).
thf(f2160,plain,
! [X13: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld @ ( mrel @ Y13 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2159,f358]) ).
thf(f2159,plain,
! [X12: mworld,X13: mworld] :
( $true
= ( ( mrel @ X12 @ X13 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ?? @ mworld @ ( mrel @ Y13 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v5 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v6 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v7 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v8 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v13 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v14 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2158]) ).
thf(f2158,plain,
! [X12: mworld,X13: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld @ ( mrel @ Y14 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X13 ) ),
inference(pi_clausification,[status(thm)],[f2157]) ).
thf(f2157,plain,
! [X12: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld @ ( mrel @ Y14 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2156]) ).
thf(f2156,plain,
! [X12: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld @ ( mrel @ Y14 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f2153,f2154]) ).
thf(f2154,plain,
! [X12: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2153]) ).
thf(f2153,plain,
! [X12: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld @ ( mrel @ Y14 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2152]) ).
thf(f2152,plain,
! [X12: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld @ ( mrel @ Y14 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2151,f358]) ).
thf(f2151,plain,
! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ?? @ mworld @ ( mrel @ Y14 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v5 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v6 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v7 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v8 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v13 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v14 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v15 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2150]) ).
thf(f2150,plain,
! [X11: mworld,X12: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld @ ( mrel @ Y15 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X12 )
= $true ),
inference(pi_clausification,[status(thm)],[f2149]) ).
thf(f2149,plain,
! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld @ ( mrel @ Y15 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2148]) ).
thf(f2148,plain,
! [X11: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld @ ( mrel @ Y15 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2147,f1603]) ).
thf(f2147,plain,
! [X11: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld @ ( mrel @ Y15 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X11 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2146]) ).
thf(f2146,plain,
! [X11: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld @ ( mrel @ Y15 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X11 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2145,f358]) ).
thf(f2145,plain,
! [X10: mworld,X11: mworld] :
( ( ( mrel @ X10 @ X11 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ?? @ mworld @ ( mrel @ Y15 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v5 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v6 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v7 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v8 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v13 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v14 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v15 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v16 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X11 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2144]) ).
thf(f2144,plain,
! [X10: mworld,X11: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld @ ( mrel @ Y16 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X11 )
= $true ),
inference(pi_clausification,[status(thm)],[f2112]) ).
thf(f2112,plain,
! [X10: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld @ ( mrel @ Y16 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2111]) ).
thf(f2111,plain,
! [X10: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld @ ( mrel @ Y16 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f2110,f1603]) ).
thf(f2110,plain,
! [X10: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld @ ( mrel @ Y16 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X10 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2109]) ).
thf(f2109,plain,
! [X10: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld @ ( mrel @ Y16 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X10 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2108,f358]) ).
thf(f2108,plain,
! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ?? @ mworld @ ( mrel @ Y16 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v5 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v6 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v7 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v8 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v13 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v14 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v15 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v16 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X10 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2107]) ).
thf(f2107,plain,
! [X10: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld @ ( mrel @ Y17 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X10 )
= $true ),
inference(pi_clausification,[status(thm)],[f2106]) ).
thf(f2106,plain,
! [X9: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld @ ( mrel @ Y17 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2105]) ).
thf(f2105,plain,
! [X9: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld @ ( mrel @ Y17 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2104,f1603]) ).
thf(f2104,plain,
! [X9: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld @ ( mrel @ Y17 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X9 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2103]) ).
thf(f2103,plain,
! [X9: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld @ ( mrel @ Y17 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X9 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2102,f358]) ).
thf(f2102,plain,
! [X8: mworld,X9: mworld] :
( ( ( mrel @ X8 @ X9 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ?? @ mworld @ ( mrel @ Y17 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v5 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v6 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v7 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v8 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v13 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v14 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v15 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v16 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X9 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2101]) ).
thf(f2101,plain,
! [X8: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld @ ( mrel @ Y18 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X9 )
= $true ),
inference(pi_clausification,[status(thm)],[f2099]) ).
thf(f2099,plain,
! [X8: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld @ ( mrel @ Y18 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2098]) ).
thf(f2098,plain,
! [X8: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld @ ( mrel @ Y18 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f2097,f1603]) ).
thf(f2097,plain,
! [X8: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld @ ( mrel @ Y18 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X8 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2096]) ).
thf(f2096,plain,
! [X8: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld @ ( mrel @ Y18 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X8 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2095,f358]) ).
thf(f2095,plain,
! [X8: mworld,X7: mworld] :
( ( ( mrel @ X7 @ X8 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ?? @ mworld @ ( mrel @ Y18 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v5 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v6 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v7 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v8 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v13 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v14 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v15 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v16 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X8 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2094]) ).
thf(f2094,plain,
! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld @ ( mrel @ Y19 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X8 )
= $true ),
inference(pi_clausification,[status(thm)],[f1817]) ).
thf(f1817,plain,
! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld @ ( mrel @ Y19 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1811]) ).
thf(f1811,plain,
! [X7: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld @ ( mrel @ Y19 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1810]) ).
thf(f1810,plain,
! [X7: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld @ ( mrel @ Y19 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1809,f358]) ).
thf(f1809,plain,
! [X6: mworld,X7: mworld] :
( $true
= ( ( mrel @ X6 @ X7 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ?? @ mworld @ ( mrel @ Y19 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v5 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v6 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v7 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v8 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v13 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v14 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v15 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v16 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1808]) ).
thf(f1808,plain,
! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld @ ( mrel @ Y20 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f1803]) ).
thf(f1803,plain,
! [X6: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld @ ( mrel @ Y20 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1802]) ).
thf(f1802,plain,
! [X6: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld @ ( mrel @ Y20 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f1793,f1800]) ).
thf(f1800,plain,
! [X6: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1793]) ).
thf(f1793,plain,
! [X6: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld @ ( mrel @ Y20 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1792]) ).
thf(f1792,plain,
! [X6: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld @ ( mrel @ Y20 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1791,f358]) ).
thf(f1791,plain,
! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ?? @ mworld @ ( mrel @ Y20 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v5 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v6 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v7 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v8 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v13 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v14 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v15 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v16 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v21 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1790]) ).
thf(f1790,plain,
! [X6: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld @ ( mrel @ Y21 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f1760]) ).
thf(f1760,plain,
! [X5: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld @ ( mrel @ Y21 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1758]) ).
thf(f1758,plain,
! [X5: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld @ ( mrel @ Y21 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1757]) ).
thf(f1757,plain,
! [X5: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld @ ( mrel @ Y21 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1756,f358]) ).
thf(f1756,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ?? @ mworld @ ( mrel @ Y21 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y18 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v5 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v6 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v7 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) )
& ( ?? @ mworld
@ ^ [Y15: mworld] :
( ~ ( v8 @ Y15 )
& ( mrel @ Y14 @ Y15 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y10 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v13 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v14 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v15 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) )
& ( ?? @ mworld
@ ^ [Y7: mworld] :
( ~ ( v16 @ Y7 )
& ( mrel @ Y6 @ Y7 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y2 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v21 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v22 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v23 @ Y0 )
& ( mrel @ X5 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1755]) ).
thf(f1755,plain,
! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld @ ( mrel @ Y22 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f1627]) ).
thf(f1627,plain,
! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld @ ( mrel @ Y22 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1625]) ).
thf(f1625,plain,
! [X4: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld @ ( mrel @ Y22 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1624]) ).
thf(f1624,plain,
! [X4: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld @ ( mrel @ Y22 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1623,f358]) ).
thf(f1623,plain,
! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ?? @ mworld @ ( mrel @ Y22 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y19 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v5 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v6 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v7 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) )
& ( ?? @ mworld
@ ^ [Y16: mworld] :
( ~ ( v8 @ Y16 )
& ( mrel @ Y15 @ Y16 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y11 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v13 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v14 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v15 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) )
& ( ?? @ mworld
@ ^ [Y8: mworld] :
( ~ ( v16 @ Y8 )
& ( mrel @ Y7 @ Y8 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y3 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v21 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v22 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v23 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1622]) ).
thf(f1622,plain,
! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld @ ( mrel @ Y23 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f1621]) ).
thf(f1621,plain,
! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld @ ( mrel @ Y23 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1620]) ).
thf(f1620,plain,
! [X3: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld @ ( mrel @ Y23 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1619,f1603]) ).
thf(f1619,plain,
! [X3: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld @ ( mrel @ Y23 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X3 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1618]) ).
thf(f1618,plain,
! [X3: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld @ ( mrel @ Y23 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X3 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1617,f358]) ).
thf(f1617,plain,
! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ?? @ mworld @ ( mrel @ Y23 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y20 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v5 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v6 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v7 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) )
& ( ?? @ mworld
@ ^ [Y17: mworld] :
( ~ ( v8 @ Y17 )
& ( mrel @ Y16 @ Y17 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y12 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v13 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v14 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v15 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) )
& ( ?? @ mworld
@ ^ [Y9: mworld] :
( ~ ( v16 @ Y9 )
& ( mrel @ Y8 @ Y9 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y4 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v21 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v22 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v23 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ~ ( v24 @ Y1 )
& ( mrel @ Y0 @ Y1 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1616]) ).
thf(f1616,plain,
! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld @ ( mrel @ Y24 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1615]) ).
thf(f1615,plain,
! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld @ ( mrel @ Y24 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1614]) ).
thf(f1614,plain,
! [X2: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld @ ( mrel @ Y24 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1613,f1603]) ).
thf(f1613,plain,
! [X2: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld @ ( mrel @ Y24 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X2 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1612]) ).
thf(f1612,plain,
! [X2: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld @ ( mrel @ Y24 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X2 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1611,f358]) ).
thf(f1611,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ( mrel @ X1 @ X2 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ?? @ mworld @ ( mrel @ Y24 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y21 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v5 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v6 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v7 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) )
& ( ?? @ mworld
@ ^ [Y18: mworld] :
( ~ ( v8 @ Y18 )
& ( mrel @ Y17 @ Y18 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y13 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v13 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v14 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v15 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) )
& ( ?? @ mworld
@ ^ [Y10: mworld] :
( ~ ( v16 @ Y10 )
& ( mrel @ Y9 @ Y10 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y5 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v21 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v22 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v23 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) )
& ( ?? @ mworld
@ ^ [Y2: mworld] :
( ~ ( v24 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1610]) ).
thf(f1610,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld @ ( mrel @ Y25 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1608]) ).
thf(f1608,plain,
! [X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld @ ( mrel @ Y25 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1607]) ).
thf(f1607,plain,
! [X1: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( ( !! @ mworld
@ ^ [Y25: mworld] :
( ( mrel @ Y24 @ Y25 )
=> ( ?? @ mworld @ ( mrel @ Y25 ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y24 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y23 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y22 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) )
& ( ?? @ mworld
@ ^ [Y22: mworld] :
( ~ ( v5 @ Y22 )
& ( mrel @ Y21 @ Y22 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) )
& ( ?? @ mworld
@ ^ [Y21: mworld] :
( ~ ( v6 @ Y21 )
& ( mrel @ Y20 @ Y21 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) )
& ( ?? @ mworld
@ ^ [Y20: mworld] :
( ~ ( v7 @ Y20 )
& ( mrel @ Y19 @ Y20 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) )
& ( ?? @ mworld
@ ^ [Y19: mworld] :
( ~ ( v8 @ Y19 )
& ( mrel @ Y18 @ Y19 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y17 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y16 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y15 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y14 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) )
& ( ?? @ mworld
@ ^ [Y14: mworld] :
( ~ ( v13 @ Y14 )
& ( mrel @ Y13 @ Y14 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) )
& ( ?? @ mworld
@ ^ [Y13: mworld] :
( ~ ( v14 @ Y13 )
& ( mrel @ Y12 @ Y13 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) )
& ( ?? @ mworld
@ ^ [Y12: mworld] :
( ~ ( v15 @ Y12 )
& ( mrel @ Y11 @ Y12 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) )
& ( ?? @ mworld
@ ^ [Y11: mworld] :
( ~ ( v16 @ Y11 )
& ( mrel @ Y10 @ Y11 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y9 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y8 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y7 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y6 ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) )
& ( ?? @ mworld
@ ^ [Y6: mworld] :
( ~ ( v21 @ Y6 )
& ( mrel @ Y5 @ Y6 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) )
& ( ?? @ mworld
@ ^ [Y5: mworld] :
( ~ ( v22 @ Y5 )
& ( mrel @ Y4 @ Y5 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) )
& ( ?? @ mworld
@ ^ [Y4: mworld] :
( ~ ( v23 @ Y4 )
& ( mrel @ Y3 @ Y4 ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
& ( ?? @ mworld
@ ^ [Y3: mworld] :
( ~ ( v24 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y1 ) ) ) ) )
& ( ?? @ mworld @ ( mrel @ Y0 ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f1601,f1603]) ).
thf(f4745,plain,
( spl0_21
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f4744,f1046,f2908]) ).
thf(f2908,definition,
( spl0_21
<=> ! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f1046,definition,
( spl0_6
<=> ! [X19: mworld] :
( $true
= ( v10 @ X19 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f4744,plain,
( ! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) )
= $true )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f4743]) ).
thf(f4743,plain,
( ! [X13: mworld] :
( ( $true = $false )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) )
= $true ) )
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f4742]) ).
thf(f4742,plain,
( ! [X13: mworld] :
( ( ( ~ $true ) = $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) )
= $true ) )
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f3092,f1047]) ).
thf(f1047,plain,
( ! [X19: mworld] :
( $true
= ( v10 @ X19 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f1046]) ).
thf(f3092,plain,
! [X12: mworld,X13: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) )
= $true )
| ( $true
= ( ~ ( v10 @ X12 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f3091]) ).
thf(f3091,plain,
! [X12: mworld,X13: mworld] :
( ( $true
= ( ~ ( v10 @ X12 ) ) )
| ( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f3089,f358]) ).
thf(f3089,plain,
! [X12: mworld,X13: mworld] :
( ( ( ( mrel @ X12 @ X13 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) ) )
= $true )
| ( $true
= ( ~ ( v10 @ X12 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3087]) ).
thf(f3087,plain,
! [X12: mworld,X13: mworld] :
( ( $true
= ( ~ ( v10 @ X12 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) )
@ X13 ) ) ),
inference(pi_clausification,[status(thm)],[f2142]) ).
thf(f2142,plain,
! [X12: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( v10 @ X12 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2079]) ).
thf(f2079,plain,
! [X12: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
| ~ ( v10 @ X12 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2078]) ).
thf(f2078,plain,
! [X12: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
| ~ ( v10 @ X12 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2077,f358]) ).
thf(f2077,plain,
! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v5 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y0 ) ) ) )
| ~ ( v10 @ X12 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2076]) ).
thf(f2076,plain,
! [X11: mworld,X12: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) )
@ X12 ) ),
inference(pi_clausification,[status(thm)],[f2071]) ).
thf(f2071,plain,
! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2070]) ).
thf(f2070,plain,
! [X11: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2069,f358]) ).
thf(f2069,plain,
! [X10: mworld,X11: mworld] :
( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v5 @ Y5 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y1 ) ) ) )
| ~ ( v10 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2068]) ).
thf(f2068,plain,
! [X10: mworld,X11: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) )
@ X11 )
= $true ),
inference(pi_clausification,[status(thm)],[f2063]) ).
thf(f2063,plain,
! [X10: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2062]) ).
thf(f2062,plain,
! [X10: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2061,f358]) ).
thf(f2061,plain,
! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v5 @ Y6 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y2 ) ) ) )
| ~ ( v10 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2060]) ).
thf(f2060,plain,
! [X10: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) )
@ X10 ) ),
inference(pi_clausification,[status(thm)],[f2055]) ).
thf(f2055,plain,
! [X9: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2054]) ).
thf(f2054,plain,
! [X9: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2053,f358]) ).
thf(f2053,plain,
! [X8: mworld,X9: mworld] :
( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v5 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y3 ) ) ) )
| ~ ( v10 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2052]) ).
thf(f2052,plain,
! [X8: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) )
@ X9 )
= $true ),
inference(pi_clausification,[status(thm)],[f2047]) ).
thf(f2047,plain,
! [X8: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2046]) ).
thf(f2046,plain,
! [X8: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2045,f358]) ).
thf(f2045,plain,
! [X8: mworld,X7: mworld] :
( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v5 @ Y8 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y4 ) ) ) )
| ~ ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2044]) ).
thf(f2044,plain,
! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true ),
inference(pi_clausification,[status(thm)],[f2039]) ).
thf(f2039,plain,
! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2038]) ).
thf(f2038,plain,
! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2037,f358]) ).
thf(f2037,plain,
! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v5 @ Y9 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y5 ) ) ) )
| ~ ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2036]) ).
thf(f2036,plain,
! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f2031]) ).
thf(f2031,plain,
! [X6: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2030]) ).
thf(f2030,plain,
! [X6: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2029,f358]) ).
thf(f2029,plain,
! [X6: mworld,X5: mworld] :
( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v5 @ Y10 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y6 ) ) ) )
| ~ ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2028]) ).
thf(f2028,plain,
! [X6: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f2021]) ).
thf(f2021,plain,
! [X5: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2020]) ).
thf(f2020,plain,
! [X5: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2019,f358]) ).
thf(f2019,plain,
! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v5 @ Y11 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y7 ) ) ) )
| ~ ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2018]) ).
thf(f2018,plain,
! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f2016]) ).
thf(f2016,plain,
! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2015]) ).
thf(f2015,plain,
! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2014,f358]) ).
thf(f2014,plain,
! [X3: mworld,X4: mworld] :
( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v5 @ Y12 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y8 ) ) ) )
| ~ ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2013]) ).
thf(f2013,plain,
! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f2008]) ).
thf(f2008,plain,
! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2007]) ).
thf(f2007,plain,
! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2006,f358]) ).
thf(f2006,plain,
! [X2: mworld,X3: mworld] :
( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v5 @ Y13 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y9 ) ) ) )
| ~ ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2005]) ).
thf(f2005,plain,
! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f2000]) ).
thf(f2000,plain,
! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1999]) ).
thf(f1999,plain,
! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1998,f358]) ).
thf(f1998,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v5 @ Y14 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y10 ) ) ) )
| ~ ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1997]) ).
thf(f1997,plain,
! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1992]) ).
thf(f1992,plain,
! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1991]) ).
thf(f1991,plain,
! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1990,f358]) ).
thf(f1990,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK8 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v5 @ Y15 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y11 ) ) ) )
| ~ ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1987]) ).
thf(f1987,plain,
! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK8 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1824]) ).
thf(f1824,plain,
! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK8 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1823]) ).
thf(f1823,plain,
! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK8 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[status(thm)],[f1820]) ).
thf(f1820,plain,
! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK8 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ $true )
= $true ),
inference(superposition,[status(thm)],[f888,f1815]) ).
thf(f1815,plain,
! [X6: mworld] :
( $true
= ( v22 @ ( sK8 @ X6 ) ) ),
inference(boolean_simplification,[status(thm)],[f1814]) ).
thf(f1814,plain,
! [X6: mworld] :
( ( ( v22 @ ( sK8 @ X6 ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f1813,f358]) ).
thf(f1813,plain,
! [X6: mworld] :
( $true
= ( ( v22 @ ( sK8 @ X6 ) )
& ( mrel @ X6 @ ( sK8 @ X6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1812]) ).
thf(f1812,plain,
! [X6: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) )
@ ( sK8 @ X6 ) ) ),
inference(sigma_clausification,[status(thm)],[f1805]) ).
thf(f1805,plain,
! [X6: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1800]) ).
thf(f888,plain,
! [X7: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f887]) ).
thf(f887,plain,
! [X7: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f886,f358]) ).
thf(f886,plain,
! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v5 @ Y16 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y12 ) ) ) )
| ~ ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ X7 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f885]) ).
thf(f885,plain,
! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f884]) ).
thf(f884,plain,
! [X6: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f883]) ).
thf(f883,plain,
! [X6: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f882,f358]) ).
thf(f882,plain,
! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v5 @ Y17 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y13 ) ) ) )
| ~ ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f881]) ).
thf(f881,plain,
! [X6: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f880]) ).
thf(f880,plain,
! [X5: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f879]) ).
thf(f879,plain,
! [X5: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f878,f358]) ).
thf(f878,plain,
! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v5 @ Y18 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y14 ) ) ) )
| ~ ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f877]) ).
thf(f877,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f876]) ).
thf(f876,plain,
! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f875]) ).
thf(f875,plain,
! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f874,f358]) ).
thf(f874,plain,
! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v5 @ Y19 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y15 ) ) ) )
| ~ ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f873]) ).
thf(f873,plain,
! [X3: mworld,X4: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f872]) ).
thf(f872,plain,
! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f871]) ).
thf(f871,plain,
! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f870,f358]) ).
thf(f870,plain,
! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v5 @ Y20 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y16 ) ) ) )
| ~ ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f869]) ).
thf(f869,plain,
! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f868]) ).
thf(f868,plain,
! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f867]) ).
thf(f867,plain,
! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f866,f358]) ).
thf(f866,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v5 @ Y21 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y17 ) ) ) )
| ~ ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f865]) ).
thf(f865,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f864]) ).
thf(f864,plain,
! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f863]) ).
thf(f863,plain,
! [X1: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f862,f358]) ).
thf(f862,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v5 @ Y22 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y18 ) ) ) )
| ~ ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f861]) ).
thf(f861,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v5 @ Y23 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y19 ) ) ) )
| ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f338]) ).
thf(f338,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v5 @ Y23 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ Y19 ) ) ) )
| ~ ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v22 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f268]) ).
thf(f268,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v22 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v10 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v9 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f215,f207,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f192,f208,f201,f201,f201,f201]) ).
thf(f192,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
thf(f144,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f143]) ).
thf(f143,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X3 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mor_def) ).
thf(f215,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f79]) ).
thf(f79,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f78]) ).
thf(f78,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod36) ).
thf(f4740,plain,
( ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f4739]) ).
thf(f4739,plain,
( $false
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f4738]) ).
thf(f4738,plain,
( ( $true = $false )
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f4737,f3027]) ).
thf(f3027,plain,
( ! [X13: mworld] :
( ( v9 @ X13 )
= $false )
| ~ spl0_13 ),
inference(not_proxy_clausification,[status(thm)],[f2121]) ).
thf(f2121,plain,
( ! [X13: mworld] :
( ( ~ ( v9 @ X13 ) )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f2120]) ).
thf(f2120,definition,
( spl0_13
<=> ! [X13: mworld] :
( ( ~ ( v9 @ X13 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f4737,plain,
( ! [X5: mworld] :
( ( v9 @ X5 )
= $true )
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f4736]) ).
thf(f4736,plain,
( ! [X5: mworld] :
( ( $true
=> ( v9 @ X5 ) )
= $true )
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f4735,f358]) ).
thf(f4735,plain,
( ! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ( v9 @ X5 ) )
= $true )
| ~ spl0_19 ),
inference(beta_eta_normalization,[status(thm)],[f4734]) ).
thf(f4734,plain,
( ! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v9 @ Y0 ) )
@ X5 )
= $true )
| ~ spl0_19 ),
inference(pi_clausification,[status(thm)],[f2807]) ).
thf(f2807,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v9 @ Y0 ) ) )
= $true )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f2806]) ).
thf(f2806,definition,
( spl0_19
<=> ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v9 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f4616,plain,
~ spl0_39,
inference(avatar_contradiction_clause,[status(thm)],[f4615]) ).
thf(f4615,plain,
( $false
| ~ spl0_39 ),
inference(trivial_inequality_removal,[status(thm)],[f4611]) ).
thf(f4611,plain,
( ( $true = $false )
| ~ spl0_39 ),
inference(superposition,[status(thm)],[f4607,f2274]) ).
thf(f2274,plain,
! [X14: mworld] :
( ( v14 @ ( sK17 @ X14 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f2273]) ).
thf(f2273,plain,
! [X14: mworld] :
( $true
= ( ~ ( v14 @ ( sK17 @ X14 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2272]) ).
thf(f2272,plain,
! [X14: mworld] :
( $true
= ( ~ ( v14 @ ( sK17 @ X14 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2271,f358]) ).
thf(f2271,plain,
! [X14: mworld] :
( $true
= ( ~ ( v14 @ ( sK17 @ X14 ) )
& ( mrel @ X14 @ ( sK17 @ X14 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2270]) ).
thf(f2270,plain,
! [X14: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) )
@ ( sK17 @ X14 ) ) ),
inference(sigma_clausification,[status(thm)],[f2260]) ).
thf(f2260,plain,
! [X14: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2259]) ).
thf(f2259,plain,
! [X14: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2258]) ).
thf(f2258,plain,
! [X14: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v14 @ Y0 )
& ( mrel @ X14 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2177,f2257]) ).
thf(f4607,plain,
( ! [X7: mworld] :
( $true
= ( v14 @ X7 ) )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4606]) ).
thf(f4606,plain,
( ! [X7: mworld] :
( ( $true
=> ( v14 @ X7 ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4605,f358]) ).
thf(f4605,plain,
( ! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( v14 @ X7 ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4604]) ).
thf(f4604,plain,
( ! [X6: mworld,X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( v14 @ Y0 ) )
@ X7 ) )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4602]) ).
thf(f4602,plain,
( ! [X6: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( v14 @ Y0 ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4601]) ).
thf(f4601,plain,
( ! [X6: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( v14 @ Y0 ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4600,f358]) ).
thf(f4600,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( v14 @ Y0 ) ) ) ) )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4599]) ).
thf(f4599,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) )
@ X6 ) )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4591]) ).
thf(f4591,plain,
( ! [X5: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) ) ) )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4590]) ).
thf(f4590,plain,
( ! [X5: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) ) ) ) )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4589,f358]) ).
thf(f4589,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v14 @ Y1 ) ) ) ) ) ) )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4588]) ).
thf(f4588,plain,
( ! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) )
@ X5 )
= $true )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4586]) ).
thf(f4586,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4585]) ).
thf(f4585,plain,
( ! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4584,f358]) ).
thf(f4584,plain,
( ! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v14 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4583]) ).
thf(f4583,plain,
( ! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v14 @ Y3 ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4581]) ).
thf(f4581,plain,
( ! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v14 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4580]) ).
thf(f4580,plain,
( ! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v14 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4579,f358]) ).
thf(f4579,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v14 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4578]) ).
thf(f4578,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v14 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X3 ) )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4576]) ).
thf(f4576,plain,
( ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4575]) ).
thf(f4575,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4574,f358]) ).
thf(f4574,plain,
( ! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v14 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4573]) ).
thf(f4573,plain,
( ! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4571]) ).
thf(f4571,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4570]) ).
thf(f4570,plain,
( ! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4569,f358]) ).
thf(f4569,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK9 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v14 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4566]) ).
thf(f4566,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK9 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4547]) ).
thf(f4547,plain,
( ! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK9 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4546]) ).
thf(f4546,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK9 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4542]) ).
thf(f4542,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK9 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ $true )
= $true )
| ~ spl0_39 ),
inference(superposition,[status(thm)],[f4534,f1850]) ).
thf(f1850,plain,
! [X7: mworld] :
( ( v21 @ ( sK9 @ X7 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1849]) ).
thf(f1849,plain,
! [X7: mworld] :
( ( ( v21 @ ( sK9 @ X7 ) )
& $true )
= $true ),
inference(forward_demodulation,[status(thm)],[f1848,f358]) ).
thf(f1848,plain,
! [X7: mworld] :
( $true
= ( ( v21 @ ( sK9 @ X7 ) )
& ( mrel @ X7 @ ( sK9 @ X7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1847]) ).
thf(f1847,plain,
! [X7: mworld] :
( ( ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) )
@ ( sK9 @ X7 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f1844]) ).
thf(f1844,plain,
! [X7: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1819]) ).
thf(f1819,plain,
! [X7: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1818]) ).
thf(f1818,plain,
! [X7: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v21 @ Y0 )
& ( mrel @ X7 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f1811,f1817]) ).
thf(f4534,plain,
( ! [X8: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ X8 ) ) )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4533]) ).
thf(f4533,plain,
( ! [X8: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ X8 ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4532,f358]) ).
thf(f4532,plain,
( ! [X8: mworld,X7: mworld] :
( ( ( mrel @ X7 @ X8 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v14 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ X8 ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4531]) ).
thf(f4531,plain,
( ! [X8: mworld,X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) )
@ X8 ) )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4525]) ).
thf(f4525,plain,
( ! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4524]) ).
thf(f4524,plain,
( ! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4523,f358]) ).
thf(f4523,plain,
( ! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v14 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4522]) ).
thf(f4522,plain,
( ! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) )
@ X7 )
= $true )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4517]) ).
thf(f4517,plain,
( ! [X6: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) ) ) )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4516]) ).
thf(f4516,plain,
( ! [X6: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4515,f358]) ).
thf(f4515,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v14 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4514]) ).
thf(f4514,plain,
( ! [X6: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) )
@ X6 )
= $true )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4507]) ).
thf(f4507,plain,
( ! [X5: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(boolean_simplification,[status(thm)],[f4506]) ).
thf(f4506,plain,
( ! [X5: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(forward_demodulation,[status(thm)],[f4505,f358]) ).
thf(f4505,plain,
( ! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v14 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_39 ),
inference(beta_eta_normalization,[status(thm)],[f4504]) ).
thf(f4504,plain,
( ! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ~ spl0_39 ),
inference(pi_clausification,[status(thm)],[f4078]) ).
thf(f4078,plain,
( ! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_39 ),
inference(avatar_component_clause,[status(thm)],[f4077]) ).
thf(f4077,definition,
( spl0_39
<=> ! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_39])],[avatar_definition]) ).
thf(f4484,plain,
( spl0_32
| spl0_31 ),
inference(avatar_split_clause,[status(thm)],[f4063,f3271,f3274]) ).
thf(f3274,definition,
( spl0_32
<=> ! [X1: mworld] :
( ( ~ ( v28 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_32])],[avatar_definition]) ).
thf(f3271,definition,
( spl0_31
<=> ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition]) ).
thf(f4063,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( ~ ( v28 @ X1 ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f4062]) ).
thf(f4062,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( ( ~ ( v28 @ X1 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4061,f358]) ).
thf(f4061,plain,
! [X2: mworld,X1: mworld] :
( ( ( ~ ( v28 @ X1 ) )
= $true )
| ( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4058]) ).
thf(f4058,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( ( ~ ( v28 @ X1 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f363]) ).
thf(f363,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( ~ ( v28 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f362]) ).
thf(f362,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ X1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f361]) ).
thf(f361,plain,
! [X1: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f360,f358]) ).
thf(f360,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v18 @ Y9 ) ) ) ) ) ) ) ) )
| ( v22 @ Y5 ) ) ) ) ) )
| ~ ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f359]) ).
thf(f359,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v18 @ Y10 ) ) ) ) ) ) ) ) )
| ( v22 @ Y6 ) ) ) ) ) )
| ~ ( v24 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f302]) ).
thf(f302,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v18 @ Y10 ) ) ) ) ) ) ) ) )
| ( v22 @ Y6 ) ) ) ) ) )
| ~ ( v24 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f259]) ).
thf(f259,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v28 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v24 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v22
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f200,f207,f201,f192,f208,f201,f201,f201,f201,f192,f208,f201,f201,f192,f201,f201,f201,f201]) ).
thf(f200,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f130]) ).
thf(f130,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f129]) ).
thf(f129,plain,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod8) ).
thf(f4483,plain,
( spl0_19
| ~ spl0_32 ),
inference(avatar_split_clause,[status(thm)],[f4482,f3274,f2806]) ).
thf(f4482,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v9 @ Y0 ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4481]) ).
thf(f4481,plain,
( ! [X4: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v9 @ Y0 ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4480,f358]) ).
thf(f4480,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( v9 @ Y0 ) ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4479]) ).
thf(f4479,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) )
@ X4 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4474]) ).
thf(f4474,plain,
( ! [X3: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4473]) ).
thf(f4473,plain,
( ! [X3: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4472,f358]) ).
thf(f4472,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v9 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4471]) ).
thf(f4471,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) )
@ X3 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4466]) ).
thf(f4466,plain,
( ! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4465]) ).
thf(f4465,plain,
( ! [X2: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4464,f358]) ).
thf(f4464,plain,
( ! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v9 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4463]) ).
thf(f4463,plain,
( ! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) )
@ X2 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4458]) ).
thf(f4458,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4457]) ).
thf(f4457,plain,
( ! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4456,f358]) ).
thf(f4456,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK17 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v9 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4453]) ).
thf(f4453,plain,
( ! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK17 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4450]) ).
thf(f4450,plain,
( ! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK17 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4449]) ).
thf(f4449,plain,
( ! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK17 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| $false ) )
| ~ spl0_32 ),
inference(superposition,[status(thm)],[f4442,f2274]) ).
thf(f4442,plain,
( ! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ X1 ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4441]) ).
thf(f4441,plain,
( ! [X1: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ X1 ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4440,f358]) ).
thf(f4440,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK14 @ X0 ) @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v9 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ X1 ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4437]) ).
thf(f4437,plain,
( ! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X0 ) @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4436]) ).
thf(f4436,plain,
( ! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X0 ) @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4435]) ).
thf(f4435,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X0 ) @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| $false )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4431]) ).
thf(f4431,plain,
( ! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X0 ) @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| ~ $true ) )
| ~ spl0_32 ),
inference(superposition,[status(thm)],[f4429,f2222]) ).
thf(f2222,plain,
! [X13: mworld] :
( $true
= ( v15 @ ( sK14 @ X13 ) ) ),
inference(boolean_simplification,[status(thm)],[f2221]) ).
thf(f2221,plain,
! [X13: mworld] :
( $true
= ( ( v15 @ ( sK14 @ X13 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2216,f358]) ).
thf(f2216,plain,
! [X13: mworld] :
( $true
= ( ( v15 @ ( sK14 @ X13 ) )
& ( mrel @ X13 @ ( sK14 @ X13 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2215]) ).
thf(f2215,plain,
! [X13: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) )
@ ( sK14 @ X13 ) ) ),
inference(sigma_clausification,[status(thm)],[f2207]) ).
thf(f2207,plain,
! [X13: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v15 @ Y0 )
& ( mrel @ X13 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2166]) ).
thf(f4429,plain,
( ! [X14: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| ~ ( v15 @ X14 ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4428]) ).
thf(f4428,plain,
( ! [X14: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| ~ ( v15 @ X14 ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4427,f358]) ).
thf(f4427,plain,
( ! [X14: mworld,X13: mworld] :
( $true
= ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v9 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y0 ) ) ) )
| ~ ( v15 @ X14 ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4426]) ).
thf(f4426,plain,
( ! [X14: mworld,X13: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) )
@ X14 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4425]) ).
thf(f4425,plain,
( ! [X13: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4424]) ).
thf(f4424,plain,
( ! [X13: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4423,f358]) ).
thf(f4423,plain,
( ! [X12: mworld,X13: mworld] :
( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v9 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y1 ) ) ) )
| ~ ( v15 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4422]) ).
thf(f4422,plain,
( ! [X12: mworld,X13: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) )
@ X13 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4421]) ).
thf(f4421,plain,
( ! [X12: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4420]) ).
thf(f4420,plain,
( ! [X12: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4419,f358]) ).
thf(f4419,plain,
( ! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v9 @ Y7 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y2 ) ) ) )
| ~ ( v15 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4418]) ).
thf(f4418,plain,
( ! [X11: mworld,X12: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) )
@ X12 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4417]) ).
thf(f4417,plain,
( ! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4416]) ).
thf(f4416,plain,
( ! [X11: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4415,f358]) ).
thf(f4415,plain,
( ! [X10: mworld,X11: mworld] :
( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v9 @ Y8 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y3 ) ) ) )
| ~ ( v15 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4414]) ).
thf(f4414,plain,
( ! [X10: mworld,X11: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) )
@ X11 ) )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4413]) ).
thf(f4413,plain,
( ! [X10: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4412]) ).
thf(f4412,plain,
( ! [X10: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4411,f358]) ).
thf(f4411,plain,
( ! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v9 @ Y9 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y4 ) ) ) )
| ~ ( v15 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4410]) ).
thf(f4410,plain,
( ! [X10: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4409]) ).
thf(f4409,plain,
( ! [X9: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4408]) ).
thf(f4408,plain,
( ! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4407,f358]) ).
thf(f4407,plain,
( ! [X8: mworld,X9: mworld] :
( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v9 @ Y10 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y5 ) ) ) )
| ~ ( v15 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4406]) ).
thf(f4406,plain,
( ! [X8: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4405]) ).
thf(f4405,plain,
( ! [X8: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4404]) ).
thf(f4404,plain,
( ! [X8: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4403,f358]) ).
thf(f4403,plain,
( ! [X8: mworld,X7: mworld] :
( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v9 @ Y11 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y6 ) ) ) )
| ~ ( v15 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4402]) ).
thf(f4402,plain,
( ! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4401]) ).
thf(f4401,plain,
( ! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4400]) ).
thf(f4400,plain,
( ! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4399,f358]) ).
thf(f4399,plain,
( ! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v9 @ Y12 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y7 ) ) ) )
| ~ ( v15 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4398]) ).
thf(f4398,plain,
( ! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4391]) ).
thf(f4391,plain,
( ! [X6: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4390]) ).
thf(f4390,plain,
( ! [X6: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4389,f358]) ).
thf(f4389,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v9 @ Y13 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y8 ) ) ) )
| ~ ( v15 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4388]) ).
thf(f4388,plain,
( ! [X6: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4382]) ).
thf(f4382,plain,
( ! [X5: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4381]) ).
thf(f4381,plain,
( ! [X5: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4380,f358]) ).
thf(f4380,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v9 @ Y14 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y9 ) ) ) )
| ~ ( v15 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4379]) ).
thf(f4379,plain,
( ! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4374]) ).
thf(f4374,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4373]) ).
thf(f4373,plain,
( ! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4372,f358]) ).
thf(f4372,plain,
( ! [X3: mworld,X4: mworld] :
( $true
= ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v9 @ Y15 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y10 ) ) ) )
| ~ ( v15 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4371]) ).
thf(f4371,plain,
( ! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4366]) ).
thf(f4366,plain,
( ! [X3: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4365]) ).
thf(f4365,plain,
( ! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4364,f358]) ).
thf(f4364,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v9 @ Y16 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y11 ) ) ) )
| ~ ( v15 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4363]) ).
thf(f4363,plain,
( ! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4358]) ).
thf(f4358,plain,
( ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4357]) ).
thf(f4357,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(forward_demodulation,[status(thm)],[f4356,f358]) ).
thf(f4356,plain,
( ! [X2: mworld,X1: mworld] :
( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v9 @ Y17 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y12 ) ) ) )
| ~ ( v15 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_32 ),
inference(beta_eta_normalization,[status(thm)],[f4355]) ).
thf(f4355,plain,
( ! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ~ spl0_32 ),
inference(pi_clausification,[status(thm)],[f4254]) ).
thf(f4254,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_32 ),
inference(boolean_simplification,[status(thm)],[f4241]) ).
thf(f4241,plain,
( ! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_32 ),
inference(backward_demodulation,[status(thm)],[f461,f4236]) ).
thf(f4236,plain,
( ! [X1: mworld] :
( $false
= ( v28 @ X1 ) )
| ~ spl0_32 ),
inference(not_proxy_clausification,[status(thm)],[f3275]) ).
thf(f3275,plain,
( ! [X1: mworld] :
( ( ~ ( v28 @ X1 ) )
= $true )
| ~ spl0_32 ),
inference(avatar_component_clause,[status(thm)],[f3274]) ).
thf(f461,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ X1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f460]) ).
thf(f460,plain,
! [X1: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f459,f358]) ).
thf(f459,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v9 @ Y18 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y13 ) ) ) )
| ~ ( v15 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f458]) ).
thf(f458,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y14 ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f316]) ).
thf(f316,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v9 @ Y19 ) ) ) ) ) ) ) ) ) ) )
| ( v14 @ Y14 ) ) ) )
| ~ ( v15 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v28 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f270]) ).
thf(f270,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v28
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v15 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v14
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f217,f207,f201,f192,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f192,f201,f201,f201,f201,f201]) ).
thf(f217,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f162]) ).
thf(f162,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f161]) ).
thf(f161,plain,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod4) ).
thf(f4218,plain,
( ~ spl0_31
| ~ spl0_38 ),
inference(avatar_contradiction_clause,[status(thm)],[f4217]) ).
thf(f4217,plain,
( $false
| ~ spl0_31
| ~ spl0_38 ),
inference(trivial_inequality_removal,[status(thm)],[f4214]) ).
thf(f4214,plain,
( ( $true = $false )
| ~ spl0_31
| ~ spl0_38 ),
inference(backward_demodulation,[status(thm)],[f2555,f4204]) ).
thf(f4204,plain,
( ! [X1: mworld] :
( ( v6 @ X1 )
= $false )
| ~ spl0_31
| ~ spl0_38 ),
inference(not_proxy_clausification,[status(thm)],[f4199]) ).
thf(f4199,plain,
( ! [X1: mworld] :
( ( ~ ( v6 @ X1 ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4198]) ).
thf(f4198,plain,
( ! [X1: mworld] :
( ( $true
=> ~ ( v6 @ X1 ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4196,f358]) ).
thf(f4196,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK24 @ X0 ) @ X1 )
=> ~ ( v6 @ X1 ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4194]) ).
thf(f4194,plain,
( ! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK24 @ X0 ) @ Y0 )
=> ~ ( v6 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4187]) ).
thf(f4187,plain,
( ! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK24 @ X0 ) @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4186]) ).
thf(f4186,plain,
( ! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK24 @ X0 ) @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
| $false ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4184]) ).
thf(f4184,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK24 @ X0 ) @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
| ~ $true )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(superposition,[status(thm)],[f4182,f2579]) ).
thf(f2579,plain,
! [X21: mworld] :
( $true
= ( v7 @ ( sK24 @ X21 ) ) ),
inference(boolean_simplification,[status(thm)],[f2578]) ).
thf(f2578,plain,
! [X21: mworld] :
( $true
= ( ( v7 @ ( sK24 @ X21 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2573,f358]) ).
thf(f2573,plain,
! [X21: mworld] :
( ( ( v7 @ ( sK24 @ X21 ) )
& ( mrel @ X21 @ ( sK24 @ X21 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2572]) ).
thf(f2572,plain,
! [X21: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) )
@ ( sK24 @ X21 ) ) ),
inference(sigma_clausification,[status(thm)],[f2571]) ).
thf(f2571,plain,
! [X21: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2570]) ).
thf(f2570,plain,
! [X21: mworld] :
( $true
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f2515,f2568]) ).
thf(f2568,plain,
! [X21: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v7 @ Y0 )
& ( mrel @ X21 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2515]) ).
thf(f4182,plain,
( ! [X22: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
| ~ ( v7 @ X22 ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4181]) ).
thf(f4181,plain,
( ! [X22: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
| ~ ( v7 @ X22 ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4180,f358]) ).
thf(f4180,plain,
( ! [X21: mworld,X22: mworld] :
( $true
= ( ( mrel @ X21 @ X22 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ~ ( v6 @ Y0 ) ) )
| ~ ( v7 @ X22 ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4179]) ).
thf(f4179,plain,
( ! [X21: mworld,X22: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) )
| ~ ( v7 @ Y0 ) ) )
@ X22 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4178]) ).
thf(f4178,plain,
( ! [X21: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) )
| ~ ( v7 @ Y0 ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4177]) ).
thf(f4177,plain,
( ! [X21: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) )
| ~ ( v7 @ Y0 ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4176,f358]) ).
thf(f4176,plain,
( ! [X21: mworld,X20: mworld] :
( ( ( mrel @ X20 @ X21 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v6 @ Y1 ) ) )
| ~ ( v7 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4175]) ).
thf(f4175,plain,
( ! [X21: mworld,X20: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) )
| ~ ( v7 @ Y1 ) ) ) ) )
@ X21 ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4174]) ).
thf(f4174,plain,
( ! [X20: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) )
| ~ ( v7 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4173]) ).
thf(f4173,plain,
( ! [X20: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) )
| ~ ( v7 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4172,f358]) ).
thf(f4172,plain,
( ! [X19: mworld,X20: mworld] :
( ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v6 @ Y2 ) ) )
| ~ ( v7 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4171]) ).
thf(f4171,plain,
( ! [X19: mworld,X20: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) )
| ~ ( v7 @ Y2 ) ) ) ) ) ) )
@ X20 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4170]) ).
thf(f4170,plain,
( ! [X19: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) )
| ~ ( v7 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4169]) ).
thf(f4169,plain,
( ! [X19: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) )
| ~ ( v7 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4168,f358]) ).
thf(f4168,plain,
( ! [X18: mworld,X19: mworld] :
( ( ( mrel @ X18 @ X19 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v6 @ Y3 ) ) )
| ~ ( v7 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4167]) ).
thf(f4167,plain,
( ! [X18: mworld,X19: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) )
| ~ ( v7 @ Y3 ) ) ) ) ) ) ) ) )
@ X19 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4166]) ).
thf(f4166,plain,
( ! [X18: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) )
| ~ ( v7 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4165]) ).
thf(f4165,plain,
( ! [X18: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) )
| ~ ( v7 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4164,f358]) ).
thf(f4164,plain,
( ! [X18: mworld,X17: mworld] :
( ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v6 @ Y4 ) ) )
| ~ ( v7 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4163]) ).
thf(f4163,plain,
( ! [X18: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) )
| ~ ( v7 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X18 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4162]) ).
thf(f4162,plain,
( ! [X17: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) )
| ~ ( v7 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4161]) ).
thf(f4161,plain,
( ! [X17: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) )
| ~ ( v7 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4160,f358]) ).
thf(f4160,plain,
( ! [X16: mworld,X17: mworld] :
( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v6 @ Y5 ) ) )
| ~ ( v7 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4159]) ).
thf(f4159,plain,
( ! [X16: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) )
| ~ ( v7 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X17 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4158]) ).
thf(f4158,plain,
( ! [X16: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) )
| ~ ( v7 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4157]) ).
thf(f4157,plain,
( ! [X16: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) )
| ~ ( v7 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4156,f358]) ).
thf(f4156,plain,
( ! [X16: mworld,X15: mworld] :
( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v6 @ Y6 ) ) )
| ~ ( v7 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4155]) ).
thf(f4155,plain,
( ! [X16: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) )
| ~ ( v7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4154]) ).
thf(f4154,plain,
( ! [X15: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) )
| ~ ( v7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4153]) ).
thf(f4153,plain,
( ! [X15: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) )
| ~ ( v7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4152,f358]) ).
thf(f4152,plain,
( ! [X14: mworld,X15: mworld] :
( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v6 @ Y7 ) ) )
| ~ ( v7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4151]) ).
thf(f4151,plain,
( ! [X14: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) )
| ~ ( v7 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4150]) ).
thf(f4150,plain,
( ! [X14: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) )
| ~ ( v7 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4149]) ).
thf(f4149,plain,
( ! [X14: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) )
| ~ ( v7 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4148,f358]) ).
thf(f4148,plain,
( ! [X14: mworld,X13: mworld] :
( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v6 @ Y8 ) ) )
| ~ ( v7 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4147]) ).
thf(f4147,plain,
( ! [X14: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) )
| ~ ( v7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4146]) ).
thf(f4146,plain,
( ! [X13: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) )
| ~ ( v7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4145]) ).
thf(f4145,plain,
( ! [X13: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) )
| ~ ( v7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4144,f358]) ).
thf(f4144,plain,
( ! [X12: mworld,X13: mworld] :
( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v6 @ Y9 ) ) )
| ~ ( v7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4143]) ).
thf(f4143,plain,
( ! [X12: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) )
| ~ ( v7 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4142]) ).
thf(f4142,plain,
( ! [X12: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) )
| ~ ( v7 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4141]) ).
thf(f4141,plain,
( ! [X12: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) )
| ~ ( v7 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4140,f358]) ).
thf(f4140,plain,
( ! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v6 @ Y10 ) ) )
| ~ ( v7 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4139]) ).
thf(f4139,plain,
( ! [X11: mworld,X12: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4138]) ).
thf(f4138,plain,
( ! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4137]) ).
thf(f4137,plain,
( ! [X11: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_31
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4136]) ).
thf(f4136,plain,
( ! [X11: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ $true ) )
| ~ spl0_31
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4135,f3328]) ).
thf(f3328,plain,
( ! [X4: mworld] :
( ( v18 @ X4 )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3327]) ).
thf(f3327,plain,
( ! [X4: mworld] :
( ( $true
=> ( v18 @ X4 ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3326,f358]) ).
thf(f3326,plain,
( ! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( v18 @ X4 ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3325]) ).
thf(f3325,plain,
( ! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v18 @ Y0 ) )
@ X4 )
= $true )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3324]) ).
thf(f3324,plain,
( ! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v18 @ Y0 ) ) )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3323]) ).
thf(f3323,plain,
( ! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v18 @ Y0 ) ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3322,f358]) ).
thf(f3322,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( v18 @ Y0 ) ) ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3321]) ).
thf(f3321,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) )
@ X3 ) )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3320]) ).
thf(f3320,plain,
( ! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) ) )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3319]) ).
thf(f3319,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3318,f358]) ).
thf(f3318,plain,
( ! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v18 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3317]) ).
thf(f3317,plain,
( ! [X2: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) )
@ X2 ) )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3316]) ).
thf(f3316,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3315]) ).
thf(f3315,plain,
( ! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3314,f358]) ).
thf(f3314,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK11 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v18 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3311]) ).
thf(f3311,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK11 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) )
@ X1 ) )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3310]) ).
thf(f3310,plain,
( ! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK11 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3308]) ).
thf(f3308,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK11 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_31 ),
inference(superposition,[status(thm)],[f3305,f1884]) ).
thf(f1884,plain,
! [X6: mworld] :
( ( v22 @ ( sK11 @ X6 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f1883]) ).
thf(f1883,plain,
! [X6: mworld] :
( ( ~ ( v22 @ ( sK11 @ X6 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1882]) ).
thf(f1882,plain,
! [X6: mworld] :
( $true
= ( ~ ( v22 @ ( sK11 @ X6 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1881,f358]) ).
thf(f1881,plain,
! [X6: mworld] :
( ( ~ ( v22 @ ( sK11 @ X6 ) )
& ( mrel @ X6 @ ( sK11 @ X6 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1880]) ).
thf(f1880,plain,
! [X6: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) )
@ ( sK11 @ X6 ) ) ),
inference(sigma_clausification,[status(thm)],[f1807]) ).
thf(f1807,plain,
! [X6: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1806]) ).
thf(f1806,plain,
! [X6: mworld] :
( $true
= ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v22 @ Y0 )
& ( mrel @ X6 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1800,f1805]) ).
thf(f3305,plain,
( ! [X2: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
| ( v22 @ X2 ) )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3304]) ).
thf(f3304,plain,
( ! [X2: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
| ( v22 @ X2 ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3303,f358]) ).
thf(f3303,plain,
( ! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v18 @ Y3 ) ) ) ) ) ) ) ) )
| ( v22 @ X2 ) ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3302]) ).
thf(f3302,plain,
( ! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3301]) ).
thf(f3301,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3300]) ).
thf(f3300,plain,
( ! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3298,f358]) ).
thf(f3298,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK4 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v18 @ Y4 ) ) ) ) ) ) ) ) )
| ( v22 @ Y0 ) ) ) ) ) )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3296]) ).
thf(f3296,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) )
@ X1 ) )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3293]) ).
thf(f3293,plain,
( ! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) ) )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3292]) ).
thf(f3292,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3290]) ).
thf(f3290,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK4 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| ~ $true )
= $true )
| ~ spl0_31 ),
inference(superposition,[status(thm)],[f3288,f1637]) ).
thf(f1637,plain,
! [X4: mworld] :
( $true
= ( v24 @ ( sK4 @ X4 ) ) ),
inference(boolean_simplification,[status(thm)],[f1636]) ).
thf(f1636,plain,
! [X4: mworld] :
( $true
= ( ( v24 @ ( sK4 @ X4 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1635,f358]) ).
thf(f1635,plain,
! [X4: mworld] :
( $true
= ( ( v24 @ ( sK4 @ X4 ) )
& ( mrel @ X4 @ ( sK4 @ X4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1634]) ).
thf(f1634,plain,
! [X4: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) )
@ ( sK4 @ X4 ) ) ),
inference(sigma_clausification,[status(thm)],[f1631]) ).
thf(f1631,plain,
! [X4: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f1629]) ).
thf(f1629,plain,
! [X4: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1628]) ).
thf(f1628,plain,
! [X4: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f1625,f1627]) ).
thf(f3288,plain,
( ! [X5: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| ~ ( v24 @ X5 ) ) )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3287]) ).
thf(f3287,plain,
( ! [X5: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| ~ ( v24 @ X5 ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3286,f358]) ).
thf(f3286,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v18 @ Y5 ) ) ) ) ) ) ) ) )
| ( v22 @ Y1 ) ) ) ) ) )
| ~ ( v24 @ X5 ) ) ) )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3285]) ).
thf(f3285,plain,
( ! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) )
@ X5 )
= $true )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3284]) ).
thf(f3284,plain,
( ! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3283]) ).
thf(f3283,plain,
( ! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3282,f358]) ).
thf(f3282,plain,
( ! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v18 @ Y6 ) ) ) ) ) ) ) ) )
| ( v22 @ Y2 ) ) ) ) ) )
| ~ ( v24 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3281]) ).
thf(f3281,plain,
( ! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) )
@ X4 )
= $true )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3280]) ).
thf(f3280,plain,
( ! [X3: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) )
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f3279]) ).
thf(f3279,plain,
( ! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f3278,f358]) ).
thf(f3278,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v18 @ Y7 ) ) ) ) ) ) ) ) )
| ( v22 @ Y3 ) ) ) ) ) )
| ~ ( v24 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(beta_eta_normalization,[status(thm)],[f3277]) ).
thf(f3277,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) )
@ X3 ) )
| ~ spl0_31 ),
inference(pi_clausification,[status(thm)],[f3272]) ).
thf(f3272,plain,
( ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v18 @ Y8 ) ) ) ) ) ) ) ) )
| ( v22 @ Y4 ) ) ) ) ) )
| ~ ( v24 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_31 ),
inference(avatar_component_clause,[status(thm)],[f3271]) ).
thf(f4135,plain,
( ! [X11: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ X11 ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4134]) ).
thf(f4134,plain,
( ! [X11: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ X11 ) ) ) )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4133,f358]) ).
thf(f4133,plain,
( ! [X10: mworld,X11: mworld] :
( ( ( mrel @ X10 @ X11 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v6 @ Y11 ) ) )
| ~ ( v7 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ X11 ) ) )
= $true )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4132]) ).
thf(f4132,plain,
( ! [X10: mworld,X11: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) )
| ~ ( v7 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) )
@ X11 )
= $true )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4131]) ).
thf(f4131,plain,
( ! [X10: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) )
| ~ ( v7 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4130]) ).
thf(f4130,plain,
( ! [X10: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) )
| ~ ( v7 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4129,f358]) ).
thf(f4129,plain,
( ! [X10: mworld,X9: mworld] :
( $true
= ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v6 @ Y12 ) ) )
| ~ ( v7 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y0 ) ) ) ) ) )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4128]) ).
thf(f4128,plain,
( ! [X10: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) )
| ~ ( v7 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) )
@ X10 ) )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4127]) ).
thf(f4127,plain,
( ! [X9: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) )
| ~ ( v7 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4126]) ).
thf(f4126,plain,
( ! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) )
| ~ ( v7 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4125,f358]) ).
thf(f4125,plain,
( ! [X8: mworld,X9: mworld] :
( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v6 @ Y13 ) ) )
| ~ ( v7 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4124]) ).
thf(f4124,plain,
( ! [X8: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) )
| ~ ( v7 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) )
@ X9 ) )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4123]) ).
thf(f4123,plain,
( ! [X8: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) )
| ~ ( v7 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4122]) ).
thf(f4122,plain,
( ! [X8: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) )
| ~ ( v7 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4121,f358]) ).
thf(f4121,plain,
( ! [X8: mworld,X7: mworld] :
( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v6 @ Y14 ) ) )
| ~ ( v7 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4120]) ).
thf(f4120,plain,
( ! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) )
| ~ ( v7 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4119]) ).
thf(f4119,plain,
( ! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) )
| ~ ( v7 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4118]) ).
thf(f4118,plain,
( ! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) )
| ~ ( v7 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4117,f358]) ).
thf(f4117,plain,
( ! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v6 @ Y15 ) ) )
| ~ ( v7 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4116]) ).
thf(f4116,plain,
( ! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) )
| ~ ( v7 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4115]) ).
thf(f4115,plain,
( ! [X6: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) )
| ~ ( v7 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4114]) ).
thf(f4114,plain,
( ! [X6: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) )
| ~ ( v7 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4113,f358]) ).
thf(f4113,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v6 @ Y16 ) ) )
| ~ ( v7 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4112]) ).
thf(f4112,plain,
( ! [X6: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) )
| ~ ( v7 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 ) )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4111]) ).
thf(f4111,plain,
( ! [X5: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) )
| ~ ( v7 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4110]) ).
thf(f4110,plain,
( ! [X5: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) )
| ~ ( v7 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4109,f358]) ).
thf(f4109,plain,
( ! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v6 @ Y17 ) ) )
| ~ ( v7 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4108]) ).
thf(f4108,plain,
( ! [X4: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) )
| ~ ( v7 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4107]) ).
thf(f4107,plain,
( ! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) )
| ~ ( v7 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4106]) ).
thf(f4106,plain,
( ! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) )
| ~ ( v7 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(forward_demodulation,[status(thm)],[f4105,f358]) ).
thf(f4105,plain,
( ! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v6 @ Y18 ) ) )
| ~ ( v7 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(beta_eta_normalization,[status(thm)],[f4104]) ).
thf(f4104,plain,
( ! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true )
| ~ spl0_38 ),
inference(pi_clausification,[status(thm)],[f4093]) ).
thf(f4093,plain,
( ! [X3: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_38 ),
inference(trivial_inequality_removal,[status(thm)],[f4092]) ).
thf(f4092,plain,
( ! [X3: mworld] :
( ( $true = $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) )
| ~ spl0_38 ),
inference(boolean_simplification,[status(thm)],[f4085]) ).
thf(f4085,plain,
( ! [X3: mworld] :
( ( ( ~ $true ) = $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) )
| ~ spl0_38 ),
inference(backward_demodulation,[status(thm)],[f832,f3929]) ).
thf(f3929,plain,
( ! [X3: mworld] :
( $true
= ( v26 @ X3 ) )
| ~ spl0_38 ),
inference(avatar_component_clause,[status(thm)],[f3928]) ).
thf(f3928,definition,
( spl0_38
<=> ! [X3: mworld] :
( $true
= ( v26 @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_38])],[avatar_definition]) ).
thf(f832,plain,
! [X3: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( v26 @ X3 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f831]) ).
thf(f831,plain,
! [X3: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ X3 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f830]) ).
thf(f830,plain,
! [X3: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ X3 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f829,f358]) ).
thf(f829,plain,
! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v6 @ Y19 ) ) )
| ~ ( v7 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f828]) ).
thf(f828,plain,
! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) )
| ~ ( v7 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f827]) ).
thf(f827,plain,
! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) )
| ~ ( v7 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f826]) ).
thf(f826,plain,
! [X2: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) )
| ~ ( v7 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f825,f358]) ).
thf(f825,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v6 @ Y20 ) ) )
| ~ ( v7 @ Y19 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f824]) ).
thf(f824,plain,
! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) )
| ~ ( v7 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f805]) ).
thf(f805,plain,
! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) )
| ~ ( v7 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f804]) ).
thf(f804,plain,
! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) )
| ~ ( v7 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f803,f358]) ).
thf(f803,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v6 @ Y21 ) ) )
| ~ ( v7 @ Y20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f802]) ).
thf(f802,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) )
| ~ ( v7 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f320]) ).
thf(f320,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v6 @ Y22 ) ) )
| ~ ( v7 @ Y21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v18 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v26 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f283]) ).
thf(f283,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v26 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v18 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v7 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f231,f207,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f208]) ).
thf(f231,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f72]) ).
thf(f72,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod24) ).
thf(f2555,plain,
! [X22: mworld] :
( $true
= ( v6 @ ( sK22 @ X22 ) ) ),
inference(boolean_simplification,[status(thm)],[f2554]) ).
thf(f2554,plain,
! [X22: mworld] :
( $true
= ( ( v6 @ ( sK22 @ X22 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2542,f358]) ).
thf(f2542,plain,
! [X22: mworld] :
( ( ( v6 @ ( sK22 @ X22 ) )
& ( mrel @ X22 @ ( sK22 @ X22 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2541]) ).
thf(f2541,plain,
! [X22: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) )
@ ( sK22 @ X22 ) ) ),
inference(sigma_clausification,[status(thm)],[f2540]) ).
thf(f2540,plain,
! [X22: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2539]) ).
thf(f2539,plain,
! [X22: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f2536,f2537]) ).
thf(f2537,plain,
! [X22: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2536]) ).
thf(f2536,plain,
! [X22: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2535]) ).
thf(f2535,plain,
! [X22: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2527,f2534]) ).
thf(f4079,plain,
( spl0_38
| spl0_39
| ~ spl0_36 ),
inference(avatar_split_clause,[status(thm)],[f4075,f3399,f4077,f3928]) ).
thf(f3399,definition,
( spl0_36
<=> ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_36])],[avatar_definition]) ).
thf(f4075,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_36 ),
inference(boolean_simplification,[status(thm)],[f4074]) ).
thf(f4074,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) )
| ~ spl0_36 ),
inference(forward_demodulation,[status(thm)],[f4073,f358]) ).
thf(f4073,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v14 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ) )
| ~ spl0_36 ),
inference(beta_eta_normalization,[status(thm)],[f4070]) ).
thf(f4070,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ) )
| ~ spl0_36 ),
inference(pi_clausification,[status(thm)],[f4046]) ).
thf(f4046,plain,
( ! [X3: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) )
| ~ spl0_36 ),
inference(binary_proxy_clausification,[status(thm)],[f4045]) ).
thf(f4045,plain,
( ! [X3: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) ) )
| ~ spl0_36 ),
inference(boolean_simplification,[status(thm)],[f4044]) ).
thf(f4044,plain,
( ! [X3: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) ) )
= $true )
| ~ spl0_36 ),
inference(forward_demodulation,[status(thm)],[f4043,f358]) ).
thf(f4043,plain,
( ! [X2: mworld,X3: mworld] :
( $true
= ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v14 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) ) ) )
| ~ spl0_36 ),
inference(beta_eta_normalization,[status(thm)],[f4042]) ).
thf(f4042,plain,
( ! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) )
@ X3 )
= $true )
| ~ spl0_36 ),
inference(pi_clausification,[status(thm)],[f3400]) ).
thf(f3400,plain,
( ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) )
= $true )
| ~ spl0_36 ),
inference(avatar_component_clause,[status(thm)],[f3399]) ).
thf(f4004,plain,
~ spl0_37,
inference(avatar_contradiction_clause,[status(thm)],[f4003]) ).
thf(f4003,plain,
( $false
| ~ spl0_37 ),
inference(trivial_inequality_removal,[status(thm)],[f4002]) ).
thf(f4002,plain,
( ( $true = $false )
| ~ spl0_37 ),
inference(backward_demodulation,[status(thm)],[f2304,f3992]) ).
thf(f3992,plain,
( ! [X3: mworld] :
( ( v13 @ X3 )
= $false )
| ~ spl0_37 ),
inference(not_proxy_clausification,[status(thm)],[f3987]) ).
thf(f3987,plain,
( ! [X3: mworld] :
( ( ~ ( v13 @ X3 ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3986]) ).
thf(f3986,plain,
( ! [X3: mworld] :
( ( $true
=> ~ ( v13 @ X3 ) )
= $true )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3985,f358]) ).
thf(f3985,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ~ ( v13 @ X3 ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3984]) ).
thf(f3984,plain,
( ! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v13 @ Y0 ) )
@ X3 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3983]) ).
thf(f3983,plain,
( ! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v13 @ Y0 ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3982]) ).
thf(f3982,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v13 @ Y0 ) ) ) )
= $true )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3981,f358]) ).
thf(f3981,plain,
( ! [X2: mworld,X1: mworld] :
( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ~ ( v13 @ Y0 ) ) ) ) )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3980]) ).
thf(f3980,plain,
( ! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) )
@ X2 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3979]) ).
thf(f3979,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3978]) ).
thf(f3978,plain,
( ! [X1: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3976,f358]) ).
thf(f3976,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ( mrel @ ( sK12 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v13 @ Y1 ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3974]) ).
thf(f3974,plain,
( ! [X0: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3973]) ).
thf(f3973,plain,
( ! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3972]) ).
thf(f3972,plain,
( ! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| $false ) )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3968]) ).
thf(f3968,plain,
( ! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK12 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| ~ $true )
= $true )
| ~ spl0_37 ),
inference(superposition,[status(thm)],[f3966,f2186]) ).
thf(f2186,plain,
! [X12: mworld] :
( $true
= ( v16 @ ( sK12 @ X12 ) ) ),
inference(boolean_simplification,[status(thm)],[f2185]) ).
thf(f2185,plain,
! [X12: mworld] :
( $true
= ( ( v16 @ ( sK12 @ X12 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2171,f358]) ).
thf(f2171,plain,
! [X12: mworld] :
( ( ( v16 @ ( sK12 @ X12 ) )
& ( mrel @ X12 @ ( sK12 @ X12 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2170]) ).
thf(f2170,plain,
! [X12: mworld] :
( ( ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) )
@ ( sK12 @ X12 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f2163]) ).
thf(f2163,plain,
! [X12: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v16 @ Y0 )
& ( mrel @ X12 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2154]) ).
thf(f3966,plain,
( ! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| ~ ( v16 @ X13 ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3965]) ).
thf(f3965,plain,
( ! [X13: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| ~ ( v16 @ X13 ) ) )
= $true )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3964,f358]) ).
thf(f3964,plain,
( ! [X12: mworld,X13: mworld] :
( $true
= ( ( mrel @ X12 @ X13 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v13 @ Y2 ) ) ) ) ) ) )
| ~ ( v16 @ X13 ) ) ) )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3963]) ).
thf(f3963,plain,
( ! [X12: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) )
@ X13 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3962]) ).
thf(f3962,plain,
( ! [X12: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) ) ) )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3961]) ).
thf(f3961,plain,
( ! [X12: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) ) ) ) )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3960,f358]) ).
thf(f3960,plain,
( ! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v13 @ Y3 ) ) ) ) ) ) )
| ~ ( v16 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3959]) ).
thf(f3959,plain,
( ! [X11: mworld,X12: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) )
@ X12 ) )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3958]) ).
thf(f3958,plain,
( ! [X11: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3957]) ).
thf(f3957,plain,
( ! [X11: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3956,f358]) ).
thf(f3956,plain,
( ! [X10: mworld,X11: mworld] :
( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v13 @ Y4 ) ) ) ) ) ) )
| ~ ( v16 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3955]) ).
thf(f3955,plain,
( ! [X10: mworld,X11: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) )
@ X11 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3954]) ).
thf(f3954,plain,
( ! [X10: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3953]) ).
thf(f3953,plain,
( ! [X10: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3952,f358]) ).
thf(f3952,plain,
( ! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v13 @ Y5 ) ) ) ) ) ) )
| ~ ( v16 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3951]) ).
thf(f3951,plain,
( ! [X10: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) )
@ X10 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3950]) ).
thf(f3950,plain,
( ! [X9: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3949]) ).
thf(f3949,plain,
( ! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3948,f358]) ).
thf(f3948,plain,
( ! [X8: mworld,X9: mworld] :
( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v13 @ Y6 ) ) ) ) ) ) )
| ~ ( v16 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3947]) ).
thf(f3947,plain,
( ! [X8: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X9 ) )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3946]) ).
thf(f3946,plain,
( ! [X8: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3945]) ).
thf(f3945,plain,
( ! [X8: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3944,f358]) ).
thf(f3944,plain,
( ! [X8: mworld,X7: mworld] :
( $true
= ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v13 @ Y7 ) ) ) ) ) ) )
| ~ ( v16 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3943]) ).
thf(f3943,plain,
( ! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3942]) ).
thf(f3942,plain,
( ! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3941]) ).
thf(f3941,plain,
( ! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3940,f358]) ).
thf(f3940,plain,
( ! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v13 @ Y8 ) ) ) ) ) ) )
| ~ ( v16 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3939]) ).
thf(f3939,plain,
( ! [X6: mworld,X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3938]) ).
thf(f3938,plain,
( ! [X6: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3937]) ).
thf(f3937,plain,
( ! [X6: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3936,f358]) ).
thf(f3936,plain,
( ! [X6: mworld,X5: mworld] :
( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v13 @ Y9 ) ) ) ) ) ) )
| ~ ( v16 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3935]) ).
thf(f3935,plain,
( ! [X6: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3934]) ).
thf(f3934,plain,
( ! [X5: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(boolean_simplification,[status(thm)],[f3933]) ).
thf(f3933,plain,
( ! [X5: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(forward_demodulation,[status(thm)],[f3932,f358]) ).
thf(f3932,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v13 @ Y10 ) ) ) ) ) ) )
| ~ ( v16 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl0_37 ),
inference(beta_eta_normalization,[status(thm)],[f3931]) ).
thf(f3931,plain,
( ! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) )
| ~ spl0_37 ),
inference(pi_clausification,[status(thm)],[f3926]) ).
thf(f3926,plain,
( ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_37 ),
inference(avatar_component_clause,[status(thm)],[f3925]) ).
thf(f3925,definition,
( spl0_37
<=> ! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_37])],[avatar_definition]) ).
thf(f2304,plain,
! [X15: mworld] :
( ( v13 @ ( sK18 @ X15 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2303]) ).
thf(f2303,plain,
! [X15: mworld] :
( $true
= ( ( v13 @ ( sK18 @ X15 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2302,f358]) ).
thf(f2302,plain,
! [X15: mworld] :
( ( ( v13 @ ( sK18 @ X15 ) )
& ( mrel @ X15 @ ( sK18 @ X15 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2301]) ).
thf(f2301,plain,
! [X15: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) )
@ ( sK18 @ X15 ) ) ),
inference(sigma_clausification,[status(thm)],[f2300]) ).
thf(f2300,plain,
! [X15: mworld] :
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2299]) ).
thf(f2299,plain,
! [X15: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f2296,f2297]) ).
thf(f2297,plain,
! [X15: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2296]) ).
thf(f2296,plain,
! [X15: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2295]) ).
thf(f2295,plain,
! [X15: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v13 @ Y0 )
& ( mrel @ X15 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2288,f2294]) ).
thf(f3930,plain,
( spl0_37
| spl0_38
| ~ spl0_35 ),
inference(avatar_split_clause,[status(thm)],[f3923,f3396,f3928,f3925]) ).
thf(f3396,definition,
( spl0_35
<=> ! [X1: mworld] :
( $true
= ( v28 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition]) ).
thf(f3923,plain,
( ! [X3: mworld,X4: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( v26 @ X3 ) ) )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f3922]) ).
thf(f3922,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) )
| ~ spl0_35 ),
inference(forward_demodulation,[status(thm)],[f3920,f358]) ).
thf(f3920,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v13 @ Y11 ) ) ) ) ) ) )
| ~ ( v16 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ) )
| ~ spl0_35 ),
inference(beta_eta_normalization,[status(thm)],[f3918]) ).
thf(f3918,plain,
( ! [X3: mworld,X4: mworld] :
( ( $true
= ( v26 @ X3 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ) )
| ~ spl0_35 ),
inference(pi_clausification,[status(thm)],[f3470]) ).
thf(f3470,plain,
( ! [X3: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( v26 @ X3 ) ) )
| ~ spl0_35 ),
inference(binary_proxy_clausification,[status(thm)],[f3469]) ).
thf(f3469,plain,
( ! [X3: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) )
= $true )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f3468]) ).
thf(f3468,plain,
( ! [X3: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) ) )
= $true )
| ~ spl0_35 ),
inference(forward_demodulation,[status(thm)],[f3467,f358]) ).
thf(f3467,plain,
( ! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v13 @ Y12 ) ) ) ) ) ) )
| ~ ( v16 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ X3 ) ) )
= $true )
| ~ spl0_35 ),
inference(beta_eta_normalization,[status(thm)],[f3466]) ).
thf(f3466,plain,
( ! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) )
@ X3 )
= $true )
| ~ spl0_35 ),
inference(pi_clausification,[status(thm)],[f3465]) ).
thf(f3465,plain,
( ! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) ) )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f3464]) ).
thf(f3464,plain,
( ! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_35 ),
inference(forward_demodulation,[status(thm)],[f3463,f358]) ).
thf(f3463,plain,
( ! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v13 @ Y13 ) ) ) ) ) ) )
| ~ ( v16 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_35 ),
inference(beta_eta_normalization,[status(thm)],[f3462]) ).
thf(f3462,plain,
( ! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ~ spl0_35 ),
inference(pi_clausification,[status(thm)],[f3450]) ).
thf(f3450,plain,
( ! [X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) ) )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f3449]) ).
thf(f3449,plain,
( ! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| $false )
= $true )
| ~ spl0_35 ),
inference(boolean_simplification,[status(thm)],[f3405]) ).
thf(f3405,plain,
( ! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ~ $true )
= $true )
| ~ spl0_35 ),
inference(backward_demodulation,[status(thm)],[f398,f3397]) ).
thf(f3397,plain,
( ! [X1: mworld] :
( $true
= ( v28 @ X1 ) )
| ~ spl0_35 ),
inference(avatar_component_clause,[status(thm)],[f3396]) ).
thf(f398,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ~ ( v28 @ X1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f397]) ).
thf(f397,plain,
! [X1: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ~ ( v28 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f396,f358]) ).
thf(f396,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v13 @ Y14 ) ) ) ) ) ) )
| ~ ( v16 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ~ ( v28 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f395]) ).
thf(f395,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v13 @ Y15 ) ) ) ) ) ) )
| ~ ( v16 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y2 ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f311]) ).
thf(f311,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v13 @ Y15 ) ) ) ) ) ) )
| ~ ( v16 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y2 ) ) ) ) ) )
| ~ ( v28 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f277]) ).
thf(f277,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v28 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v26
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v16 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f224,f207,f201,f192,f208,f201,f201,f192,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f208]) ).
thf(f224,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f114]) ).
thf(f114,plain,
( ( mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f113]) ).
thf(f113,plain,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod6) ).
thf(f3401,plain,
( spl0_35
| spl0_36 ),
inference(avatar_split_clause,[status(thm)],[f3394,f3399,f3396]) ).
thf(f3394,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f3393]) ).
thf(f3393,plain,
! [X2: mworld,X1: mworld] :
( ( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( v28 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f3391,f358]) ).
thf(f3391,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( v28 @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v14 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3389]) ).
thf(f3389,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( $true
= ( v28 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f385]) ).
thf(f385,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( v28 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f384]) ).
thf(f384,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ( v28 @ X1 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f383]) ).
thf(f383,plain,
! [X1: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ( v28 @ X1 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f382,f358]) ).
thf(f382,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v14 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y1 ) ) ) ) ) )
| ( v28 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f381]) ).
thf(f381,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v14 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y2 ) ) ) ) ) )
| ( v28 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f345]) ).
thf(f345,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v14 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( v21 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v26 @ Y2 ) ) ) ) ) )
| ( v28 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v28
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v26
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v21 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f191,f207,f201,f192,f201,f201,f192,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201]) ).
thf(f191,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f180]) ).
thf(f180,plain,
( ( mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f179]) ).
thf(f179,plain,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod2) ).
thf(f3142,plain,
( ~ spl0_16
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f3141]) ).
thf(f3141,plain,
( $false
| ~ spl0_16
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f3140]) ).
thf(f3140,plain,
( ( $true = $false )
| ~ spl0_16
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3139]) ).
thf(f3139,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f3138,f3019]) ).
thf(f3019,plain,
( ! [X25: mworld] :
( ( v4 @ X25 )
= $true )
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f3018]) ).
thf(f3018,plain,
( ! [X25: mworld] :
( ( $true
=> ( v4 @ X25 ) )
= $true )
| ~ spl0_16 ),
inference(forward_demodulation,[status(thm)],[f3017,f358]) ).
thf(f3017,plain,
( ! [X24: mworld,X25: mworld] :
( $true
= ( ( mrel @ X24 @ X25 )
=> ( v4 @ X25 ) ) )
| ~ spl0_16 ),
inference(beta_eta_normalization,[status(thm)],[f3016]) ).
thf(f3016,plain,
( ! [X24: mworld,X25: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( v4 @ Y0 ) )
@ X25 )
= $true )
| ~ spl0_16 ),
inference(pi_clausification,[status(thm)],[f2395]) ).
thf(f2395,plain,
( ! [X24: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( v4 @ Y0 ) ) )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f2394]) ).
thf(f2394,definition,
( spl0_16
<=> ! [X24: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( v4 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f3138,plain,
( ! [X1: mworld] :
( ( ~ ( v4 @ X1 ) )
= $true )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3137]) ).
thf(f3137,plain,
( ! [X1: mworld] :
( $true
= ( $true
=> ~ ( v4 @ X1 ) ) )
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f3135,f358]) ).
thf(f3135,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK27 @ X0 ) @ X1 )
=> ~ ( v4 @ X1 ) )
= $true )
| ~ spl0_25 ),
inference(beta_eta_normalization,[status(thm)],[f3133]) ).
thf(f3133,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK27 @ X0 ) @ Y0 )
=> ~ ( v4 @ Y0 ) )
@ X1 ) )
| ~ spl0_25 ),
inference(pi_clausification,[status(thm)],[f3132]) ).
thf(f3132,plain,
( ! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK27 @ X0 ) @ Y0 )
=> ~ ( v4 @ Y0 ) ) ) )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3130]) ).
thf(f3130,plain,
( ! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK27 @ X0 ) @ Y0 )
=> ~ ( v4 @ Y0 ) ) )
| $false ) )
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f3127,f2702]) ).
thf(f3127,plain,
( ! [X19: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v4 @ Y0 ) ) )
| ( v5 @ X19 ) ) )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3126]) ).
thf(f3126,plain,
( ! [X19: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v4 @ Y0 ) ) )
| ( v5 @ X19 ) ) )
= $true )
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f3125,f358]) ).
thf(f3125,plain,
( ! [X18: mworld,X19: mworld] :
( ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ~ ( v4 @ Y0 ) ) )
| ( v5 @ X19 ) ) )
= $true )
| ~ spl0_25 ),
inference(beta_eta_normalization,[status(thm)],[f3124]) ).
thf(f3124,plain,
( ! [X18: mworld,X19: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) )
| ( v5 @ Y0 ) ) )
@ X19 )
= $true )
| ~ spl0_25 ),
inference(pi_clausification,[status(thm)],[f3123]) ).
thf(f3123,plain,
( ! [X18: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) )
| ( v5 @ Y0 ) ) ) )
= $true )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3122]) ).
thf(f3122,plain,
( ! [X18: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) )
| ( v5 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f3121,f358]) ).
thf(f3121,plain,
( ! [X18: mworld,X17: mworld] :
( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( v4 @ Y1 ) ) )
| ( v5 @ Y0 ) ) ) ) ) )
| ~ spl0_25 ),
inference(beta_eta_normalization,[status(thm)],[f3120]) ).
thf(f3120,plain,
( ! [X18: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v4 @ Y2 ) ) )
| ( v5 @ Y1 ) ) ) ) )
@ X18 )
= $true )
| ~ spl0_25 ),
inference(pi_clausification,[status(thm)],[f3119]) ).
thf(f3119,plain,
( ! [X17: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v4 @ Y2 ) ) )
| ( v5 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3118]) ).
thf(f3118,plain,
( ! [X17: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v4 @ Y2 ) ) )
| ( v5 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f3117,f358]) ).
thf(f3117,plain,
( ! [X16: mworld,X17: mworld] :
( ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ~ ( v4 @ Y2 ) ) )
| ( v5 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(beta_eta_normalization,[status(thm)],[f3116]) ).
thf(f3116,plain,
( ! [X16: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v4 @ Y3 ) ) )
| ( v5 @ Y2 ) ) ) ) ) ) )
@ X17 )
= $true )
| ~ spl0_25 ),
inference(pi_clausification,[status(thm)],[f3115]) ).
thf(f3115,plain,
( ! [X16: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v4 @ Y3 ) ) )
| ( v5 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(boolean_simplification,[status(thm)],[f3114]) ).
thf(f3114,plain,
( ! [X16: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v4 @ Y3 ) ) )
| ( v5 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(forward_demodulation,[status(thm)],[f3113,f358]) ).
thf(f3113,plain,
( ! [X16: mworld,X15: mworld] :
( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ~ ( v4 @ Y3 ) ) )
| ( v5 @ Y2 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(beta_eta_normalization,[status(thm)],[f3112]) ).
thf(f3112,plain,
( ! [X16: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v4 @ Y4 ) ) )
| ( v5 @ Y3 ) ) ) ) ) ) ) ) )
@ X16 )
= $true )
| ~ spl0_25 ),
inference(pi_clausification,[status(thm)],[f3110]) ).
thf(f3110,plain,
( ! [X15: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v4 @ Y4 ) ) )
| ( v5 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f3109]) ).
thf(f3109,definition,
( spl0_25
<=> ! [X15: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v4 @ Y4 ) ) )
| ( v5 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f3111,plain,
( spl0_6
| spl0_25 ),
inference(avatar_split_clause,[status(thm)],[f3107,f3109,f1046]) ).
thf(f3107,plain,
! [X14: mworld,X15: mworld] :
( ( $true
= ( v10 @ X14 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v4 @ Y4 ) ) )
| ( v5 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f3106]) ).
thf(f3106,plain,
! [X14: mworld,X15: mworld] :
( ( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v4 @ Y4 ) ) )
| ( v5 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( v10 @ X14 ) ) ),
inference(forward_demodulation,[status(thm)],[f3105,f358]) ).
thf(f3105,plain,
! [X14: mworld,X15: mworld] :
( ( $true
= ( v10 @ X14 ) )
| ( ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ~ ( v4 @ Y4 ) ) )
| ( v5 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f3102]) ).
thf(f3102,plain,
! [X14: mworld,X15: mworld] :
( ( $true
= ( v10 @ X14 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v4 @ Y5 ) ) )
| ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f2143]) ).
thf(f2143,plain,
! [X14: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v4 @ Y5 ) ) )
| ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( v10 @ X14 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1752]) ).
thf(f1752,plain,
! [X14: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v4 @ Y5 ) ) )
| ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ X14 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1751]) ).
thf(f1751,plain,
! [X14: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v4 @ Y5 ) ) )
| ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ X14 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1750,f358]) ).
thf(f1750,plain,
! [X14: mworld,X13: mworld] :
( ( ( mrel @ X13 @ X14 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ~ ( v4 @ Y5 ) ) )
| ( v5 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ X14 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1749]) ).
thf(f1749,plain,
! [X14: mworld,X13: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v4 @ Y6 ) ) )
| ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) )
@ X14 ) ),
inference(pi_clausification,[status(thm)],[f1748]) ).
thf(f1748,plain,
! [X13: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v4 @ Y6 ) ) )
| ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1747]) ).
thf(f1747,plain,
! [X13: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v4 @ Y6 ) ) )
| ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1746,f358]) ).
thf(f1746,plain,
! [X12: mworld,X13: mworld] :
( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ~ ( v4 @ Y6 ) ) )
| ( v5 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1745]) ).
thf(f1745,plain,
! [X12: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v4 @ Y7 ) ) )
| ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) )
@ X13 )
= $true ),
inference(pi_clausification,[status(thm)],[f1744]) ).
thf(f1744,plain,
! [X12: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v4 @ Y7 ) ) )
| ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1743]) ).
thf(f1743,plain,
! [X12: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v4 @ Y7 ) ) )
| ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1742,f358]) ).
thf(f1742,plain,
! [X11: mworld,X12: mworld] :
( ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ~ ( v4 @ Y7 ) ) )
| ( v5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1741]) ).
thf(f1741,plain,
! [X11: mworld,X12: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v4 @ Y8 ) ) )
| ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) )
@ X12 ) ),
inference(pi_clausification,[status(thm)],[f1740]) ).
thf(f1740,plain,
! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v4 @ Y8 ) ) )
| ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1739]) ).
thf(f1739,plain,
! [X11: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v4 @ Y8 ) ) )
| ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1738,f358]) ).
thf(f1738,plain,
! [X10: mworld,X11: mworld] :
( $true
= ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ~ ( v4 @ Y8 ) ) )
| ( v5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1737]) ).
thf(f1737,plain,
! [X10: mworld,X11: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v4 @ Y9 ) ) )
| ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) )
@ X11 ) ),
inference(pi_clausification,[status(thm)],[f1736]) ).
thf(f1736,plain,
! [X10: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v4 @ Y9 ) ) )
| ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1735]) ).
thf(f1735,plain,
! [X10: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v4 @ Y9 ) ) )
| ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1734,f358]) ).
thf(f1734,plain,
! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ~ ( v4 @ Y9 ) ) )
| ( v5 @ Y8 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1733]) ).
thf(f1733,plain,
! [X10: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v4 @ Y10 ) ) )
| ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true ),
inference(pi_clausification,[status(thm)],[f1732]) ).
thf(f1732,plain,
! [X9: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v4 @ Y10 ) ) )
| ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1731]) ).
thf(f1731,plain,
! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v4 @ Y10 ) ) )
| ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1730,f358]) ).
thf(f1730,plain,
! [X8: mworld,X9: mworld] :
( $true
= ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ~ ( v4 @ Y10 ) ) )
| ( v5 @ Y9 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1729]) ).
thf(f1729,plain,
! [X8: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v4 @ Y11 ) ) )
| ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 )
= $true ),
inference(pi_clausification,[status(thm)],[f1727]) ).
thf(f1727,plain,
! [X8: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v4 @ Y11 ) ) )
| ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1726]) ).
thf(f1726,plain,
! [X8: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v4 @ Y11 ) ) )
| ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1725,f358]) ).
thf(f1725,plain,
! [X8: mworld,X7: mworld] :
( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ~ ( v4 @ Y11 ) ) )
| ( v5 @ Y10 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1724]) ).
thf(f1724,plain,
! [X8: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v4 @ Y12 ) ) )
| ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 )
= $true ),
inference(pi_clausification,[status(thm)],[f1719]) ).
thf(f1719,plain,
! [X7: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v4 @ Y12 ) ) )
| ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1718]) ).
thf(f1718,plain,
! [X7: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v4 @ Y12 ) ) )
| ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1717,f358]) ).
thf(f1717,plain,
! [X6: mworld,X7: mworld] :
( $true
= ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ~ ( v4 @ Y12 ) ) )
| ( v5 @ Y11 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1716]) ).
thf(f1716,plain,
! [X6: mworld,X7: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v4 @ Y13 ) ) )
| ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f1711]) ).
thf(f1711,plain,
! [X6: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v4 @ Y13 ) ) )
| ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1710]) ).
thf(f1710,plain,
! [X6: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v4 @ Y13 ) ) )
| ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1709,f358]) ).
thf(f1709,plain,
! [X6: mworld,X5: mworld] :
( ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ~ ( v4 @ Y13 ) ) )
| ( v5 @ Y12 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1708]) ).
thf(f1708,plain,
! [X6: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v4 @ Y14 ) ) )
| ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f1703]) ).
thf(f1703,plain,
! [X5: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v4 @ Y14 ) ) )
| ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1702]) ).
thf(f1702,plain,
! [X5: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v4 @ Y14 ) ) )
| ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1701,f358]) ).
thf(f1701,plain,
! [X4: mworld,X5: mworld] :
( ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ~ ( v4 @ Y14 ) ) )
| ( v5 @ Y13 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1700]) ).
thf(f1700,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v4 @ Y15 ) ) )
| ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f1695]) ).
thf(f1695,plain,
! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v4 @ Y15 ) ) )
| ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1694]) ).
thf(f1694,plain,
! [X4: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v4 @ Y15 ) ) )
| ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1693,f358]) ).
thf(f1693,plain,
! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ~ ( v4 @ Y15 ) ) )
| ( v5 @ Y14 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1692]) ).
thf(f1692,plain,
! [X3: mworld,X4: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v4 @ Y16 ) ) )
| ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f1685]) ).
thf(f1685,plain,
! [X3: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v4 @ Y16 ) ) )
| ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1684]) ).
thf(f1684,plain,
! [X3: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v4 @ Y16 ) ) )
| ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1683,f358]) ).
thf(f1683,plain,
! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ~ ( v4 @ Y16 ) ) )
| ( v5 @ Y15 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1682]) ).
thf(f1682,plain,
! [X2: mworld,X3: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v4 @ Y17 ) ) )
| ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1680]) ).
thf(f1680,plain,
! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v4 @ Y17 ) ) )
| ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1679]) ).
thf(f1679,plain,
! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v4 @ Y17 ) ) )
| ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1678,f358]) ).
thf(f1678,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ~ ( v4 @ Y17 ) ) )
| ( v5 @ Y16 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1677]) ).
thf(f1677,plain,
! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v4 @ Y18 ) ) )
| ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1670]) ).
thf(f1670,plain,
! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v4 @ Y18 ) ) )
| ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1669]) ).
thf(f1669,plain,
! [X1: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v4 @ Y18 ) ) )
| ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1667,f358]) ).
thf(f1667,plain,
! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK5 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ~ ( v4 @ Y18 ) ) )
| ( v5 @ Y17 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1665]) ).
thf(f1665,plain,
! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK5 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v4 @ Y19 ) ) )
| ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1662]) ).
thf(f1662,plain,
! [X0: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK5 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v4 @ Y19 ) ) )
| ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1657]) ).
thf(f1657,plain,
! [X0: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK5 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v4 @ Y19 ) ) )
| ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| $false )
= $true ),
inference(superposition,[status(thm)],[f991,f1650]) ).
thf(f1650,plain,
! [X4: mworld] :
( $false
= ( v24 @ ( sK5 @ X4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1641]) ).
thf(f1641,plain,
! [X4: mworld] :
( ( ~ ( v24 @ ( sK5 @ X4 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1640]) ).
thf(f1640,plain,
! [X4: mworld] :
( $true
= ( ~ ( v24 @ ( sK5 @ X4 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f1639,f358]) ).
thf(f1639,plain,
! [X4: mworld] :
( ( ~ ( v24 @ ( sK5 @ X4 ) )
& ( mrel @ X4 @ ( sK5 @ X4 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1638]) ).
thf(f1638,plain,
! [X4: mworld] :
( ( ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) )
@ ( sK5 @ X4 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f1633]) ).
thf(f1633,plain,
! [X4: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f1632]) ).
thf(f1632,plain,
! [X4: mworld] :
( ( $true
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v24 @ Y0 )
& ( mrel @ X4 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f1629,f1631]) ).
thf(f991,plain,
! [X5: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v4 @ Y19 ) ) )
| ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ X5 ) ) ),
inference(boolean_simplification,[status(thm)],[f990]) ).
thf(f990,plain,
! [X5: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v4 @ Y19 ) ) )
| ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ X5 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f989,f358]) ).
thf(f989,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ~ ( v4 @ Y19 ) ) )
| ( v5 @ Y18 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ X5 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f988]) ).
thf(f988,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v4 @ Y20 ) ) )
| ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y0 ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f987]) ).
thf(f987,plain,
! [X4: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v4 @ Y20 ) ) )
| ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f986]) ).
thf(f986,plain,
! [X4: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v4 @ Y20 ) ) )
| ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f985,f358]) ).
thf(f985,plain,
! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ~ ( v4 @ Y20 ) ) )
| ( v5 @ Y19 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f984]) ).
thf(f984,plain,
! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v4 @ Y21 ) ) )
| ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y1 ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f983]) ).
thf(f983,plain,
! [X3: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v4 @ Y21 ) ) )
| ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f982]) ).
thf(f982,plain,
! [X3: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v4 @ Y21 ) ) )
| ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y1 ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f981,f358]) ).
thf(f981,plain,
! [X2: mworld,X3: mworld] :
( ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ~ ( v4 @ Y21 ) ) )
| ( v5 @ Y20 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f980]) ).
thf(f980,plain,
! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v4 @ Y22 ) ) )
| ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y2 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f979]) ).
thf(f979,plain,
! [X2: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v4 @ Y22 ) ) )
| ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f978]) ).
thf(f978,plain,
! [X2: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v4 @ Y22 ) ) )
| ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f977,f358]) ).
thf(f977,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ~ ( v4 @ Y22 ) ) )
| ( v5 @ Y21 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f976]) ).
thf(f976,plain,
! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ~ ( v4 @ Y23 ) ) )
| ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f975]) ).
thf(f975,plain,
! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ~ ( v4 @ Y23 ) ) )
| ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f974]) ).
thf(f974,plain,
! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ~ ( v4 @ Y23 ) ) )
| ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f973,f358]) ).
thf(f973,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ~ ( v4 @ Y23 ) ) )
| ( v5 @ Y22 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f972]) ).
thf(f972,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ~ ( v4 @ Y24 ) ) )
| ( v5 @ Y23 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f354]) ).
thf(f354,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ~ ( v4 @ Y24 ) ) )
| ( v5 @ Y23 ) ) ) ) ) ) ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( v24 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f271]) ).
thf(f271,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v24
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v10
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v5
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f218,f207,f201,f201,f201,f201,f201,f192,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f201,f201,f201,f201,f201,f192,f201,f208]) ).
thf(f218,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f112]) ).
thf(f112,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f111]) ).
thf(f111,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod31) ).
thf(f2990,plain,
( spl0_7
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f2628,f1043,f1300]) ).
thf(f1300,definition,
( spl0_7
<=> ! [X22: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v4 @ Y2 ) ) ) ) )
| ( v6 @ Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1043,definition,
( spl0_5
<=> ! [X20: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v4 @ Y4 ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) )
| ( v8 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f2628,plain,
( ! [X1: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v4 @ Y2 ) ) ) ) )
| ( v6 @ Y0 ) ) ) )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f2627]) ).
thf(f2627,plain,
( ! [X1: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v4 @ Y2 ) ) ) ) )
| ( v6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f2626,f358]) ).
thf(f2626,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( mrel @ ( sK21 @ X0 ) @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v4 @ Y2 ) ) ) ) )
| ( v6 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f2623]) ).
thf(f2623,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v4 @ Y3 ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f2532]) ).
thf(f2532,plain,
( ! [X0: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v4 @ Y3 ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f2529]) ).
thf(f2529,plain,
( ! [X0: mworld] :
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X0 ) @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v4 @ Y3 ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) )
| $false ) )
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f2134,f2519]) ).
thf(f2519,plain,
! [X20: mworld] :
( $false
= ( v8 @ ( sK21 @ X20 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f2514]) ).
thf(f2514,plain,
! [X20: mworld] :
( $true
= ( ~ ( v8 @ ( sK21 @ X20 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2513]) ).
thf(f2513,plain,
! [X20: mworld] :
( $true
= ( ~ ( v8 @ ( sK21 @ X20 ) )
& $true ) ),
inference(forward_demodulation,[status(thm)],[f2512,f358]) ).
thf(f2512,plain,
! [X20: mworld] :
( ( ~ ( v8 @ ( sK21 @ X20 ) )
& ( mrel @ X20 @ ( sK21 @ X20 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2511]) ).
thf(f2511,plain,
! [X20: mworld] :
( ( ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) )
@ ( sK21 @ X20 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f2483]) ).
thf(f2483,plain,
! [X20: mworld] :
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ~ ( v8 @ Y0 )
& ( mrel @ X20 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2479]) ).
thf(f2134,plain,
( ! [X21: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v4 @ Y3 ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) )
| ( v8 @ X21 ) )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f2133]) ).
thf(f2133,plain,
( ! [X21: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v4 @ Y3 ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) )
| ( v8 @ X21 ) ) ) )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f2132,f358]) ).
thf(f2132,plain,
( ! [X21: mworld,X20: mworld] :
( ( ( mrel @ X20 @ X21 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X21 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v4 @ Y3 ) ) ) ) )
| ( v6 @ Y1 ) ) ) ) ) )
| ( v8 @ X21 ) ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f2131]) ).
thf(f2131,plain,
( ! [X21: mworld,X20: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v4 @ Y4 ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) )
| ( v8 @ Y0 ) ) )
@ X21 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f1044]) ).
thf(f1044,plain,
( ! [X20: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v4 @ Y4 ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) )
| ( v8 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f1043]) ).
thf(f2927,plain,
( spl0_13
| spl0_14
| ~ spl0_21 ),
inference(avatar_split_clause,[status(thm)],[f2926,f2908,f2123,f2120]) ).
thf(f2926,plain,
( ! [X14: mworld,X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( v9 @ X13 ) )
= $true ) )
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f2925]) ).
thf(f2925,plain,
( ! [X14: mworld,X13: mworld] :
( ( ( ~ ( v9 @ X13 ) )
= $true )
| ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) ) ) ) )
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f2923,f358]) ).
thf(f2923,plain,
( ! [X14: mworld,X13: mworld] :
( ( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v5 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( ~ ( v9 @ X13 ) )
= $true ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f2921]) ).
thf(f2921,plain,
( ! [X14: mworld,X13: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) )
@ X14 )
= $true )
| ( ( ~ ( v9 @ X13 ) )
= $true ) )
| ~ spl0_21 ),
inference(pi_clausification,[status(thm)],[f2914]) ).
thf(f2914,plain,
( ! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ~ ( v9 @ X13 ) )
= $true ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f2909]) ).
thf(f2909,plain,
( ! [X13: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( v5 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( v9 @ X13 ) )
= $true )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f2908]) ).
thf(f2551,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[status(thm)],[f2550]) ).
thf(f2550,plain,
( $false
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f2549]) ).
thf(f2549,plain,
( ( $true = $false )
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f2548]) ).
thf(f2548,plain,
( ! [X22: mworld] :
( $true
= ( $false
& ( mrel @ X22 @ ( sK23 @ X22 ) ) ) )
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f2547]) ).
thf(f2547,plain,
( ! [X22: mworld] :
( ( ~ $true
& ( mrel @ X22 @ ( sK23 @ X22 ) ) )
= $true )
| ~ spl0_15 ),
inference(forward_demodulation,[status(thm)],[f2546,f2392]) ).
thf(f2392,plain,
( ! [X23: mworld] :
( $true
= ( v6 @ X23 ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f2391]) ).
thf(f2391,definition,
( spl0_15
<=> ! [X23: mworld] :
( $true
= ( v6 @ X23 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f2546,plain,
! [X22: mworld] :
( ( ~ ( v6 @ ( sK23 @ X22 ) )
& ( mrel @ X22 @ ( sK23 @ X22 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2545]) ).
thf(f2545,plain,
! [X22: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ~ ( v6 @ Y0 )
& ( mrel @ X22 @ Y0 ) )
@ ( sK23 @ X22 ) ) ),
inference(sigma_clausification,[status(thm)],[f2537]) ).
thf(f2396,plain,
( spl0_15
| spl0_16
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f2389,f1300,f2394,f2391]) ).
thf(f2389,plain,
( ! [X24: mworld,X23: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( v4 @ Y0 ) ) )
= $true )
| ( $true
= ( v6 @ X23 ) ) )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f2388]) ).
thf(f2388,plain,
( ! [X24: mworld,X23: mworld] :
( ( $true
= ( v6 @ X23 ) )
| ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( v4 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f2387,f358]) ).
thf(f2387,plain,
( ! [X24: mworld,X23: mworld] :
( ( $true
= ( v6 @ X23 ) )
| ( ( ( mrel @ X23 @ X24 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X24 @ Y0 )
=> ( v4 @ Y0 ) ) ) )
= $true ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f2384]) ).
thf(f2384,plain,
( ! [X24: mworld,X23: mworld] :
( ( $true
= ( v6 @ X23 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) )
@ X24 )
= $true ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f2130]) ).
thf(f2130,plain,
( ! [X23: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( v6 @ X23 ) ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f2129]) ).
thf(f2129,plain,
( ! [X23: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( v6 @ X23 ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f2128]) ).
thf(f2128,plain,
( ! [X23: mworld] :
( ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( v6 @ X23 ) ) )
= $true )
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f2127,f358]) ).
thf(f2127,plain,
( ! [X22: mworld,X23: mworld] :
( ( ( mrel @ X22 @ X23 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X23 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( v4 @ Y1 ) ) ) ) )
| ( v6 @ X23 ) ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f2126]) ).
thf(f2126,plain,
( ! [X22: mworld,X23: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v4 @ Y2 ) ) ) ) )
| ( v6 @ Y0 ) ) )
@ X23 ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1301]) ).
thf(f1301,plain,
( ! [X22: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X22 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( v4 @ Y2 ) ) ) ) )
| ( v6 @ Y0 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f1300]) ).
thf(f1048,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f1041,f1046,f1043]) ).
thf(f1041,plain,
! [X19: mworld,X20: mworld] :
( ( $true
= ( v10 @ X19 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v4 @ Y4 ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) )
| ( v8 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f1040]) ).
thf(f1040,plain,
! [X19: mworld,X20: mworld] :
( ( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v4 @ Y4 ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) )
| ( v8 @ Y0 ) ) ) ) ) )
| ( $true
= ( v10 @ X19 ) ) ),
inference(forward_demodulation,[status(thm)],[f1038,f358]) ).
thf(f1038,plain,
! [X19: mworld,X20: mworld] :
( ( ( ( mrel @ X19 @ X20 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X20 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( v4 @ Y4 ) ) ) ) )
| ( v6 @ Y2 ) ) ) ) ) )
| ( v8 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( v10 @ X19 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1036]) ).
thf(f1036,plain,
! [X19: mworld,X20: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v4 @ Y5 ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) )
| ( v8 @ Y1 ) ) ) ) )
@ X20 )
= $true )
| ( $true
= ( v10 @ X19 ) ) ),
inference(pi_clausification,[status(thm)],[f971]) ).
thf(f971,plain,
! [X19: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v4 @ Y5 ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) )
| ( v8 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( v10 @ X19 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f970]) ).
thf(f970,plain,
! [X19: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v4 @ Y5 ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) )
| ( v8 @ Y1 ) ) ) ) ) )
| ( v10 @ X19 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f969]) ).
thf(f969,plain,
! [X19: mworld] :
( $true
= ( $true
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v4 @ Y5 ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) )
| ( v8 @ Y1 ) ) ) ) ) )
| ( v10 @ X19 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f968,f358]) ).
thf(f968,plain,
! [X18: mworld,X19: mworld] :
( ( ( mrel @ X18 @ X19 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X19 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( v4 @ Y5 ) ) ) ) )
| ( v6 @ Y3 ) ) ) ) ) )
| ( v8 @ Y1 ) ) ) ) ) )
| ( v10 @ X19 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f967]) ).
thf(f967,plain,
! [X18: mworld,X19: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v4 @ Y6 ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) )
| ( v8 @ Y2 ) ) ) ) ) )
| ( v10 @ Y0 ) ) )
@ X19 )
= $true ),
inference(pi_clausification,[status(thm)],[f966]) ).
thf(f966,plain,
! [X18: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v4 @ Y6 ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) )
| ( v8 @ Y2 ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f965]) ).
thf(f965,plain,
! [X18: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v4 @ Y6 ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) )
| ( v8 @ Y2 ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f964,f358]) ).
thf(f964,plain,
! [X18: mworld,X17: mworld] :
( $true
= ( ( mrel @ X17 @ X18 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X18 @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( v4 @ Y6 ) ) ) ) )
| ( v6 @ Y4 ) ) ) ) ) )
| ( v8 @ Y2 ) ) ) ) ) )
| ( v10 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f963]) ).
thf(f963,plain,
! [X18: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v4 @ Y7 ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) )
| ( v8 @ Y3 ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) )
@ X18 )
= $true ),
inference(pi_clausification,[status(thm)],[f962]) ).
thf(f962,plain,
! [X17: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v4 @ Y7 ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) )
| ( v8 @ Y3 ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f961]) ).
thf(f961,plain,
! [X17: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v4 @ Y7 ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) )
| ( v8 @ Y3 ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f960,f358]) ).
thf(f960,plain,
! [X16: mworld,X17: mworld] :
( $true
= ( ( mrel @ X16 @ X17 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X17 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( v4 @ Y7 ) ) ) ) )
| ( v6 @ Y5 ) ) ) ) ) )
| ( v8 @ Y3 ) ) ) ) ) )
| ( v10 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f959]) ).
thf(f959,plain,
! [X16: mworld,X17: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v4 @ Y8 ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) )
| ( v8 @ Y4 ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) )
@ X17 )
= $true ),
inference(pi_clausification,[status(thm)],[f958]) ).
thf(f958,plain,
! [X16: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v4 @ Y8 ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) )
| ( v8 @ Y4 ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f957]) ).
thf(f957,plain,
! [X16: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v4 @ Y8 ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) )
| ( v8 @ Y4 ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f956,f358]) ).
thf(f956,plain,
! [X16: mworld,X15: mworld] :
( ( ( mrel @ X15 @ X16 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X16 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( v4 @ Y8 ) ) ) ) )
| ( v6 @ Y6 ) ) ) ) ) )
| ( v8 @ Y4 ) ) ) ) ) )
| ( v10 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f955]) ).
thf(f955,plain,
! [X16: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v4 @ Y9 ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) )
| ( v8 @ Y5 ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) )
@ X16 )
= $true ),
inference(pi_clausification,[status(thm)],[f954]) ).
thf(f954,plain,
! [X15: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v4 @ Y9 ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) )
| ( v8 @ Y5 ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f953]) ).
thf(f953,plain,
! [X15: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v4 @ Y9 ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) )
| ( v8 @ Y5 ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f952,f358]) ).
thf(f952,plain,
! [X14: mworld,X15: mworld] :
( $true
= ( ( mrel @ X14 @ X15 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X15 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( v4 @ Y9 ) ) ) ) )
| ( v6 @ Y7 ) ) ) ) ) )
| ( v8 @ Y5 ) ) ) ) ) )
| ( v10 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f951]) ).
thf(f951,plain,
! [X14: mworld,X15: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v4 @ Y10 ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) )
| ( v8 @ Y6 ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X15 )
= $true ),
inference(pi_clausification,[status(thm)],[f950]) ).
thf(f950,plain,
! [X14: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v4 @ Y10 ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) )
| ( v8 @ Y6 ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f949]) ).
thf(f949,plain,
! [X14: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v4 @ Y10 ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) )
| ( v8 @ Y6 ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f948,f358]) ).
thf(f948,plain,
! [X14: mworld,X13: mworld] :
( ( ( mrel @ X13 @ X14 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X14 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( v4 @ Y10 ) ) ) ) )
| ( v6 @ Y8 ) ) ) ) ) )
| ( v8 @ Y6 ) ) ) ) ) )
| ( v10 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f947]) ).
thf(f947,plain,
! [X14: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v4 @ Y11 ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) )
| ( v8 @ Y7 ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X14 )
= $true ),
inference(pi_clausification,[status(thm)],[f946]) ).
thf(f946,plain,
! [X13: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v4 @ Y11 ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) )
| ( v8 @ Y7 ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f945]) ).
thf(f945,plain,
! [X13: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v4 @ Y11 ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) )
| ( v8 @ Y7 ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f944,f358]) ).
thf(f944,plain,
! [X12: mworld,X13: mworld] :
( ( ( mrel @ X12 @ X13 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X13 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( v4 @ Y11 ) ) ) ) )
| ( v6 @ Y9 ) ) ) ) ) )
| ( v8 @ Y7 ) ) ) ) ) )
| ( v10 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f943]) ).
thf(f943,plain,
! [X12: mworld,X13: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v4 @ Y12 ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) )
| ( v8 @ Y8 ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X13 )
= $true ),
inference(pi_clausification,[status(thm)],[f942]) ).
thf(f942,plain,
! [X12: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v4 @ Y12 ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) )
| ( v8 @ Y8 ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f941]) ).
thf(f941,plain,
! [X12: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v4 @ Y12 ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) )
| ( v8 @ Y8 ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f940,f358]) ).
thf(f940,plain,
! [X11: mworld,X12: mworld] :
( $true
= ( ( mrel @ X11 @ X12 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X12 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( v4 @ Y12 ) ) ) ) )
| ( v6 @ Y10 ) ) ) ) ) )
| ( v8 @ Y8 ) ) ) ) ) )
| ( v10 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f939]) ).
thf(f939,plain,
! [X11: mworld,X12: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v4 @ Y13 ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) )
| ( v8 @ Y9 ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X12 )
= $true ),
inference(pi_clausification,[status(thm)],[f938]) ).
thf(f938,plain,
! [X11: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v4 @ Y13 ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) )
| ( v8 @ Y9 ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f937]) ).
thf(f937,plain,
! [X11: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v4 @ Y13 ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) )
| ( v8 @ Y9 ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f936,f358]) ).
thf(f936,plain,
! [X10: mworld,X11: mworld] :
( ( ( mrel @ X10 @ X11 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X11 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( v4 @ Y13 ) ) ) ) )
| ( v6 @ Y11 ) ) ) ) ) )
| ( v8 @ Y9 ) ) ) ) ) )
| ( v10 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f935]) ).
thf(f935,plain,
! [X10: mworld,X11: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v4 @ Y14 ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) )
| ( v8 @ Y10 ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X11 ) ),
inference(pi_clausification,[status(thm)],[f934]) ).
thf(f934,plain,
! [X10: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v4 @ Y14 ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) )
| ( v8 @ Y10 ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f933]) ).
thf(f933,plain,
! [X10: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v4 @ Y14 ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) )
| ( v8 @ Y10 ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f932,f358]) ).
thf(f932,plain,
! [X10: mworld,X9: mworld] :
( ( ( mrel @ X9 @ X10 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X10 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( v4 @ Y14 ) ) ) ) )
| ( v6 @ Y12 ) ) ) ) ) )
| ( v8 @ Y10 ) ) ) ) ) )
| ( v10 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f931]) ).
thf(f931,plain,
! [X10: mworld,X9: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v4 @ Y15 ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) )
| ( v8 @ Y11 ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X10 )
= $true ),
inference(pi_clausification,[status(thm)],[f930]) ).
thf(f930,plain,
! [X9: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v4 @ Y15 ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) )
| ( v8 @ Y11 ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f929]) ).
thf(f929,plain,
! [X9: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v4 @ Y15 ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) )
| ( v8 @ Y11 ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f928,f358]) ).
thf(f928,plain,
! [X8: mworld,X9: mworld] :
( ( ( mrel @ X8 @ X9 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X9 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( v4 @ Y15 ) ) ) ) )
| ( v6 @ Y13 ) ) ) ) ) )
| ( v8 @ Y11 ) ) ) ) ) )
| ( v10 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f927]) ).
thf(f927,plain,
! [X8: mworld,X9: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v4 @ Y16 ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) )
| ( v8 @ Y12 ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X9 ) ),
inference(pi_clausification,[status(thm)],[f926]) ).
thf(f926,plain,
! [X8: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v4 @ Y16 ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) )
| ( v8 @ Y12 ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f925]) ).
thf(f925,plain,
! [X8: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v4 @ Y16 ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) )
| ( v8 @ Y12 ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f924,f358]) ).
thf(f924,plain,
! [X8: mworld,X7: mworld] :
( ( ( mrel @ X7 @ X8 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X8 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( v4 @ Y16 ) ) ) ) )
| ( v6 @ Y14 ) ) ) ) ) )
| ( v8 @ Y12 ) ) ) ) ) )
| ( v10 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f923]) ).
thf(f923,plain,
! [X8: mworld,X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v4 @ Y17 ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) )
| ( v8 @ Y13 ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X8 ) ),
inference(pi_clausification,[status(thm)],[f922]) ).
thf(f922,plain,
! [X7: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v4 @ Y17 ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) )
| ( v8 @ Y13 ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f921]) ).
thf(f921,plain,
! [X7: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v4 @ Y17 ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) )
| ( v8 @ Y13 ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f920,f358]) ).
thf(f920,plain,
! [X6: mworld,X7: mworld] :
( ( ( mrel @ X6 @ X7 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X7 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( v4 @ Y17 ) ) ) ) )
| ( v6 @ Y15 ) ) ) ) ) )
| ( v8 @ Y13 ) ) ) ) ) )
| ( v10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f919]) ).
thf(f919,plain,
! [X6: mworld,X7: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v4 @ Y18 ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) )
| ( v8 @ Y14 ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f918]) ).
thf(f918,plain,
! [X6: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v4 @ Y18 ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) )
| ( v8 @ Y14 ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f917]) ).
thf(f917,plain,
! [X6: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v4 @ Y18 ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) )
| ( v8 @ Y14 ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f916,f358]) ).
thf(f916,plain,
! [X6: mworld,X5: mworld] :
( $true
= ( ( mrel @ X5 @ X6 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X6 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( v4 @ Y18 ) ) ) ) )
| ( v6 @ Y16 ) ) ) ) ) )
| ( v8 @ Y14 ) ) ) ) ) )
| ( v10 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f915]) ).
thf(f915,plain,
! [X6: mworld,X5: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v4 @ Y19 ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) )
| ( v8 @ Y15 ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f914]) ).
thf(f914,plain,
! [X5: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v4 @ Y19 ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) )
| ( v8 @ Y15 ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f913]) ).
thf(f913,plain,
! [X5: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v4 @ Y19 ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) )
| ( v8 @ Y15 ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f912,f358]) ).
thf(f912,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ( mrel @ X4 @ X5 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X5 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( v4 @ Y19 ) ) ) ) )
| ( v6 @ Y17 ) ) ) ) ) )
| ( v8 @ Y15 ) ) ) ) ) )
| ( v10 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f911]) ).
thf(f911,plain,
! [X4: mworld,X5: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v4 @ Y20 ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) )
| ( v8 @ Y16 ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f910]) ).
thf(f910,plain,
! [X4: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v4 @ Y20 ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) )
| ( v8 @ Y16 ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f909]) ).
thf(f909,plain,
! [X4: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v4 @ Y20 ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) )
| ( v8 @ Y16 ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f908,f358]) ).
thf(f908,plain,
! [X3: mworld,X4: mworld] :
( ( ( mrel @ X3 @ X4 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( v4 @ Y20 ) ) ) ) )
| ( v6 @ Y18 ) ) ) ) ) )
| ( v8 @ Y16 ) ) ) ) ) )
| ( v10 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f907]) ).
thf(f907,plain,
! [X3: mworld,X4: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v4 @ Y21 ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) )
| ( v8 @ Y17 ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f906]) ).
thf(f906,plain,
! [X3: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v4 @ Y21 ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) )
| ( v8 @ Y17 ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f905]) ).
thf(f905,plain,
! [X3: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v4 @ Y21 ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) )
| ( v8 @ Y17 ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f904,f358]) ).
thf(f904,plain,
! [X2: mworld,X3: mworld] :
( $true
= ( ( mrel @ X2 @ X3 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X3 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( v4 @ Y21 ) ) ) ) )
| ( v6 @ Y19 ) ) ) ) ) )
| ( v8 @ Y17 ) ) ) ) ) )
| ( v10 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f903]) ).
thf(f903,plain,
! [X2: mworld,X3: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v4 @ Y22 ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) )
| ( v8 @ Y18 ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f902]) ).
thf(f902,plain,
! [X2: mworld] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v4 @ Y22 ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) )
| ( v8 @ Y18 ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f901]) ).
thf(f901,plain,
! [X2: mworld] :
( ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v4 @ Y22 ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) )
| ( v8 @ Y18 ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f900,f358]) ).
thf(f900,plain,
! [X2: mworld,X1: mworld] :
( $true
= ( ( mrel @ X1 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( v4 @ Y22 ) ) ) ) )
| ( v6 @ Y20 ) ) ) ) ) )
| ( v8 @ Y18 ) ) ) ) ) )
| ( v10 @ Y16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f899]) ).
thf(f899,plain,
! [X2: mworld,X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v4 @ Y23 ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) )
| ( v8 @ Y19 ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f898]) ).
thf(f898,plain,
! [X1: mworld] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v4 @ Y23 ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) )
| ( v8 @ Y19 ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f897]) ).
thf(f897,plain,
! [X1: mworld] :
( $true
= ( $true
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v4 @ Y23 ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) )
| ( v8 @ Y19 ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f896,f358]) ).
thf(f896,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( v4 @ Y23 ) ) ) ) )
| ( v6 @ Y21 ) ) ) ) ) )
| ( v8 @ Y19 ) ) ) ) ) )
| ( v10 @ Y17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f895]) ).
thf(f895,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( v4 @ Y24 ) ) ) ) )
| ( v6 @ Y22 ) ) ) ) ) )
| ( v8 @ Y20 ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f334]) ).
thf(f334,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( !! @ mworld
@ ^ [Y7: mworld] :
( ( mrel @ Y6 @ Y7 )
=> ( !! @ mworld
@ ^ [Y8: mworld] :
( ( mrel @ Y7 @ Y8 )
=> ( !! @ mworld
@ ^ [Y9: mworld] :
( ( mrel @ Y8 @ Y9 )
=> ( !! @ mworld
@ ^ [Y10: mworld] :
( ( mrel @ Y9 @ Y10 )
=> ( !! @ mworld
@ ^ [Y11: mworld] :
( ( mrel @ Y10 @ Y11 )
=> ( !! @ mworld
@ ^ [Y12: mworld] :
( ( mrel @ Y11 @ Y12 )
=> ( !! @ mworld
@ ^ [Y13: mworld] :
( ( mrel @ Y12 @ Y13 )
=> ( !! @ mworld
@ ^ [Y14: mworld] :
( ( mrel @ Y13 @ Y14 )
=> ( !! @ mworld
@ ^ [Y15: mworld] :
( ( mrel @ Y14 @ Y15 )
=> ( !! @ mworld
@ ^ [Y16: mworld] :
( ( mrel @ Y15 @ Y16 )
=> ( !! @ mworld
@ ^ [Y17: mworld] :
( ( mrel @ Y16 @ Y17 )
=> ( !! @ mworld
@ ^ [Y18: mworld] :
( ( mrel @ Y17 @ Y18 )
=> ( ( !! @ mworld
@ ^ [Y19: mworld] :
( ( mrel @ Y18 @ Y19 )
=> ( !! @ mworld
@ ^ [Y20: mworld] :
( ( mrel @ Y19 @ Y20 )
=> ( ( !! @ mworld
@ ^ [Y21: mworld] :
( ( mrel @ Y20 @ Y21 )
=> ( !! @ mworld
@ ^ [Y22: mworld] :
( ( mrel @ Y21 @ Y22 )
=> ( ( !! @ mworld
@ ^ [Y23: mworld] :
( ( mrel @ Y22 @ Y23 )
=> ( !! @ mworld
@ ^ [Y24: mworld] :
( ( mrel @ Y23 @ Y24 )
=> ( v4 @ Y24 ) ) ) ) )
| ( v6 @ Y22 ) ) ) ) ) )
| ( v8 @ Y20 ) ) ) ) ) )
| ( v10 @ Y18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f263]) ).
thf(f263,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v10
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v8
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ v6
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f206,f207,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f201,f201,f192,f201,f201,f192,f201,f201]) ).
thf(f206,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f83]) ).
thf(f83,plain,
( ( mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f82]) ).
thf(f82,plain,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f57]) ).
thf(f57,axiom,
mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod48) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO904^12 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 14:54:34 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : SYO904^12 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.49 % Domain : Syntactic
% 0.30/0.49 % Problem : QBF-CNFSSS-K=4 C=50 V=4 D=6.1
% 0.30/0.49 % Version : [BP13] axioms.
% 0.30/0.49 % English :
% 0.30/0.49
% 0.30/0.49 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.49 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.49 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.49 % Source : [TPTP]
% 0.30/0.49 % Names : SYM361+1 [QMLTP]
% 0.30/0.49
% 0.30/0.49 % Status : ContradictoryAxioms
% 0.30/0.49 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.62 v8.1.0
% 0.30/0.49 % Syntax : Number of formulae : 100 ( 9 unt; 39 typ; 8 def)
% 0.30/0.49 % Number of atoms : 1830 ( 8 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 159 ( 30 avg)
% 0.30/0.49 % Number of connectives : 1784 ( 1 ~; 1 |; 2 &;1777 @)
% 0.30/0.49 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 85 ( 25 avg)
% 0.30/0.49 % Number of types : 2 ( 1 usr)
% 0.30/0.49 % Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 41 ( 38 usr; 3 con; 0-3 aty)
% 0.30/0.49 % Number of variables : 40 ( 36 ^; 3 !; 1 ?; 40 :)
% 0.30/0.49 % SPC : TH0_CAX_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.49 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.49 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.49 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.30/0.49 % $modalities == $modal_system_S5U].
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf(mworld,type,
% 0.30/0.49 mworld: $tType ).
% 0.30/0.49
% 0.30/0.49 thf(mrel_type,type,
% 0.30/0.49 mrel: mworld > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mactual_type,type,
% 0.30/0.49 mactual: mworld ).
% 0.30/0.49
% 0.30/0.49 thf(mlocal_type,type,
% 0.30/0.49 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mlocal_def,definition,
% 0.30/0.49 ( mlocal
% 0.30/0.49 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mnot_type,type,
% 0.30/0.49 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mand_type,type,
% 0.30/0.49 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mor_type,type,
% 0.30/0.49 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mimplies_type,type,
% 0.30/0.49 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mequiv_type,type,
% 0.30/0.49 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mnot_def,definition,
% 0.30/0.49 ( mnot
% 0.30/0.49 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.49 ~ ( A @ W ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mand_def,definition,
% 0.30/0.49 ( mand
% 0.30/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.49 ( ( A @ W )
% 0.30/0.49 & ( B @ W ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mor_def,definition,
% 0.30/0.49 ( mor
% 0.30/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.49 ( ( A @ W )
% 0.30/0.49 | ( B @ W ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mimplies_def,definition,
% 0.30/0.49 ( mimplies
% 0.30/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.49 ( ( A @ W )
% 0.30/0.49 => ( B @ W ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mequiv_def,definition,
% 0.30/0.49 ( mequiv
% 0.30/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.49 ( ( A @ W )
% 0.30/0.49 <=> ( B @ W ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mbox_type,type,
% 0.30/0.49 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mbox_def,definition,
% 0.30/0.49 ( mbox
% 0.30/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.49 ! [V: mworld] :
% 0.30/0.49 ( ( mrel @ W @ V )
% 0.30/0.49 => ( Phi @ V ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mdia_type,type,
% 0.30/0.49 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mdia_def,definition,
% 0.30/0.49 ( mdia
% 0.30/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.49 ? [V: mworld] :
% 0.30/0.49 ( ( mrel @ W @ V )
% 0.30/0.49 & ( Phi @ V ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mrel_universal,axiom,
% 0.30/0.49 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 0.30/0.49
% 0.30/0.49 %%% This output was generated by tptputils, version 1.2.
% 0.30/0.49 %%% Generated on Wed Apr 27 15:40:49 CEST 2022 using command 'downgrade(tff)'.
% 0.30/0.49 thf(v1_decl,type,
% 0.30/0.49 v1: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v2_decl,type,
% 0.30/0.49 v2: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v3_decl,type,
% 0.30/0.49 v3: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v4_decl,type,
% 0.30/0.49 v4: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v5_decl,type,
% 0.30/0.49 v5: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v6_decl,type,
% 0.30/0.49 v6: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v7_decl,type,
% 0.30/0.49 v7: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v8_decl,type,
% 0.30/0.49 v8: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v9_decl,type,
% 0.30/0.49 v9: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v10_decl,type,
% 0.30/0.49 v10: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v12_decl,type,
% 0.30/0.49 v12: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v11_decl,type,
% 0.30/0.49 v11: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v14_decl,type,
% 0.30/0.49 v14: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v13_decl,type,
% 0.30/0.49 v13: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v16_decl,type,
% 0.30/0.49 v16: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v15_decl,type,
% 0.30/0.49 v15: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v18_decl,type,
% 0.30/0.49 v18: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v17_decl,type,
% 0.30/0.49 v17: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v19_decl,type,
% 0.30/0.49 v19: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v21_decl,type,
% 0.30/0.49 v21: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v20_decl,type,
% 0.30/0.49 v20: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v23_decl,type,
% 0.30/0.49 v23: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v22_decl,type,
% 0.30/0.49 v22: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v25_decl,type,
% 0.30/0.49 v25: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v24_decl,type,
% 0.30/0.49 v24: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v27_decl,type,
% 0.30/0.49 v27: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v26_decl,type,
% 0.30/0.49 v26: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(v28_decl,type,
% 0.30/0.49 v28: mworld > $o ).
% 0.30/0.49
% 0.30/0.49 thf(mod1,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod2,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod3,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod4,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod5,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod6,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod7,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod8,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod9,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod10,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod11,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod12,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod13,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ v27 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod14,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod15,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod16,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod17,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod18,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod19,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod20,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod21,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod22,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod23,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod24,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod25,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod26,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v9 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod27,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod28,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ v16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod29,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod30,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod31,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod32,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod33,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v17 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod34,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v2 ) @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod35,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod36,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod37,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v9 @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod38,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v18 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod39,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod40,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod41,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod42,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod43,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod44,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mor @ v12 @ ( mbox @ v11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod45,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod46,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod47,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mor @ v3 @ ( mbox @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod48,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod49,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(mod50,axiom,
% 0.30/0.49 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(alt1,axiom,
% 0.30/0.49 ( mlocal
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mand
% 0.30/0.49 @ ( mbox
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
% 0.30/0.49 @ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) )
% 0.30/0.49 @ ( mdia
% 0.30/0.49 @ ^ [W: mworld] : $true ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(result1,conjecture,
% 0.30/0.49 ( mlocal
% 0.30/0.49 @ ^ [W: mworld] : $false ) ).
% 0.30/0.49
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 ------------------------
% 2.57/1.64 ---- Embedded in THF ---
% 2.57/1.64 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.57/1.64 %%% Generated on Tue Feb 24 14:54:35 EST 2026
% 2.57/1.64 %%% using '$$dhol' embedding, version 1.3.0.
% 2.57/1.64 %%% Logic specification used:
% 2.57/1.64 %%% thf(spec, logic, $$dhol).
% 2.57/1.64
% 2.57/1.64 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2DTF23992.p
% See solution above
% 2.57/1.64 ------------------------
% 2.57/1.67 ---- Cleaned THF ---
% 2.57/1.67 thf(mworld,type,
% 2.57/1.67 mworld: $tType ).
% 2.57/1.67
% 2.57/1.67 thf(mrel_type,type,
% 2.57/1.67 mrel: mworld > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mactual_type,type,
% 2.57/1.67 mactual: mworld ).
% 2.57/1.67
% 2.57/1.67 thf(mlocal_type,type,
% 2.57/1.67 mlocal: ( mworld > $o ) > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mlocal_def,definition,
% 2.57/1.67 ( mlocal
% 2.57/1.67 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mnot_type,type,
% 2.57/1.67 mnot: ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mand_type,type,
% 2.57/1.67 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mor_type,type,
% 2.57/1.67 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mimplies_type,type,
% 2.57/1.67 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mequiv_type,type,
% 2.57/1.67 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mnot_def,definition,
% 2.57/1.67 ( mnot
% 2.57/1.67 = ( ^ [A: mworld > $o,W: mworld] :
% 2.57/1.67 ~ ( A @ W ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mand_def,definition,
% 2.57/1.67 ( mand
% 2.57/1.67 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.57/1.67 ( ( A @ W )
% 2.57/1.67 & ( B @ W ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mor_def,definition,
% 2.57/1.67 ( mor
% 2.57/1.67 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.57/1.67 ( ( A @ W )
% 2.57/1.67 | ( B @ W ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mimplies_def,definition,
% 2.57/1.67 ( mimplies
% 2.57/1.67 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.57/1.67 ( ( A @ W )
% 2.57/1.67 => ( B @ W ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mequiv_def,definition,
% 2.57/1.67 ( mequiv
% 2.57/1.67 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 2.57/1.67 ( ( A @ W )
% 2.57/1.67 <=> ( B @ W ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mbox_type,type,
% 2.57/1.67 mbox: ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mbox_def,definition,
% 2.57/1.67 ( mbox
% 2.57/1.67 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.57/1.67 ! [V: mworld] :
% 2.57/1.67 ( ( mrel @ W @ V )
% 2.57/1.67 => ( Phi @ V ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mdia_type,type,
% 2.57/1.67 mdia: ( mworld > $o ) > mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mdia_def,definition,
% 2.57/1.67 ( mdia
% 2.57/1.67 = ( ^ [Phi: mworld > $o,W: mworld] :
% 2.57/1.67 ? [V: mworld] :
% 2.57/1.67 ( ( mrel @ W @ V )
% 2.57/1.67 & ( Phi @ V ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mrel_universal,axiom,
% 2.57/1.67 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 2.57/1.67
% 2.57/1.67 thf(v1_decl,type,
% 2.57/1.67 v1: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v2_decl,type,
% 2.57/1.67 v2: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v3_decl,type,
% 2.57/1.67 v3: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v4_decl,type,
% 2.57/1.67 v4: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v5_decl,type,
% 2.57/1.67 v5: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v6_decl,type,
% 2.57/1.67 v6: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v7_decl,type,
% 2.57/1.67 v7: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v8_decl,type,
% 2.57/1.67 v8: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v9_decl,type,
% 2.57/1.67 v9: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v10_decl,type,
% 2.57/1.67 v10: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v12_decl,type,
% 2.57/1.67 v12: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v11_decl,type,
% 2.57/1.67 v11: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v14_decl,type,
% 2.57/1.67 v14: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v13_decl,type,
% 2.57/1.67 v13: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v16_decl,type,
% 2.57/1.67 v16: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v15_decl,type,
% 2.57/1.67 v15: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v18_decl,type,
% 2.57/1.67 v18: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v17_decl,type,
% 2.57/1.67 v17: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v19_decl,type,
% 2.57/1.67 v19: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v21_decl,type,
% 2.57/1.67 v21: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v20_decl,type,
% 2.57/1.67 v20: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v23_decl,type,
% 2.57/1.67 v23: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v22_decl,type,
% 2.57/1.67 v22: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v25_decl,type,
% 2.57/1.67 v25: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v24_decl,type,
% 2.57/1.67 v24: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v27_decl,type,
% 2.57/1.67 v27: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v26_decl,type,
% 2.57/1.67 v26: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(v28_decl,type,
% 2.57/1.67 v28: mworld > $o ).
% 2.57/1.67
% 2.57/1.67 thf(mod1,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod2,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod3,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ v12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod4,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ v28 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod5,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod6,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v16 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod7,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod8,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod9,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod10,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod11,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod12,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mor @ ( mnot @ v28 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod13,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ v27 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod14,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod15,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod16,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod17,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mnot @ v13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod18,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod19,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v27 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod20,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod21,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v26 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v14 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod22,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod23,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod24,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v26 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v18 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod25,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod26,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v25 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v9 @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod27,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod28,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ v16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod29,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v21 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod30,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v25 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod31,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v24 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod32,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mor @ ( mnot @ v23 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod33,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v24 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v17 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod34,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v23 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v2 ) @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod35,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v22 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ v6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod36,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v22 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v10 ) @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod37,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v9 @ ( mbox @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod38,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v18 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod39,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v17 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod40,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v21 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v12 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod41,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod42,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v20 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod43,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v19 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mor @ ( mnot @ v12 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod44,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v13 ) @ ( mbox @ ( mor @ v12 @ ( mbox @ v11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod45,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v16 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v6 ) @ ( mbox @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod46,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v15 ) @ ( mbox @ ( mor @ v14 @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v11 ) @ ( mbox @ ( mbox @ v9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod47,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v13 @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v5 @ ( mbox @ ( mbox @ ( mor @ v3 @ ( mbox @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod48,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ v10 @ ( mbox @ ( mbox @ ( mor @ v8 @ ( mbox @ ( mbox @ ( mor @ v6 @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod49,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v9 ) @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v5 ) @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(mod50,axiom,
% 2.57/1.67 mlocal @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v8 ) @ ( mbox @ ( mor @ ( mnot @ v7 ) @ ( mbox @ ( mbox @ ( mbox @ ( mor @ ( mnot @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(alt1,axiom,
% 2.57/1.67 ( mlocal
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mand
% 2.57/1.67 @ ( mbox
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v5 ) @ ( mdia @ ( mnot @ v5 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v6 ) @ ( mdia @ ( mnot @ v6 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v7 ) @ ( mdia @ ( mnot @ v7 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v8 ) @ ( mdia @ ( mnot @ v8 ) ) ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v13 ) @ ( mdia @ ( mnot @ v13 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v14 ) @ ( mdia @ ( mnot @ v14 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v15 ) @ ( mdia @ ( mnot @ v15 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v16 ) @ ( mdia @ ( mnot @ v16 ) ) ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v21 ) @ ( mdia @ ( mnot @ v21 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v22 ) @ ( mdia @ ( mnot @ v22 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v23 ) @ ( mdia @ ( mnot @ v23 ) ) ) ) )
% 2.57/1.67 @ ( mand @ ( mdia @ v24 ) @ ( mdia @ ( mnot @ v24 ) ) ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) )
% 2.57/1.67 @ ( mdia
% 2.57/1.67 @ ^ [W: mworld] : $true ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(result1,conjecture,
% 2.57/1.67 ( mlocal
% 2.57/1.67 @ ^ [W: mworld] : $false ) ).
% 2.57/1.67 ------------------------
% 2.66/1.70 % (24094)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/2Mi)
% 2.66/1.70 % (24096)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/18Mi)
% 2.66/1.70 % (24090)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/183Mi)
% 2.66/1.70 % (24092)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/27Mi)
% 2.66/1.70 % (24093)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/2Mi)
% 2.66/1.70 % (24091)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/4Mi)
% 2.66/1.70 % (24095)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/275Mi)
% 2.66/1.70 % (24093)Instruction limit reached!
% 2.66/1.70 % (24093)------------------------------
% 2.66/1.70 % (24093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.70 % (24093)Termination reason: Unknown
% 2.66/1.70 % (24093)Termination phase: shuffling
% 2.66/1.70 % (24094)Instruction limit reached!
% 2.66/1.70 % (24094)------------------------------
% 2.66/1.70 % (24094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.70
% 2.66/1.70 % (24093)Memory used [KB]: 1151
% 2.66/1.70 % (24093)Time elapsed: 0.003 s
% 2.66/1.70 % (24093)Instructions burned: 2 (million)
% 2.66/1.70 % (24093)------------------------------
% 2.66/1.70 % (24093)------------------------------
% 2.66/1.70 % (24094)Termination reason: Unknown
% 2.66/1.70 % (24094)Termination phase: shuffling
% 2.66/1.70
% 2.66/1.70 % (24094)Memory used [KB]: 1151
% 2.66/1.70 % (24094)Time elapsed: 0.003 s
% 2.66/1.70 % (24094)Instructions burned: 3 (million)
% 2.66/1.70 % (24094)------------------------------
% 2.66/1.70 % (24094)------------------------------
% 2.66/1.70 % (24091)Instruction limit reached!
% 2.66/1.70 % (24091)------------------------------
% 2.66/1.70 % (24091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.70 % (24091)Termination reason: Unknown
% 2.66/1.70 % (24091)Termination phase: shuffling
% 2.66/1.70
% 2.66/1.70 % (24091)Memory used [KB]: 1151
% 2.66/1.70 % (24091)Time elapsed: 0.004 s
% 2.66/1.70 % (24091)Instructions burned: 4 (million)
% 2.66/1.70 % (24091)------------------------------
% 2.66/1.70 % (24091)------------------------------
% 2.66/1.70 % (24096)Instruction limit reached!
% 2.66/1.70 % (24096)------------------------------
% 2.66/1.70 % (24096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.70 % (24096)Termination reason: Unknown
% 2.66/1.70 % (24096)Termination phase: shuffling
% 2.66/1.70
% 2.66/1.70 % (24096)Memory used [KB]: 1151
% 2.66/1.71 % (24096)Time elapsed: 0.009 s
% 2.66/1.71 % (24096)Instructions burned: 18 (million)
% 2.66/1.71 % (24096)------------------------------
% 2.66/1.71 % (24096)------------------------------
% 2.66/1.71 % (24092)Instruction limit reached!
% 2.66/1.71 % (24092)------------------------------
% 2.66/1.71 % (24092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.71 % (24092)Termination reason: Unknown
% 2.66/1.71 % (24092)Termination phase: shuffling
% 2.66/1.71
% 2.66/1.71 % (24092)Memory used [KB]: 1151
% 2.66/1.71 % (24092)Time elapsed: 0.013 s
% 2.66/1.71 % (24092)Instructions burned: 28 (million)
% 2.66/1.71 % (24092)------------------------------
% 2.66/1.71 % (24092)------------------------------
% 2.66/1.72 % (24097)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/3Mi)
% 2.66/1.72 % (24098)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/37Mi)
% 2.66/1.72 % (24099)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/15Mi)
% 2.66/1.72 % (24097)Instruction limit reached!
% 2.66/1.72 % (24097)------------------------------
% 2.66/1.72 % (24097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.72 % (24097)Termination reason: Unknown
% 2.66/1.72 % (24097)Termination phase: shuffling
% 2.66/1.72
% 2.66/1.72 % (24097)Memory used [KB]: 1151
% 2.66/1.72 % (24097)Time elapsed: 0.003 s
% 2.66/1.72 % (24097)Instructions burned: 4 (million)
% 2.66/1.72 % (24097)------------------------------
% 2.66/1.72 % (24097)------------------------------
% 2.66/1.72 % (24095)Refutation not found, incomplete strategy
% 2.66/1.72 % (24095)------------------------------
% 2.66/1.72 % (24095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.72 % (24095)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.72
% 2.66/1.72
% 2.66/1.72 % (24095)Memory used [KB]: 5756
% 2.66/1.72 % (24095)Time elapsed: 0.023 s
% 2.66/1.72 % (24095)Instructions burned: 54 (million)
% 2.66/1.72 % (24095)------------------------------
% 2.66/1.72 % (24095)------------------------------
% 2.66/1.72 % (24100)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/3Mi)
% 2.66/1.72 % (24099)Instruction limit reached!
% 2.66/1.72 % (24099)------------------------------
% 2.66/1.72 % (24099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.72 % (24099)Termination reason: Unknown
% 2.66/1.72 % (24099)Termination phase: shuffling
% 2.66/1.72
% 2.66/1.72 % (24099)Memory used [KB]: 1151
% 2.66/1.72 % (24099)Time elapsed: 0.008 s
% 2.66/1.72 % (24099)Instructions burned: 17 (million)
% 2.66/1.72 % (24099)------------------------------
% 2.66/1.72 % (24099)------------------------------
% 2.66/1.72 % (24100)Instruction limit reached!
% 2.66/1.72 % (24100)------------------------------
% 2.66/1.72 % (24100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.72 % (24100)Termination reason: Unknown
% 2.66/1.72 % (24100)Termination phase: shuffling
% 2.66/1.72
% 2.66/1.72 % (24100)Memory used [KB]: 1151
% 2.66/1.72 % (24100)Time elapsed: 0.003 s
% 2.66/1.72 % (24100)Instructions burned: 4 (million)
% 2.66/1.72 % (24100)------------------------------
% 2.66/1.72 % (24100)------------------------------
% 2.66/1.72 % (24101)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/1041Mi)
% 2.66/1.73 % (24098)Instruction limit reached!
% 2.66/1.73 % (24098)------------------------------
% 2.66/1.73 % (24098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.73 % (24098)Termination reason: Unknown
% 2.66/1.73 % (24098)Termination phase: Function definition elimination
% 2.66/1.73
% 2.66/1.73 % (24098)Memory used [KB]: 1407
% 2.66/1.73 % (24098)Time elapsed: 0.017 s
% 2.66/1.73 % (24098)Instructions burned: 38 (million)
% 2.66/1.73 % (24098)------------------------------
% 2.66/1.73 % (24098)------------------------------
% 2.66/1.73 % (24102)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/7Mi)
% 2.66/1.73 % (24102)Instruction limit reached!
% 2.66/1.73 % (24102)------------------------------
% 2.66/1.73 % (24102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.73 % (24102)Termination reason: Unknown
% 2.66/1.73 % (24102)Termination phase: shuffling
% 2.66/1.73
% 2.66/1.73 % (24102)Memory used [KB]: 1151
% 2.66/1.73 % (24102)Time elapsed: 0.004 s
% 2.66/1.73 % (24102)Instructions burned: 7 (million)
% 2.66/1.73 % (24102)------------------------------
% 2.66/1.73 % (24102)------------------------------
% 2.66/1.74 % (24103)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/16Mi)
% 2.66/1.74 % (24104)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/3Mi)
% 2.66/1.74 % (24105)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/3Mi)
% 2.66/1.74 % (24104)Instruction limit reached!
% 2.66/1.74 % (24104)------------------------------
% 2.66/1.74 % (24104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.74 % (24104)Termination reason: Unknown
% 2.66/1.74 % (24104)Termination phase: shuffling
% 2.66/1.74
% 2.66/1.74 % (24104)Memory used [KB]: 1151
% 2.66/1.74 % (24104)Time elapsed: 0.003 s
% 2.66/1.74 % (24104)Instructions burned: 4 (million)
% 2.66/1.74 % (24104)------------------------------
% 2.66/1.74 % (24104)------------------------------
% 2.66/1.74 % (24105)Instruction limit reached!
% 2.66/1.74 % (24105)------------------------------
% 2.66/1.74 % (24105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.74 % (24105)Termination reason: Unknown
% 2.66/1.74 % (24105)Termination phase: shuffling
% 2.66/1.74
% 2.66/1.74 % (24105)Memory used [KB]: 1151
% 2.66/1.74 % (24105)Time elapsed: 0.003 s
% 2.66/1.74 % (24105)Instructions burned: 4 (million)
% 2.66/1.74 % (24105)------------------------------
% 2.66/1.74 % (24105)------------------------------
% 2.66/1.74 % (24103)Instruction limit reached!
% 2.66/1.74 % (24103)------------------------------
% 2.66/1.74 % (24103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.74 % (24103)Termination reason: Unknown
% 2.66/1.74 % (24103)Termination phase: shuffling
% 2.66/1.74
% 2.66/1.74 % (24103)Memory used [KB]: 1279
% 2.66/1.74 % (24103)Time elapsed: 0.008 s
% 2.66/1.74 % (24103)Instructions burned: 18 (million)
% 2.66/1.74 % (24103)------------------------------
% 2.66/1.74 % (24103)------------------------------
% 2.66/1.75 % (24106)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/7Mi)
% 2.66/1.75 % (24106)Instruction limit reached!
% 2.66/1.75 % (24106)------------------------------
% 2.66/1.75 % (24106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.75 % (24106)Termination reason: Unknown
% 2.66/1.75 % (24106)Termination phase: shuffling
% 2.66/1.75
% 2.66/1.75 % (24106)Memory used [KB]: 1151
% 2.66/1.75 % (24106)Time elapsed: 0.004 s
% 2.66/1.75 % (24106)Instructions burned: 8 (million)
% 2.66/1.75 % (24106)------------------------------
% 2.66/1.75 % (24106)------------------------------
% 2.66/1.75 % (24107)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/3Mi)
% 2.66/1.75 % (24107)Instruction limit reached!
% 2.66/1.75 % (24107)------------------------------
% 2.66/1.75 % (24107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.75 % (24107)Termination reason: Unknown
% 2.66/1.75 % (24107)Termination phase: shuffling
% 2.66/1.75
% 2.66/1.75 % (24107)Memory used [KB]: 1151
% 2.66/1.75 % (24107)Time elapsed: 0.003 s
% 2.66/1.75 % (24107)Instructions burned: 4 (million)
% 2.66/1.75 % (24107)------------------------------
% 2.66/1.75 % (24107)------------------------------
% 2.66/1.76 % (24108)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/4Mi)
% 2.66/1.76 % (24109)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/18Mi)
% 2.66/1.76 % (24108)Instruction limit reached!
% 2.66/1.76 % (24108)------------------------------
% 2.66/1.76 % (24108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.76 % (24108)Termination reason: Unknown
% 2.66/1.76 % (24108)Termination phase: shuffling
% 2.66/1.76
% 2.66/1.76 % (24108)Memory used [KB]: 1151
% 2.66/1.76 % (24108)Time elapsed: 0.003 s
% 2.66/1.76 % (24108)Instructions burned: 4 (million)
% 2.66/1.76 % (24108)------------------------------
% 2.66/1.76 % (24108)------------------------------
% 2.66/1.76 % (24110)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/710Mi)
% 2.66/1.76 % (24109)Instruction limit reached!
% 2.66/1.76 % (24109)------------------------------
% 2.66/1.76 % (24109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.76 % (24109)Termination reason: Unknown
% 2.66/1.76 % (24109)Termination phase: shuffling
% 2.66/1.76
% 2.66/1.76 % (24109)Memory used [KB]: 1151
% 2.66/1.76 % (24109)Time elapsed: 0.009 s
% 2.66/1.76 % (24109)Instructions burned: 21 (million)
% 2.66/1.76 % (24109)------------------------------
% 2.66/1.76 % (24109)------------------------------
% 2.66/1.76 % (24111)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/6Mi)
% 2.66/1.77 % (24111)Instruction limit reached!
% 2.66/1.77 % (24111)------------------------------
% 2.66/1.77 % (24111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.77 % (24111)Termination reason: Unknown
% 2.66/1.77 % (24111)Termination phase: shuffling
% 2.66/1.77
% 2.66/1.77 % (24111)Memory used [KB]: 1151
% 2.66/1.77 % (24111)Time elapsed: 0.004 s
% 2.66/1.77 % (24111)Instructions burned: 7 (million)
% 2.66/1.77 % (24111)------------------------------
% 2.66/1.77 % (24111)------------------------------
% 2.66/1.77 % (24112)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/902Mi)
% 2.66/1.77 % (24090)Instruction limit reached!
% 2.66/1.77 % (24090)------------------------------
% 2.66/1.77 % (24090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.77 % (24090)Termination reason: Unknown
% 2.66/1.77 % (24090)Termination phase: Saturation
% 2.66/1.77
% 2.66/1.77 % (24090)Memory used [KB]: 6140
% 2.66/1.77 % (24090)Time elapsed: 0.076 s
% 2.66/1.77 % (24090)Instructions burned: 184 (million)
% 2.66/1.77 % (24090)------------------------------
% 2.66/1.77 % (24090)------------------------------
% 2.66/1.77 % (24113)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/21Mi)
% 2.66/1.78 % (24114)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/5Mi)
% 2.66/1.78 % (24110)Refutation not found, incomplete strategy
% 2.66/1.78 % (24110)------------------------------
% 2.66/1.78 % (24110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.78 % (24110)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.78
% 2.66/1.78
% 2.66/1.78 % (24110)Memory used [KB]: 5756
% 2.66/1.78 % (24110)Time elapsed: 0.022 s
% 2.66/1.78 % (24110)Instructions burned: 53 (million)
% 2.66/1.78 % (24110)------------------------------
% 2.66/1.78 % (24110)------------------------------
% 2.66/1.78 % (24113)Instruction limit reached!
% 2.66/1.78 % (24113)------------------------------
% 2.66/1.78 % (24113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.78 % (24113)Termination reason: Unknown
% 2.66/1.78 % (24113)Termination phase: shuffling
% 2.66/1.78
% 2.66/1.78 % (24113)Memory used [KB]: 1151
% 2.66/1.78 % (24113)Time elapsed: 0.010 s
% 2.66/1.78 % (24113)Instructions burned: 22 (million)
% 2.66/1.78 % (24113)------------------------------
% 2.66/1.78 % (24113)------------------------------
% 2.66/1.78 % (24114)Instruction limit reached!
% 2.66/1.78 % (24114)------------------------------
% 2.66/1.78 % (24114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.78 % (24114)Termination reason: Unknown
% 2.66/1.78 % (24114)Termination phase: shuffling
% 2.66/1.78
% 2.66/1.78 % (24114)Memory used [KB]: 1279
% 2.66/1.78 % (24114)Time elapsed: 0.004 s
% 2.66/1.78 % (24114)Instructions burned: 6 (million)
% 2.66/1.78 % (24114)------------------------------
% 2.66/1.78 % (24114)------------------------------
% 2.66/1.78 % (24115)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/6Mi)
% 2.66/1.79 % (24115)Instruction limit reached!
% 2.66/1.79 % (24115)------------------------------
% 2.66/1.79 % (24115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.79 % (24115)Termination reason: Unknown
% 2.66/1.79 % (24115)Termination phase: shuffling
% 2.66/1.79
% 2.66/1.79 % (24115)Memory used [KB]: 1279
% 2.66/1.79 % (24115)Time elapsed: 0.004 s
% 2.66/1.79 % (24115)Instructions burned: 6 (million)
% 2.66/1.79 % (24115)------------------------------
% 2.66/1.79 % (24115)------------------------------
% 2.66/1.79 % (24116)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23992 for (2999ds/377Mi)
% 2.66/1.80 % (24117)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/779Mi)
% 2.66/1.80 % (24118)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/19Mi)
% 2.66/1.80 % (24119)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/879Mi)
% 2.66/1.80 % (24112)Refutation not found, incomplete strategy
% 2.66/1.80 % (24112)------------------------------
% 2.66/1.80 % (24112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.80 % (24112)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.80
% 2.66/1.80
% 2.66/1.80 % (24112)Memory used [KB]: 5884
% 2.66/1.80 % (24112)Time elapsed: 0.032 s
% 2.66/1.80 % (24112)Instructions burned: 75 (million)
% 2.66/1.80 % (24112)------------------------------
% 2.66/1.80 % (24112)------------------------------
% 2.66/1.80 % (24120)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/17Mi)
% 2.66/1.81 % (24118)Instruction limit reached!
% 2.66/1.81 % (24118)------------------------------
% 2.66/1.81 % (24118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.81 % (24118)Termination reason: Unknown
% 2.66/1.81 % (24118)Termination phase: SInE selection
% 2.66/1.81
% 2.66/1.81 % (24118)Memory used [KB]: 1279
% 2.66/1.81 % (24118)Time elapsed: 0.010 s
% 2.66/1.81 % (24118)Instructions burned: 21 (million)
% 2.66/1.81 % (24118)------------------------------
% 2.66/1.81 % (24118)------------------------------
% 2.66/1.81 % (24120)Instruction limit reached!
% 2.66/1.81 % (24120)------------------------------
% 2.66/1.81 % (24120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.81 % (24120)Termination reason: Unknown
% 2.66/1.81 % (24120)Termination phase: shuffling
% 2.66/1.81
% 2.66/1.81 % (24120)Memory used [KB]: 1151
% 2.66/1.81 % (24120)Time elapsed: 0.008 s
% 2.66/1.81 % (24120)Instructions burned: 17 (million)
% 2.66/1.81 % (24120)------------------------------
% 2.66/1.81 % (24120)------------------------------
% 2.66/1.81 % (24117)Refutation not found, incomplete strategy
% 2.66/1.81 % (24117)------------------------------
% 2.66/1.81 % (24117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.81 % (24117)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.81
% 2.66/1.81
% 2.66/1.81 % (24117)Memory used [KB]: 5756
% 2.66/1.81 % (24117)Time elapsed: 0.015 s
% 2.66/1.81 % (24117)Instructions burned: 33 (million)
% 2.66/1.81 % (24117)------------------------------
% 2.66/1.81 % (24117)------------------------------
% 2.66/1.82 % (24121)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/3Mi)
% 2.66/1.82 % (24121)Instruction limit reached!
% 2.66/1.82 % (24121)------------------------------
% 2.66/1.82 % (24121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.82 % (24121)Termination reason: Unknown
% 2.66/1.82 % (24121)Termination phase: shuffling
% 2.66/1.82
% 2.66/1.82 % (24121)Memory used [KB]: 1151
% 2.66/1.82 % (24121)Time elapsed: 0.003 s
% 2.66/1.82 % (24121)Instructions burned: 4 (million)
% 2.66/1.82 % (24121)------------------------------
% 2.66/1.82 % (24121)------------------------------
% 2.66/1.82 % (24122)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/30Mi)
% 2.66/1.82 % (24123)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/127Mi)
% 2.66/1.83 % (24124)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/100Mi)
% 2.66/1.83 % (24122)Instruction limit reached!
% 2.66/1.83 % (24122)------------------------------
% 2.66/1.83 % (24122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.83 % (24122)Termination reason: Unknown
% 2.66/1.83 % (24122)Termination phase: shuffling
% 2.66/1.83
% 2.66/1.83 % (24122)Memory used [KB]: 1279
% 2.66/1.83 % (24122)Time elapsed: 0.013 s
% 2.66/1.83 % (24122)Instructions burned: 31 (million)
% 2.66/1.83 % (24122)------------------------------
% 2.66/1.83 % (24122)------------------------------
% 2.66/1.83 % (24125)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/3Mi)
% 2.66/1.83 % (24125)Instruction limit reached!
% 2.66/1.83 % (24125)------------------------------
% 2.66/1.83 % (24125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.83 % (24125)Termination reason: Unknown
% 2.66/1.83 % (24125)Termination phase: shuffling
% 2.66/1.83
% 2.66/1.83 % (24125)Memory used [KB]: 1151
% 2.66/1.83 % (24125)Time elapsed: 0.003 s
% 2.66/1.83 % (24125)Instructions burned: 4 (million)
% 2.66/1.83 % (24125)------------------------------
% 2.66/1.83 % (24125)------------------------------
% 2.66/1.85 % (24126)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/20Mi)
% 2.66/1.85 % (24127)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/86Mi)
% 2.66/1.86 % (24126)Instruction limit reached!
% 2.66/1.86 % (24126)------------------------------
% 2.66/1.86 % (24126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.86 % (24126)Termination reason: Unknown
% 2.66/1.86 % (24126)Termination phase: shuffling
% 2.66/1.86
% 2.66/1.86 % (24126)Memory used [KB]: 1279
% 2.66/1.86 % (24126)Time elapsed: 0.009 s
% 2.66/1.86 % (24126)Instructions burned: 20 (million)
% 2.66/1.86 % (24126)------------------------------
% 2.66/1.86 % (24126)------------------------------
% 2.66/1.87 % (24124)Instruction limit reached!
% 2.66/1.87 % (24124)------------------------------
% 2.66/1.87 % (24124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.87 % (24124)Termination reason: Unknown
% 2.66/1.87 % (24124)Termination phase: Property scanning
% 2.66/1.87
% 2.66/1.87 % (24124)Memory used [KB]: 1407
% 2.66/1.87 % (24124)Time elapsed: 0.043 s
% 2.66/1.87 % (24124)Instructions burned: 101 (million)
% 2.66/1.87 % (24124)------------------------------
% 2.66/1.87 % (24124)------------------------------
% 2.66/1.87 % (24128)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/107Mi)
% 2.66/1.88 % (24123)Instruction limit reached!
% 2.66/1.88 % (24123)------------------------------
% 2.66/1.88 % (24123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.88 % (24123)Termination reason: Unknown
% 2.66/1.88 % (24123)Termination phase: Property scanning
% 2.66/1.88
% 2.66/1.88 % (24123)Memory used [KB]: 1407
% 2.66/1.88 % (24123)Time elapsed: 0.053 s
% 2.66/1.88 % (24123)Instructions burned: 129 (million)
% 2.66/1.88 % (24123)------------------------------
% 2.66/1.88 % (24123)------------------------------
% 2.66/1.88 % (24129)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/39Mi)
% 2.66/1.88 % (24127)Instruction limit reached!
% 2.66/1.88 % (24127)------------------------------
% 2.66/1.88 % (24127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.88 % (24127)Termination reason: Unknown
% 2.66/1.88 % (24127)Termination phase: Property scanning
% 2.66/1.88
% 2.66/1.88 % (24127)Memory used [KB]: 1407
% 2.66/1.88 % (24127)Time elapsed: 0.035 s
% 2.66/1.88 % (24127)Instructions burned: 86 (million)
% 2.66/1.88 % (24127)------------------------------
% 2.66/1.88 % (24127)------------------------------
% 2.66/1.89 % (24130)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_23992 for (2998ds/448Mi)
% 2.66/1.90 % (24129)Instruction limit reached!
% 2.66/1.90 % (24129)------------------------------
% 2.66/1.90 % (24129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.90 % (24129)Termination reason: Unknown
% 2.66/1.90 % (24129)Termination phase: Function definition elimination
% 2.66/1.90
% 2.66/1.90 % (24129)Memory used [KB]: 1407
% 2.66/1.90 % (24129)Time elapsed: 0.017 s
% 2.66/1.90 % (24129)Instructions burned: 39 (million)
% 2.66/1.90 % (24129)------------------------------
% 2.66/1.90 % (24129)------------------------------
% 2.66/1.90 % (24131)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/46Mi)
% 2.66/1.90 % (24130)Refutation not found, incomplete strategy
% 2.66/1.90 % (24130)------------------------------
% 2.66/1.90 % (24130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.90 % (24130)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.90
% 2.66/1.90
% 2.66/1.90 % (24130)Memory used [KB]: 5756
% 2.66/1.90 % (24130)Time elapsed: 0.013 s
% 2.66/1.90 % (24130)Instructions burned: 29 (million)
% 2.66/1.90 % (24130)------------------------------
% 2.66/1.90 % (24130)------------------------------
% 2.66/1.91 % (24128)Instruction limit reached!
% 2.66/1.91 % (24128)------------------------------
% 2.66/1.91 % (24128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.91 % (24128)Termination reason: Unknown
% 2.66/1.91 % (24128)Termination phase: Saturation
% 2.66/1.91
% 2.66/1.91 % (24128)Memory used [KB]: 6012
% 2.66/1.91 % (24128)Time elapsed: 0.043 s
% 2.66/1.91 % (24128)Instructions burned: 108 (million)
% 2.66/1.91 % (24128)------------------------------
% 2.66/1.91 % (24128)------------------------------
% 2.66/1.92 % (24132)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/98Mi)
% 2.66/1.92 % (24131)Instruction limit reached!
% 2.66/1.92 % (24131)------------------------------
% 2.66/1.92 % (24131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.92 % (24131)Termination reason: Unknown
% 2.66/1.92 % (24131)Termination phase: Property scanning
% 2.66/1.92
% 2.66/1.92 % (24131)Memory used [KB]: 1279
% 2.66/1.92 % (24131)Time elapsed: 0.019 s
% 2.66/1.92 % (24131)Instructions burned: 46 (million)
% 2.66/1.92 % (24131)------------------------------
% 2.66/1.92 % (24131)------------------------------
% 2.66/1.92 % (24133)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/507Mi)
% 2.66/1.93 % (24134)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/149Mi)
% 2.66/1.93 % (24135)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/39Mi)
% 2.66/1.93 % (24116)Instruction limit reached!
% 2.66/1.93 % (24116)------------------------------
% 2.66/1.93 % (24116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.93 % (24116)Termination reason: Unknown
% 2.66/1.93 % (24116)Termination phase: Saturation
% 2.66/1.93
% 2.66/1.93 % (24116)Memory used [KB]: 6396
% 2.66/1.93 % (24116)Time elapsed: 0.148 s
% 2.66/1.93 % (24116)Instructions burned: 377 (million)
% 2.66/1.93 % (24116)------------------------------
% 2.66/1.93 % (24116)------------------------------
% 2.66/1.95 % (24135)Instruction limit reached!
% 2.66/1.95 % (24135)------------------------------
% 2.66/1.95 % (24135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.95 % (24135)Termination reason: Unknown
% 2.66/1.95 % (24135)Termination phase: shuffling
% 2.66/1.95
% 2.66/1.95 % (24135)Memory used [KB]: 1279
% 2.66/1.95 % (24135)Time elapsed: 0.016 s
% 2.66/1.95 % (24135)Instructions burned: 39 (million)
% 2.66/1.95 % (24135)------------------------------
% 2.66/1.95 % (24135)------------------------------
% 2.66/1.95 % (24136)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/6Mi)
% 2.66/1.95 % (24136)Instruction limit reached!
% 2.66/1.95 % (24136)------------------------------
% 2.66/1.95 % (24136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.95 % (24136)Termination reason: Unknown
% 2.66/1.95 % (24136)Termination phase: shuffling
% 2.66/1.95
% 2.66/1.95 % (24136)Memory used [KB]: 1151
% 2.66/1.95 % (24136)Time elapsed: 0.004 s
% 2.66/1.95 % (24136)Instructions burned: 6 (million)
% 2.66/1.95 % (24136)------------------------------
% 2.66/1.95 % (24136)------------------------------
% 2.66/1.96 % (24132)Instruction limit reached!
% 2.66/1.96 % (24132)------------------------------
% 2.66/1.96 % (24132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.96 % (24132)Termination reason: Unknown
% 2.66/1.96 % (24132)Termination phase: Property scanning
% 2.66/1.96
% 2.66/1.96 % (24132)Memory used [KB]: 1407
% 2.66/1.96 % (24132)Time elapsed: 0.042 s
% 2.66/1.96 % (24132)Instructions burned: 98 (million)
% 2.66/1.96 % (24132)------------------------------
% 2.66/1.96 % (24132)------------------------------
% 2.66/1.96 % (24137)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/1087Mi)
% 2.66/1.97 % (24138)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/47Mi)
% 2.66/1.97 % (24139)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_23992 for (2997ds/44Mi)
% 2.66/1.98 % (24139)Refutation not found, incomplete strategy
% 2.66/1.98 % (24139)------------------------------
% 2.66/1.98 % (24139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.98 % (24139)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.98
% 2.66/1.98
% 2.66/1.98 % (24139)Memory used [KB]: 1279
% 2.66/1.98 % (24139)Time elapsed: 0.012 s
% 2.66/1.98 % (24139)Instructions burned: 26 (million)
% 2.66/1.98 % (24139)------------------------------
% 2.66/1.98 % (24139)------------------------------
% 2.66/1.99 % (24137)Refutation not found, incomplete strategy
% 2.66/1.99 % (24137)------------------------------
% 2.66/1.99 % (24137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.99 % (24137)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.99
% 2.66/1.99
% 2.66/1.99 % (24137)Memory used [KB]: 5756
% 2.66/1.99 % (24137)Time elapsed: 0.023 s
% 2.66/1.99 % (24137)Instructions burned: 55 (million)
% 2.66/1.99 % (24137)------------------------------
% 2.66/1.99 % (24137)------------------------------
% 2.66/1.99 % (24138)Instruction limit reached!
% 2.66/1.99 % (24138)------------------------------
% 2.66/1.99 % (24138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.99 % (24138)Termination reason: Unknown
% 2.66/1.99 % (24138)Termination phase: Property scanning
% 2.66/1.99
% 2.66/1.99 % (24138)Memory used [KB]: 1279
% 2.66/1.99 % (24138)Time elapsed: 0.020 s
% 2.66/1.99 % (24138)Instructions burned: 48 (million)
% 2.66/1.99 % (24138)------------------------------
% 2.66/1.99 % (24138)------------------------------
% 2.66/1.99 % (24134)Instruction limit reached!
% 2.66/1.99 % (24134)------------------------------
% 2.66/1.99 % (24134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.99 % (24134)Termination reason: Unknown
% 2.66/1.99 % (24134)Termination phase: Saturation
% 2.66/1.99
% 2.66/1.99 % (24134)Memory used [KB]: 6140
% 2.66/1.99 % (24134)Time elapsed: 0.062 s
% 2.66/1.99 % (24134)Instructions burned: 150 (million)
% 2.66/1.99 % (24134)------------------------------
% 2.66/1.99 % (24134)------------------------------
% 2.66/2.00 % (24140)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/432Mi)
% 2.66/2.00 % (24141)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/62Mi)
% 2.66/2.00 % (24142)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/31Mi)
% 2.66/2.01 % (24143)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/96Mi)
% 2.66/2.01 % (24142)Instruction limit reached!
% 2.66/2.01 % (24142)------------------------------
% 2.66/2.01 % (24142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/2.01 % (24142)Termination reason: Unknown
% 2.66/2.01 % (24142)Termination phase: shuffling
% 2.66/2.01
% 2.66/2.01 % (24142)Memory used [KB]: 1279
% 2.66/2.01 % (24142)Time elapsed: 0.013 s
% 2.66/2.01 % (24142)Instructions burned: 31 (million)
% 2.66/2.01 % (24142)------------------------------
% 2.66/2.01 % (24142)------------------------------
% 5.00/2.03 % (24141)Instruction limit reached!
% 5.00/2.03 % (24141)------------------------------
% 5.00/2.03 % (24141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.03 % (24141)Termination reason: Unknown
% 5.00/2.03 % (24141)Termination phase: Property scanning
% 5.00/2.03
% 5.00/2.03 % (24141)Memory used [KB]: 1407
% 5.00/2.03 % (24141)Time elapsed: 0.027 s
% 5.00/2.03 % (24141)Instructions burned: 63 (million)
% 5.00/2.03 % (24141)------------------------------
% 5.00/2.03 % (24141)------------------------------
% 5.00/2.03 % (24144)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/453Mi)
% 5.00/2.04 % (24143)Instruction limit reached!
% 5.00/2.04 % (24143)------------------------------
% 5.00/2.04 % (24143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.04 % (24143)Termination reason: Unknown
% 5.00/2.04 % (24143)Termination phase: Property scanning
% 5.00/2.04
% 5.00/2.04 % (24143)Memory used [KB]: 1407
% 5.00/2.04 % (24143)Time elapsed: 0.039 s
% 5.00/2.04 % (24143)Instructions burned: 96 (million)
% 5.00/2.04 % (24143)------------------------------
% 5.00/2.04 % (24143)------------------------------
% 5.00/2.04 % (24145)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/71Mi)
% 5.00/2.06 % (24146)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/83Mi)
% 5.00/2.07 % (24145)Instruction limit reached!
% 5.00/2.07 % (24145)------------------------------
% 5.00/2.07 % (24145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.07 % (24145)Termination reason: Unknown
% 5.00/2.07 % (24145)Termination phase: Function definition elimination
% 5.00/2.07
% 5.00/2.07 % (24145)Memory used [KB]: 1407
% 5.00/2.07 % (24145)Time elapsed: 0.029 s
% 5.00/2.07 % (24145)Instructions burned: 71 (million)
% 5.00/2.07 % (24145)------------------------------
% 5.00/2.07 % (24145)------------------------------
% 5.00/2.08 % (24146)Refutation not found, incomplete strategy
% 5.00/2.08 % (24146)------------------------------
% 5.00/2.08 % (24146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.08 % (24146)Termination reason: Refutation not found, incomplete strategy
% 5.00/2.08
% 5.00/2.08
% 5.00/2.08 % (24146)Memory used [KB]: 5756
% 5.00/2.08 % (24146)Time elapsed: 0.024 s
% 5.00/2.08 % (24146)Instructions burned: 58 (million)
% 5.00/2.08 % (24146)------------------------------
% 5.00/2.08 % (24146)------------------------------
% 5.00/2.09 % (24133)Refutation not found, incomplete strategy
% 5.00/2.09 % (24133)------------------------------
% 5.00/2.09 % (24133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.09 % (24133)Termination reason: Refutation not found, incomplete strategy
% 5.00/2.09
% 5.00/2.09
% 5.00/2.09 % (24133)Memory used [KB]: 7547
% 5.00/2.09 % (24133)Time elapsed: 0.166 s
% 5.00/2.09 % (24133)Instructions burned: 450 (million)
% 5.00/2.09 % (24133)------------------------------
% 5.00/2.09 % (24133)------------------------------
% 5.00/2.09 % (24147)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23992 for (2996ds/11Mi)
% 5.00/2.09 % (24147)Instruction limit reached!
% 5.00/2.09 % (24147)------------------------------
% 5.00/2.09 % (24147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.09 % (24147)Termination reason: Unknown
% 5.00/2.09 % (24147)Termination phase: Property scanning
% 5.00/2.09
% 5.00/2.09 % (24147)Memory used [KB]: 1279
% 5.00/2.09 % (24147)Time elapsed: 0.006 s
% 5.00/2.09 % (24147)Instructions burned: 11 (million)
% 5.00/2.09 % (24147)------------------------------
% 5.00/2.09 % (24147)------------------------------
% 5.00/2.10 % (24148)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/41Mi)
% 5.00/2.10 % (24149)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/6Mi)
% 5.00/2.10 % (24149)Instruction limit reached!
% 5.00/2.10 % (24149)------------------------------
% 5.00/2.10 % (24149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.10 % (24149)Termination reason: Unknown
% 5.00/2.10 % (24149)Termination phase: shuffling
% 5.00/2.10
% 5.00/2.10 % (24149)Memory used [KB]: 1151
% 5.00/2.10 % (24149)Time elapsed: 0.004 s
% 5.00/2.10 % (24149)Instructions burned: 7 (million)
% 5.00/2.10 % (24149)------------------------------
% 5.00/2.10 % (24149)------------------------------
% 5.00/2.11 % (24150)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/150Mi)
% 5.00/2.12 % (24148)Instruction limit reached!
% 5.00/2.12 % (24148)------------------------------
% 5.00/2.12 % (24148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.12 % (24148)Termination reason: Unknown
% 5.00/2.12 % (24148)Termination phase: Function definition elimination
% 5.00/2.12
% 5.00/2.12 % (24148)Memory used [KB]: 1407
% 5.00/2.12 % (24148)Time elapsed: 0.018 s
% 5.00/2.12 % (24148)Instructions burned: 41 (million)
% 5.00/2.12 % (24148)------------------------------
% 5.00/2.12 % (24148)------------------------------
% 5.00/2.12 % (24151)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/343Mi)
% 5.57/2.13 % (24152)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/109Mi)
% 5.57/2.14 % (24101)Instruction limit reached!
% 5.57/2.14 % (24101)------------------------------
% 5.57/2.14 % (24101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.14 % (24101)Termination reason: Unknown
% 5.57/2.14 % (24101)Termination phase: Saturation
% 5.57/2.14
% 5.57/2.14 % (24101)Memory used [KB]: 8059
% 5.57/2.14 % (24101)Time elapsed: 0.412 s
% 5.57/2.14 % (24101)Instructions burned: 1042 (million)
% 5.57/2.14 % (24101)------------------------------
% 5.57/2.14 % (24101)------------------------------
% 5.57/2.14 % (24151)Refutation not found, incomplete strategy
% 5.57/2.14 % (24151)------------------------------
% 5.57/2.14 % (24151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.14 % (24151)Termination reason: Refutation not found, incomplete strategy
% 5.57/2.14
% 5.57/2.14
% 5.57/2.14 % (24151)Memory used [KB]: 5756
% 5.57/2.14 % (24151)Time elapsed: 0.024 s
% 5.57/2.14 % (24151)Instructions burned: 59 (million)
% 5.57/2.14 % (24151)------------------------------
% 5.57/2.14 % (24151)------------------------------
% 5.57/2.15 % (24153)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/253Mi)
% 5.57/2.16 % (24140)Instruction limit reached!
% 5.57/2.16 % (24140)------------------------------
% 5.57/2.16 % (24140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.16 % (24140)Termination reason: Unknown
% 5.57/2.16 % (24140)Termination phase: Saturation
% 5.57/2.16
% 5.57/2.16 % (24140)Memory used [KB]: 3070
% 5.57/2.16 % (24140)Time elapsed: 0.160 s
% 5.57/2.16 % (24140)Instructions burned: 434 (million)
% 5.57/2.16 % (24140)------------------------------
% 5.57/2.16 % (24140)------------------------------
% 5.57/2.16 % (24154)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/140Mi)
% 5.57/2.16 % (24119)Instruction limit reached!
% 5.57/2.16 % (24119)------------------------------
% 5.57/2.16 % (24119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.16 % (24119)Termination reason: Unknown
% 5.57/2.16 % (24119)Termination phase: Saturation
% 5.57/2.16
% 5.57/2.16 % (24119)Memory used [KB]: 6780
% 5.57/2.16 % (24119)Time elapsed: 0.366 s
% 5.57/2.16 % (24119)Instructions burned: 880 (million)
% 5.57/2.16 % (24119)------------------------------
% 5.57/2.16 % (24119)------------------------------
% 5.57/2.17 % (24150)Instruction limit reached!
% 5.57/2.17 % (24150)------------------------------
% 5.57/2.17 % (24150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.17 % (24150)Termination reason: Unknown
% 5.57/2.17 % (24150)Termination phase: Saturation
% 5.57/2.17
% 5.57/2.17 % (24150)Memory used [KB]: 6140
% 5.57/2.17 % (24150)Time elapsed: 0.063 s
% 5.57/2.17 % (24150)Instructions burned: 152 (million)
% 5.57/2.17 % (24150)------------------------------
% 5.57/2.17 % (24150)------------------------------
% 5.57/2.17 % (24153)Refutation not found, incomplete strategy
% 5.57/2.17 % (24153)------------------------------
% 5.57/2.17 % (24153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.17 % (24153)Termination reason: Refutation not found, incomplete strategy
% 5.57/2.17
% 5.57/2.17
% 5.57/2.17 % (24153)Memory used [KB]: 5756
% 5.57/2.17 % (24153)Time elapsed: 0.023 s
% 5.57/2.17 % (24153)Instructions burned: 55 (million)
% 5.57/2.17 % (24153)------------------------------
% 5.57/2.17 % (24153)------------------------------
% 5.57/2.17 % (24155)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/614Mi)
% 5.57/2.17 % (24152)Instruction limit reached!
% 5.57/2.17 % (24152)------------------------------
% 5.57/2.17 % (24152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.17 % (24152)Termination reason: Unknown
% 5.57/2.17 % (24152)Termination phase: Property scanning
% 5.57/2.17
% 5.57/2.17 % (24152)Memory used [KB]: 1407
% 5.57/2.17 % (24152)Time elapsed: 0.044 s
% 5.57/2.17 % (24152)Instructions burned: 109 (million)
% 5.57/2.17 % (24152)------------------------------
% 5.57/2.17 % (24152)------------------------------
% 5.57/2.18 % (24156)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/202Mi)
% 5.57/2.19 % (24157)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/339Mi)
% 5.57/2.19 % (24158)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/283Mi)
% 5.57/2.19 % (24159)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23992 for (2995ds/134Mi)
% 5.57/2.20 % (24144)Instruction limit reached!
% 5.57/2.20 % (24144)------------------------------
% 5.57/2.20 % (24144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.20 % (24144)Termination reason: Unknown
% 5.57/2.20 % (24144)Termination phase: Saturation
% 5.57/2.20
% 5.57/2.20 % (24144)Memory used [KB]: 7547
% 5.57/2.20 % (24144)Time elapsed: 0.167 s
% 5.57/2.20 % (24144)Instructions burned: 454 (million)
% 5.57/2.20 % (24144)------------------------------
% 5.57/2.20 % (24144)------------------------------
% 5.87/2.20 % (24156)Refutation not found, incomplete strategy
% 5.87/2.20 % (24156)------------------------------
% 5.87/2.20 % (24156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.20 % (24156)Termination reason: Refutation not found, incomplete strategy
% 5.87/2.20
% 5.87/2.20
% 5.87/2.20 % (24156)Memory used [KB]: 5756
% 5.87/2.20 % (24156)Time elapsed: 0.024 s
% 5.87/2.20 % (24156)Instructions burned: 55 (million)
% 5.87/2.20 % (24156)------------------------------
% 5.87/2.20 % (24156)------------------------------
% 5.87/2.20 % (24154)Refutation not found, incomplete strategy
% 5.87/2.20 % (24154)------------------------------
% 5.87/2.20 % (24154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.20 % (24154)Termination reason: Refutation not found, incomplete strategy
% 5.87/2.20
% 5.87/2.20
% 5.87/2.20 % (24154)Memory used [KB]: 5884
% 5.87/2.20 % (24154)Time elapsed: 0.043 s
% 5.87/2.20 % (24154)Instructions burned: 114 (million)
% 5.87/2.20 % (24154)------------------------------
% 5.87/2.20 % (24154)------------------------------
% 5.87/2.21 % (24157)Refutation not found, incomplete strategy
% 5.87/2.21 % (24157)------------------------------
% 5.87/2.21 % (24157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.21 % (24157)Termination reason: Refutation not found, incomplete strategy
% 5.87/2.21
% 5.87/2.21
% 5.87/2.21 % (24157)Memory used [KB]: 5756
% 5.87/2.21 % (24157)Time elapsed: 0.024 s
% 5.87/2.21 % (24157)Instructions burned: 57 (million)
% 5.87/2.21 % (24157)------------------------------
% 5.87/2.21 % (24157)------------------------------
% 5.87/2.21 % (24160)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23992 for (2994ds/298Mi)
% 5.87/2.22 % (24161)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23992 for (2994ds/192Mi)
% 5.87/2.22 % (24162)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_23992 for (2994ds/258Mi)
% 5.87/2.23 % (24163)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_23992 for (2994ds/90Mi)
% 5.87/2.24 % (24159)Instruction limit reached!
% 5.87/2.24 % (24159)------------------------------
% 5.87/2.24 % (24159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.24 % (24159)Termination reason: Unknown
% 5.87/2.24 % (24159)Termination phase: Property scanning
% 5.87/2.24
% 5.87/2.24 % (24159)Memory used [KB]: 1407
% 5.87/2.24 % (24159)Time elapsed: 0.056 s
% 5.87/2.24 % (24159)Instructions burned: 136 (million)
% 5.87/2.24 % (24159)------------------------------
% 5.87/2.24 % (24159)------------------------------
% 5.87/2.26 % (24163)Instruction limit reached!
% 5.87/2.26 % (24163)------------------------------
% 5.87/2.26 % (24163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.26 % (24163)Termination reason: Unknown
% 5.87/2.26 % (24163)Termination phase: Property scanning
% 5.87/2.26
% 5.87/2.26 % (24163)Memory used [KB]: 1407
% 5.87/2.26 % (24163)Time elapsed: 0.037 s
% 5.87/2.26 % (24163)Instructions burned: 91 (million)
% 5.87/2.26 % (24163)------------------------------
% 5.87/2.26 % (24163)------------------------------
% 5.87/2.26 % (24164)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_23992 for (2994ds/231Mi)
% 5.87/2.28 % (24165)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_23992 for (2994ds/458Mi)
% 5.87/2.29 % (24161)Instruction limit reached!
% 5.87/2.29 % (24161)------------------------------
% 5.87/2.29 % (24161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.29 % (24161)Termination reason: Unknown
% 5.87/2.29 % (24161)Termination phase: Saturation
% 5.87/2.29
% 5.87/2.29 % (24161)Memory used [KB]: 1791
% 5.87/2.29 % (24161)Time elapsed: 0.078 s
% 5.87/2.29 % (24161)Instructions burned: 194 (million)
% 5.87/2.29 % (24161)------------------------------
% 5.87/2.29 % (24161)------------------------------
% 5.87/2.30 % (24158)Instruction limit reached!
% 5.87/2.30 % (24158)------------------------------
% 5.87/2.30 % (24158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.30 % (24158)Termination reason: Unknown
% 5.87/2.30 % (24158)Termination phase: Saturation
% 5.87/2.30
% 5.87/2.30 % (24158)Memory used [KB]: 6652
% 5.87/2.30 % (24158)Time elapsed: 0.107 s
% 5.87/2.30 % (24158)Instructions burned: 284 (million)
% 5.87/2.30 % (24158)------------------------------
% 5.87/2.30 % (24158)------------------------------
% 6.54/2.31 % (24166)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/31Mi)
% 6.54/2.31 % (24167)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/297Mi)
% 6.54/2.32 % (24162)Instruction limit reached!
% 6.54/2.32 % (24162)------------------------------
% 6.54/2.32 % (24162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.32 % (24162)Termination reason: Unknown
% 6.54/2.32 % (24162)Termination phase: Saturation
% 6.54/2.32
% 6.54/2.32 % (24162)Memory used [KB]: 2046
% 6.54/2.32 % (24162)Time elapsed: 0.100 s
% 6.54/2.32 % (24162)Instructions burned: 258 (million)
% 6.54/2.32 % (24162)------------------------------
% 6.54/2.32 % (24162)------------------------------
% 6.54/2.32 % (24166)Instruction limit reached!
% 6.54/2.32 % (24166)------------------------------
% 6.54/2.32 % (24166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.32 % (24166)Termination reason: Unknown
% 6.54/2.32 % (24166)Termination phase: shuffling
% 6.54/2.32
% 6.54/2.32 % (24166)Memory used [KB]: 1279
% 6.54/2.32 % (24166)Time elapsed: 0.014 s
% 6.54/2.32 % (24166)Instructions burned: 32 (million)
% 6.54/2.32 % (24166)------------------------------
% 6.54/2.32 % (24166)------------------------------
% 6.54/2.32 % (24167)Refutation not found, incomplete strategy
% 6.54/2.32 % (24167)------------------------------
% 6.54/2.32 % (24167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.32 % (24167)Termination reason: Refutation not found, incomplete strategy
% 6.54/2.32
% 6.54/2.32
% 6.54/2.32 % (24167)Memory used [KB]: 5756
% 6.54/2.32 % (24167)Time elapsed: 0.013 s
% 6.54/2.32 % (24167)Instructions burned: 28 (million)
% 6.54/2.32 % (24167)------------------------------
% 6.54/2.32 % (24167)------------------------------
% 6.54/2.32 % (24160)Instruction limit reached!
% 6.54/2.32 % (24160)------------------------------
% 6.54/2.32 % (24160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.32 % (24160)Termination reason: Unknown
% 6.54/2.32 % (24160)Termination phase: Saturation
% 6.54/2.32
% 6.54/2.32 % (24160)Memory used [KB]: 6652
% 6.54/2.32 % (24160)Time elapsed: 0.113 s
% 6.54/2.32 % (24160)Instructions burned: 299 (million)
% 6.54/2.32 % (24160)------------------------------
% 6.54/2.32 % (24160)------------------------------
% 6.54/2.33 % (24168)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/987Mi)
% 6.54/2.34 % (24169)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/182Mi)
% 6.54/2.34 % (24170)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/182Mi)
% 6.54/2.34 % (24171)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/154Mi)
% 6.54/2.35 % (24164)Instruction limit reached!
% 6.54/2.35 % (24164)------------------------------
% 6.54/2.35 % (24164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.35 % (24164)Termination reason: Unknown
% 6.54/2.35 % (24164)Termination phase: Saturation
% 6.54/2.35
% 6.54/2.35 % (24164)Memory used [KB]: 6524
% 6.54/2.35 % (24164)Time elapsed: 0.090 s
% 6.54/2.35 % (24164)Instructions burned: 231 (million)
% 6.54/2.35 % (24164)------------------------------
% 6.54/2.35 % (24164)------------------------------
% 6.54/2.37 % (24172)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_23992 for (2993ds/79Mi)
% 6.94/2.40 % (24172)Instruction limit reached!
% 6.94/2.40 % (24172)------------------------------
% 6.94/2.40 % (24172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.40 % (24172)Termination reason: Unknown
% 6.94/2.40 % (24172)Termination phase: Property scanning
% 6.94/2.40
% 6.94/2.40 % (24172)Memory used [KB]: 1407
% 6.94/2.40 % (24172)Time elapsed: 0.033 s
% 6.94/2.40 % (24172)Instructions burned: 80 (million)
% 6.94/2.40 % (24172)------------------------------
% 6.94/2.40 % (24172)------------------------------
% 6.94/2.40 % (24171)Instruction limit reached!
% 6.94/2.40 % (24171)------------------------------
% 6.94/2.40 % (24171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.40 % (24171)Termination reason: Unknown
% 6.94/2.40 % (24171)Termination phase: Saturation
% 6.94/2.40
% 6.94/2.40 % (24171)Memory used [KB]: 1663
% 6.94/2.40 % (24171)Time elapsed: 0.063 s
% 6.94/2.40 % (24171)Instructions burned: 155 (million)
% 6.94/2.40 % (24171)------------------------------
% 6.94/2.40 % (24171)------------------------------
% 6.94/2.40 % (24155)Instruction limit reached!
% 6.94/2.40 % (24155)------------------------------
% 6.94/2.40 % (24155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.40 % (24155)Termination reason: Unknown
% 6.94/2.40 % (24155)Termination phase: Saturation
% 6.94/2.40
% 6.94/2.40 % (24155)Memory used [KB]: 6780
% 6.94/2.40 % (24155)Time elapsed: 0.230 s
% 6.94/2.40 % (24155)Instructions burned: 615 (million)
% 6.94/2.40 % (24155)------------------------------
% 6.94/2.40 % (24155)------------------------------
% 6.94/2.41 % (24169)Instruction limit reached!
% 6.94/2.41 % (24169)------------------------------
% 6.94/2.41 % (24169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.41 % (24169)Termination reason: Unknown
% 6.94/2.41 % (24169)Termination phase: Saturation
% 6.94/2.41
% 6.94/2.41 % (24169)Memory used [KB]: 6140
% 6.94/2.41 % (24169)Time elapsed: 0.075 s
% 6.94/2.41 % (24169)Instructions burned: 184 (million)
% 6.94/2.41 % (24169)------------------------------
% 6.94/2.41 % (24169)------------------------------
% 6.94/2.41 % (24173)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/216Mi)
% 6.94/2.42 % (24174)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/114Mi)
% 6.94/2.42 % (24175)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/922Mi)
% 6.94/2.42 % (24170)Instruction limit reached!
% 6.94/2.42 % (24170)------------------------------
% 6.94/2.42 % (24170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.42 % (24170)Termination reason: Unknown
% 6.94/2.42 % (24170)Termination phase: Saturation
% 6.94/2.42
% 6.94/2.42 % (24170)Memory used [KB]: 6268
% 6.94/2.42 % (24170)Time elapsed: 0.083 s
% 6.94/2.42 % (24170)Instructions burned: 183 (million)
% 6.94/2.42 % (24170)------------------------------
% 6.94/2.42 % (24170)------------------------------
% 6.94/2.43 % (24173)Refutation not found, incomplete strategy
% 6.94/2.43 % (24173)------------------------------
% 6.94/2.43 % (24173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.43 % (24173)Termination reason: Refutation not found, incomplete strategy
% 6.94/2.43
% 6.94/2.43
% 6.94/2.43 % (24173)Memory used [KB]: 5756
% 6.94/2.43 % (24173)Time elapsed: 0.014 s
% 6.94/2.43 % (24173)Instructions burned: 30 (million)
% 6.94/2.43 % (24173)------------------------------
% 6.94/2.43 % (24173)------------------------------
% 6.94/2.43 % (24176)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/182Mi)
% 6.94/2.44 % (24177)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/164Mi)
% 6.94/2.44 % (24175)Refutation not found, incomplete strategy
% 6.94/2.44 % (24175)------------------------------
% 6.94/2.44 % (24175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.44 % (24175)Termination reason: Refutation not found, incomplete strategy
% 6.94/2.44
% 6.94/2.44
% 6.94/2.44 % (24175)Memory used [KB]: 5756
% 6.94/2.44 % (24175)Time elapsed: 0.023 s
% 6.94/2.44 % (24175)Instructions burned: 53 (million)
% 6.94/2.44 % (24175)------------------------------
% 6.94/2.44 % (24175)------------------------------
% 6.94/2.44 % (24178)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/50Mi)
% 6.94/2.45 % (24177)Refutation not found, incomplete strategy
% 6.94/2.45 % (24177)------------------------------
% 6.94/2.45 % (24177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.45 % (24177)Termination reason: Refutation not found, incomplete strategy
% 6.94/2.45
% 6.94/2.45
% 6.94/2.45 % (24177)Memory used [KB]: 1279
% 6.94/2.45 % (24177)Time elapsed: 0.013 s
% 6.94/2.45 % (24177)Instructions burned: 26 (million)
% 6.94/2.45 % (24177)------------------------------
% 6.94/2.45 % (24177)------------------------------
% 6.94/2.45 % (24165)Instruction limit reached!
% 6.94/2.45 % (24165)------------------------------
% 6.94/2.45 % (24165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.45 % (24165)Termination reason: Unknown
% 6.94/2.45 % (24165)Termination phase: Saturation
% 6.94/2.45
% 6.94/2.45 % (24165)Memory used [KB]: 6396
% 6.94/2.45 % (24165)Time elapsed: 0.179 s
% 6.94/2.45 % (24165)Instructions burned: 459 (million)
% 6.94/2.45 % (24165)------------------------------
% 6.94/2.45 % (24165)------------------------------
% 6.94/2.46 % (24179)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/368Mi)
% 6.94/2.46 % (24178)Instruction limit reached!
% 6.94/2.46 % (24178)------------------------------
% 6.94/2.46 % (24178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.46 % (24178)Termination reason: Unknown
% 6.94/2.46 % (24178)Termination phase: Property scanning
% 6.94/2.46
% 6.94/2.46 % (24178)Memory used [KB]: 1407
% 6.94/2.46 % (24178)Time elapsed: 0.022 s
% 6.94/2.46 % (24178)Instructions burned: 51 (million)
% 6.94/2.46 % (24178)------------------------------
% 6.94/2.46 % (24178)------------------------------
% 6.94/2.46 % (24174)Instruction limit reached!
% 6.94/2.46 % (24174)------------------------------
% 6.94/2.46 % (24174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.46 % (24174)Termination reason: Unknown
% 6.94/2.46 % (24174)Termination phase: Property scanning
% 6.94/2.46
% 6.94/2.46 % (24174)Memory used [KB]: 1407
% 6.94/2.46 % (24174)Time elapsed: 0.047 s
% 6.94/2.46 % (24174)Instructions burned: 114 (million)
% 6.94/2.46 % (24174)------------------------------
% 6.94/2.46 % (24174)------------------------------
% 6.94/2.46 % (24180)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/1021Mi)
% 6.94/2.47 % (24181)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/267Mi)
% 6.94/2.48 % (24182)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/204Mi)
% 6.94/2.48 % (24183)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_23992 for (2992ds/26Mi)
% 6.94/2.49 % (24183)Instruction limit reached!
% 6.94/2.49 % (24183)------------------------------
% 6.94/2.49 % (24183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.94/2.49 % (24183)Termination reason: Unknown
% 6.94/2.49 % (24183)Termination phase: Property scanning
% 6.94/2.49
% 6.94/2.49 % (24183)Memory used [KB]: 1279
% 6.94/2.49 % (24183)Time elapsed: 0.013 s
% 6.94/2.49 % (24183)Instructions burned: 27 (million)
% 6.94/2.49 % (24183)------------------------------
% 6.94/2.49 % (24183)------------------------------
% 7.91/2.50 % (24176)Instruction limit reached!
% 7.91/2.50 % (24176)------------------------------
% 7.91/2.50 % (24176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.50 % (24176)Termination reason: Unknown
% 7.91/2.50 % (24176)Termination phase: Saturation
% 7.91/2.50
% 7.91/2.50 % (24176)Memory used [KB]: 6268
% 7.91/2.50 % (24176)Time elapsed: 0.073 s
% 7.91/2.50 % (24176)Instructions burned: 182 (million)
% 7.91/2.50 % (24176)------------------------------
% 7.91/2.50 % (24176)------------------------------
% 7.91/2.51 % (24184)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_23992 for (2991ds/53Mi)
% 7.91/2.52 % (24185)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_23992 for (2991ds/4436Mi)
% 7.91/2.53 % (24184)Instruction limit reached!
% 7.91/2.53 % (24184)------------------------------
% 7.91/2.53 % (24184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.53 % (24184)Termination reason: Unknown
% 7.91/2.53 % (24184)Termination phase: Property scanning
% 7.91/2.53
% 7.91/2.53 % (24184)Memory used [KB]: 1407
% 7.91/2.53 % (24184)Time elapsed: 0.023 s
% 7.91/2.53 % (24184)Instructions burned: 54 (million)
% 7.91/2.53 % (24184)------------------------------
% 7.91/2.53 % (24184)------------------------------
% 7.91/2.54 % (24185)Refutation not found, incomplete strategy
% 7.91/2.54 % (24185)------------------------------
% 7.91/2.54 % (24185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.54 % (24185)Termination reason: Refutation not found, incomplete strategy
% 7.91/2.54
% 7.91/2.54
% 7.91/2.54 % (24185)Memory used [KB]: 5756
% 7.91/2.54 % (24185)Time elapsed: 0.023 s
% 7.91/2.54 % (24185)Instructions burned: 56 (million)
% 7.91/2.54 % (24185)------------------------------
% 7.91/2.54 % (24185)------------------------------
% 7.91/2.54 % (24186)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_23992 for (2991ds/1539Mi)
% 7.91/2.55 % (24187)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_23992 for (2991ds/408Mi)
% 7.91/2.56 % (24182)Instruction limit reached!
% 7.91/2.56 % (24182)------------------------------
% 7.91/2.56 % (24182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.56 % (24182)Termination reason: Unknown
% 7.91/2.56 % (24182)Termination phase: Saturation
% 7.91/2.56
% 7.91/2.56 % (24182)Memory used [KB]: 6268
% 7.91/2.56 % (24182)Time elapsed: 0.080 s
% 7.91/2.56 % (24182)Instructions burned: 205 (million)
% 7.91/2.56 % (24182)------------------------------
% 7.91/2.56 % (24182)------------------------------
% 7.91/2.57 % (24181)Instruction limit reached!
% 7.91/2.57 % (24181)------------------------------
% 7.91/2.57 % (24181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.57 % (24181)Termination reason: Unknown
% 7.91/2.57 % (24181)Termination phase: Saturation
% 7.91/2.57
% 7.91/2.57 % (24181)Memory used [KB]: 6652
% 7.91/2.57 % (24181)Time elapsed: 0.103 s
% 7.91/2.57 % (24181)Instructions burned: 269 (million)
% 7.91/2.57 % (24181)------------------------------
% 7.91/2.57 % (24181)------------------------------
% 7.91/2.57 % (24188)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_23992 for (2991ds/5205Mi)
% 7.91/2.59 % (24189)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_23992 for (2991ds/1913Mi)
% 8.28/2.60 % (24179)Instruction limit reached!
% 8.28/2.60 % (24179)------------------------------
% 8.28/2.60 % (24179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.28/2.60 % (24179)Termination reason: Unknown
% 8.28/2.60 % (24179)Termination phase: Saturation
% 8.28/2.60
% 8.28/2.60 % (24179)Memory used [KB]: 6268
% 8.28/2.60 % (24179)Time elapsed: 0.144 s
% 8.28/2.60 % (24179)Instructions burned: 368 (million)
% 8.28/2.60 % (24179)------------------------------
% 8.28/2.60 % (24179)------------------------------
% 8.28/2.61 % (24190)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_23992 for (2990ds/4350Mi)
% 8.28/2.64 % (24187)Refutation not found, incomplete strategy
% 8.28/2.64 % (24187)------------------------------
% 8.28/2.64 % (24187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.28/2.64 % (24187)Termination reason: Refutation not found, incomplete strategy
% 8.28/2.64
% 8.28/2.64
% 8.28/2.64 % (24187)Memory used [KB]: 6396
% 8.28/2.64 % (24187)Time elapsed: 0.088 s
% 8.28/2.64 % (24187)Instructions burned: 191 (million)
% 8.28/2.64 % (24187)------------------------------
% 8.28/2.64 % (24187)------------------------------
% 8.28/2.66 % (24190)Refutation not found, incomplete strategy
% 8.28/2.66 % (24190)------------------------------
% 8.28/2.66 % (24190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.28/2.66 % (24190)Termination reason: Refutation not found, incomplete strategy
% 8.28/2.66
% 8.28/2.66
% 8.28/2.66 % (24190)Memory used [KB]: 5884
% 8.28/2.66 % (24190)Time elapsed: 0.042 s
% 8.28/2.66 % (24190)Instructions burned: 111 (million)
% 8.28/2.66 % (24190)------------------------------
% 8.28/2.66 % (24190)------------------------------
% 8.28/2.66 % (24191)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_23992 for (2990ds/68Mi)
% 8.28/2.67 % (24192)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_23992 for (2990ds/358Mi)
% 8.28/2.68 % (24191)Instruction limit reached!
% 8.28/2.68 % (24191)------------------------------
% 8.28/2.68 % (24191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.28/2.68 % (24191)Termination reason: Unknown
% 8.28/2.68 % (24191)Termination phase: Function definition elimination
% 8.28/2.68
% 8.28/2.68 % (24191)Memory used [KB]: 1279
% 8.28/2.68 % (24191)Time elapsed: 0.028 s
% 8.28/2.68 % (24191)Instructions burned: 68 (million)
% 8.28/2.68 % (24191)------------------------------
% 8.28/2.68 % (24191)------------------------------
% 8.64/2.70 % (24189)Refutation not found, incomplete strategy
% 8.64/2.70 % (24189)------------------------------
% 8.64/2.70 % (24189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.70 % (24189)Termination reason: Refutation not found, incomplete strategy
% 8.64/2.70
% 8.64/2.70
% 8.64/2.70 % (24189)Memory used [KB]: 2174
% 8.64/2.70 % (24189)Time elapsed: 0.110 s
% 8.64/2.70 % (24189)Instructions burned: 264 (million)
% 8.64/2.70 % (24189)------------------------------
% 8.64/2.70 % (24189)------------------------------
% 8.64/2.70 % (24192)Refutation not found, incomplete strategy
% 8.64/2.70 % (24192)------------------------------
% 8.64/2.70 % (24192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.70 % (24192)Termination reason: Refutation not found, incomplete strategy
% 8.64/2.70
% 8.64/2.70
% 8.64/2.70 % (24192)Memory used [KB]: 5756
% 8.64/2.70 % (24192)Time elapsed: 0.026 s
% 8.64/2.70 % (24192)Instructions burned: 62 (million)
% 8.64/2.70 % (24192)------------------------------
% 8.64/2.70 % (24192)------------------------------
% 8.64/2.70 % (24193)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/31Mi)
% 8.64/2.71 % (24193)Instruction limit reached!
% 8.64/2.71 % (24193)------------------------------
% 8.64/2.71 % (24193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.71 % (24193)Termination reason: Unknown
% 8.64/2.71 % (24193)Termination phase: shuffling
% 8.64/2.71
% 8.64/2.71 % (24193)Memory used [KB]: 1279
% 8.64/2.71 % (24193)Time elapsed: 0.014 s
% 8.64/2.71 % (24193)Instructions burned: 33 (million)
% 8.64/2.71 % (24193)------------------------------
% 8.64/2.71 % (24193)------------------------------
% 8.64/2.71 % (24194)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/279Mi)
% 8.64/2.71 % (24195)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/258Mi)
% 8.64/2.72 % (24168)Instruction limit reached!
% 8.64/2.72 % (24168)------------------------------
% 8.64/2.72 % (24168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.72 % (24168)Termination reason: Unknown
% 8.64/2.72 % (24168)Termination phase: Saturation
% 8.64/2.72
% 8.64/2.72 % (24168)Memory used [KB]: 8059
% 8.64/2.72 % (24168)Time elapsed: 0.391 s
% 8.64/2.72 % (24168)Instructions burned: 988 (million)
% 8.64/2.72 % (24168)------------------------------
% 8.64/2.72 % (24168)------------------------------
% 8.64/2.72 % (24194)Refutation not found, incomplete strategy
% 8.64/2.72 % (24194)------------------------------
% 8.64/2.72 % (24194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.72 % (24194)Termination reason: Refutation not found, incomplete strategy
% 8.64/2.72
% 8.64/2.72
% 8.64/2.72 % (24194)Memory used [KB]: 5756
% 8.64/2.72 % (24194)Time elapsed: 0.011 s
% 8.64/2.72 % (24194)Instructions burned: 24 (million)
% 8.64/2.72 % (24194)------------------------------
% 8.64/2.72 % (24194)------------------------------
% 8.64/2.73 % (24196)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/26Mi)
% 8.64/2.74 % (24197)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/995Mi)
% 8.64/2.74 % (24198)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/373Mi)
% 8.64/2.74 % (24196)Instruction limit reached!
% 8.64/2.74 % (24196)------------------------------
% 8.64/2.74 % (24196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.74 % (24196)Termination reason: Unknown
% 8.64/2.74 % (24196)Termination phase: Property scanning
% 8.64/2.74
% 8.64/2.74 % (24196)Memory used [KB]: 1279
% 8.64/2.74 % (24196)Time elapsed: 0.013 s
% 8.64/2.74 % (24196)Instructions burned: 28 (million)
% 8.64/2.74 % (24196)------------------------------
% 8.64/2.74 % (24196)------------------------------
% 8.64/2.76 % (24199)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_23992 for (2989ds/253Mi)
% 9.30/2.83 % (24195)Instruction limit reached!
% 9.30/2.83 % (24195)------------------------------
% 9.30/2.83 % (24195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.83 % (24195)Termination reason: Unknown
% 9.30/2.83 % (24195)Termination phase: Saturation
% 9.30/2.83
% 9.30/2.83 % (24195)Memory used [KB]: 7036
% 9.30/2.83 % (24195)Time elapsed: 0.114 s
% 9.30/2.83 % (24195)Instructions burned: 259 (million)
% 9.30/2.83 % (24195)------------------------------
% 9.30/2.83 % (24195)------------------------------
% 9.30/2.84 % (24200)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_23992 for (2988ds/832Mi)
% 9.30/2.85 % (24199)Instruction limit reached!
% 9.30/2.85 % (24199)------------------------------
% 9.30/2.85 % (24199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.85 % (24199)Termination reason: Unknown
% 9.30/2.85 % (24199)Termination phase: Saturation
% 9.30/2.85
% 9.30/2.85 % (24199)Memory used [KB]: 6652
% 9.30/2.85 % (24199)Time elapsed: 0.097 s
% 9.30/2.85 % (24199)Instructions burned: 254 (million)
% 9.30/2.85 % (24199)------------------------------
% 9.30/2.85 % (24199)------------------------------
% 9.30/2.86 % (24180)Instruction limit reached!
% 9.30/2.86 % (24180)------------------------------
% 9.30/2.86 % (24180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.86 % (24180)Termination reason: Unknown
% 9.30/2.86 % (24180)Termination phase: Saturation
% 9.30/2.86
% 9.30/2.86 % (24180)Memory used [KB]: 7291
% 9.30/2.86 % (24180)Time elapsed: 0.392 s
% 9.30/2.86 % (24180)Instructions burned: 1022 (million)
% 9.30/2.86 % (24180)------------------------------
% 9.30/2.86 % (24180)------------------------------
% 9.30/2.87 % (24201)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_23992 for (2988ds/668Mi)
% 9.30/2.87 % (24202)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_23992 for (2988ds/40Mi)
% 9.30/2.88 % (24200)Refutation not found, incomplete strategy
% 9.30/2.88 % (24200)------------------------------
% 9.30/2.88 % (24200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.88 % (24200)Termination reason: Refutation not found, incomplete strategy
% 9.30/2.88
% 9.30/2.88
% 9.30/2.88 % (24200)Memory used [KB]: 6012
% 9.30/2.88 % (24200)Time elapsed: 0.038 s
% 9.30/2.88 % (24200)Instructions burned: 88 (million)
% 9.30/2.88 % (24200)------------------------------
% 9.30/2.88 % (24200)------------------------------
% 9.30/2.89 % (24198)Instruction limit reached!
% 9.30/2.89 % (24198)------------------------------
% 9.30/2.89 % (24198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.89 % (24198)Termination reason: Unknown
% 9.30/2.89 % (24198)Termination phase: Saturation
% 9.30/2.89
% 9.30/2.89 % (24198)Memory used [KB]: 6396
% 9.30/2.89 % (24198)Time elapsed: 0.148 s
% 9.30/2.89 % (24198)Instructions burned: 374 (million)
% 9.30/2.89 % (24198)------------------------------
% 9.30/2.89 % (24198)------------------------------
% 9.30/2.89 % (24202)Instruction limit reached!
% 9.30/2.89 % (24202)------------------------------
% 9.30/2.89 % (24202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.89 % (24202)Termination reason: Unknown
% 9.30/2.89 % (24202)Termination phase: Function definition elimination
% 9.30/2.89
% 9.30/2.89 % (24202)Memory used [KB]: 1407
% 9.30/2.89 % (24202)Time elapsed: 0.018 s
% 9.30/2.89 % (24202)Instructions burned: 41 (million)
% 9.30/2.89 % (24202)------------------------------
% 9.30/2.89 % (24202)------------------------------
% 9.30/2.90 % (24203)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_23992 for (2988ds/294Mi)
% 10.20/2.90 % (24204)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_23992 for (2988ds/187Mi)
% 10.20/2.90 % (24205)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23992 for (2987ds/371Mi)
% 10.20/2.93 % (24203)Refutation not found, incomplete strategy
% 10.20/2.93 % (24203)------------------------------
% 10.20/2.93 % (24203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.93 % (24203)Termination reason: Refutation not found, incomplete strategy
% 10.20/2.93
% 10.20/2.93
% 10.20/2.93 % (24203)Memory used [KB]: 5884
% 10.20/2.93 % (24203)Time elapsed: 0.031 s
% 10.20/2.93 % (24203)Instructions burned: 80 (million)
% 10.20/2.93 % (24203)------------------------------
% 10.20/2.93 % (24203)------------------------------
% 10.20/2.93 % (24205)Refutation not found, incomplete strategy
% 10.20/2.93 % (24205)------------------------------
% 10.20/2.93 % (24205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.93 % (24205)Termination reason: Refutation not found, incomplete strategy
% 10.20/2.93
% 10.20/2.93
% 10.20/2.93 % (24205)Memory used [KB]: 5756
% 10.20/2.93 % (24205)Time elapsed: 0.045 s
% 10.20/2.93 % (24205)Instructions burned: 56 (million)
% 10.20/2.93 % (24205)------------------------------
% 10.20/2.93 % (24205)------------------------------
% 10.20/2.94 % (24206)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23992 for (2987ds/1827Mi)
% 10.20/2.94 % (24207)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_23992 for (2987ds/70Mi)
% 10.20/2.97 % (24207)Instruction limit reached!
% 10.20/2.97 % (24207)------------------------------
% 10.20/2.97 % (24207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.97 % (24207)Termination reason: Unknown
% 10.20/2.97 % (24207)Termination phase: Property scanning
% 10.20/2.97
% 10.20/2.97 % (24207)Memory used [KB]: 1407
% 10.20/2.97 % (24207)Time elapsed: 0.030 s
% 10.20/2.97 % (24207)Instructions burned: 70 (million)
% 10.20/2.97 % (24207)------------------------------
% 10.20/2.97 % (24207)------------------------------
% 10.20/2.98 % (24204)Instruction limit reached!
% 10.20/2.98 % (24204)------------------------------
% 10.20/2.98 % (24204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.98 % (24204)Termination reason: Unknown
% 10.20/2.98 % (24204)Termination phase: Saturation
% 10.20/2.98
% 10.20/2.98 % (24204)Memory used [KB]: 6140
% 10.20/2.98 % (24204)Time elapsed: 0.077 s
% 10.20/2.98 % (24204)Instructions burned: 188 (million)
% 10.20/2.98 % (24204)------------------------------
% 10.20/2.98 % (24204)------------------------------
% 10.20/2.99 % (24208)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_23992 for (2986ds/316Mi)
% 10.20/2.99 % (24209)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_23992 for (2986ds/932Mi)
% 12.00/3.11 % (24208)Instruction limit reached!
% 12.00/3.11 % (24208)------------------------------
% 12.00/3.11 % (24208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.00/3.11 % (24208)Termination reason: Unknown
% 12.00/3.11 % (24208)Termination phase: Saturation
% 12.00/3.11
% 12.00/3.11 % (24208)Memory used [KB]: 2302
% 12.00/3.11 % (24208)Time elapsed: 0.121 s
% 12.00/3.11 % (24208)Instructions burned: 317 (million)
% 12.00/3.11 % (24208)------------------------------
% 12.00/3.11 % (24208)------------------------------
% 12.00/3.12 % (24210)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_23992 for (2985ds/4714Mi)
% 12.00/3.12 % (24201)Instruction limit reached!
% 12.00/3.12 % (24201)------------------------------
% 12.00/3.12 % (24201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.00/3.12 % (24201)Termination reason: Unknown
% 12.00/3.12 % (24201)Termination phase: Saturation
% 12.00/3.12
% 12.00/3.12 % (24201)Memory used [KB]: 12537
% 12.00/3.12 % (24201)Time elapsed: 0.258 s
% 12.00/3.12 % (24201)Instructions burned: 669 (million)
% 12.00/3.12 % (24201)------------------------------
% 12.00/3.12 % (24201)------------------------------
% 12.00/3.12 % (24197)Instruction limit reached!
% 12.00/3.12 % (24197)------------------------------
% 12.00/3.12 % (24197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.00/3.12 % (24197)Termination reason: Unknown
% 12.00/3.12 % (24197)Termination phase: Saturation
% 12.00/3.12
% 12.00/3.12 % (24197)Memory used [KB]: 7931
% 12.00/3.12 % (24197)Time elapsed: 0.387 s
% 12.00/3.12 % (24197)Instructions burned: 996 (million)
% 12.00/3.12 % (24197)------------------------------
% 12.00/3.12 % (24197)------------------------------
% 12.71/3.13 % (24186)Instruction limit reached!
% 12.71/3.13 % (24186)------------------------------
% 12.71/3.13 % (24186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.13 % (24186)Termination reason: Unknown
% 12.71/3.13 % (24186)Termination phase: Saturation
% 12.71/3.13
% 12.71/3.13 % (24186)Memory used [KB]: 8315
% 12.71/3.13 % (24186)Time elapsed: 0.587 s
% 12.71/3.13 % (24186)Instructions burned: 1539 (million)
% 12.71/3.13 % (24186)------------------------------
% 12.71/3.13 % (24186)------------------------------
% 12.71/3.14 % (24211)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_23992 for (2985ds/8250Mi)
% 12.71/3.14 % (24212)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_23992 for (2985ds/770Mi)
% 12.71/3.15 % (24213)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23992 for (2985ds/794Mi)
% 12.71/3.16 % (24212)Refutation not found, incomplete strategy
% 12.71/3.16 % (24212)------------------------------
% 12.71/3.16 % (24212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.16 % (24212)Termination reason: Refutation not found, incomplete strategy
% 12.71/3.16
% 12.71/3.16
% 12.71/3.16 % (24212)Memory used [KB]: 5756
% 12.71/3.16 % (24212)Time elapsed: 0.023 s
% 12.71/3.16 % (24212)Instructions burned: 55 (million)
% 12.71/3.16 % (24212)------------------------------
% 12.71/3.16 % (24212)------------------------------
% 12.71/3.18 % (24214)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_23992 for (2985ds/464Mi)
% 12.97/3.29 % (24210)Refutation not found, incomplete strategy
% 12.97/3.29 % (24210)------------------------------
% 12.97/3.29 % (24210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.29 % (24210)Termination reason: Refutation not found, incomplete strategy
% 12.97/3.29
% 12.97/3.29
% 12.97/3.29 % (24210)Memory used [KB]: 7547
% 12.97/3.29 % (24210)Time elapsed: 0.166 s
% 12.97/3.29 % (24210)Instructions burned: 450 (million)
% 12.97/3.29 % (24210)------------------------------
% 12.97/3.29 % (24210)------------------------------
% 13.45/3.31 % (24215)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_23992 for (2983ds/1376Mi)
% 13.45/3.37 % (24214)Instruction limit reached!
% 13.45/3.37 % (24214)------------------------------
% 13.45/3.37 % (24214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.45/3.37 % (24214)Termination reason: Unknown
% 13.45/3.37 % (24214)Termination phase: Saturation
% 13.45/3.37
% 13.45/3.37 % (24214)Memory used [KB]: 6140
% 13.45/3.37 % (24214)Time elapsed: 0.190 s
% 13.45/3.37 % (24214)Instructions burned: 464 (million)
% 13.45/3.37 % (24214)------------------------------
% 13.45/3.37 % (24214)------------------------------
% 13.45/3.37 % (24209)Instruction limit reached!
% 13.45/3.37 % (24209)------------------------------
% 13.45/3.37 % (24209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.45/3.37 % (24209)Termination reason: Unknown
% 13.45/3.37 % (24209)Termination phase: Saturation
% 13.45/3.37
% 13.45/3.37 % (24209)Memory used [KB]: 7803
% 13.45/3.37 % (24209)Time elapsed: 0.380 s
% 13.45/3.37 % (24209)Instructions burned: 932 (million)
% 13.45/3.37 % (24209)------------------------------
% 13.45/3.37 % (24209)------------------------------
% 13.45/3.38 % (24216)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_23992 for (2983ds/906Mi)
% 13.45/3.39 % (24217)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_23992 for (2982ds/434Mi)
% 13.94/3.41 % (24217)Refutation not found, incomplete strategy
% 13.94/3.41 % (24217)------------------------------
% 13.94/3.41 % (24217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.94/3.41 % (24217)Termination reason: Refutation not found, incomplete strategy
% 13.94/3.41
% 13.94/3.41
% 13.94/3.41 % (24217)Memory used [KB]: 5756
% 13.94/3.41 % (24217)Time elapsed: 0.022 s
% 13.94/3.41 % (24217)Instructions burned: 53 (million)
% 13.94/3.41 % (24217)------------------------------
% 13.94/3.41 % (24217)------------------------------
% 13.94/3.43 % (24218)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_23992 for (2982ds/865Mi)
% 13.94/3.44 % (24218)Refutation not found, incomplete strategy
% 13.94/3.44 % (24218)------------------------------
% 13.94/3.44 % (24218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.94/3.44 % (24218)Termination reason: Refutation not found, incomplete strategy
% 13.94/3.44
% 13.94/3.44
% 13.94/3.44 % (24218)Memory used [KB]: 5756
% 13.94/3.44 % (24218)Time elapsed: 0.012 s
% 13.94/3.44 % (24218)Instructions burned: 22 (million)
% 13.94/3.44 % (24218)------------------------------
% 13.94/3.44 % (24218)------------------------------
% 13.94/3.45 % (24213)Instruction limit reached!
% 13.94/3.45 % (24213)------------------------------
% 13.94/3.45 % (24213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.94/3.45 % (24213)Termination reason: Unknown
% 13.94/3.45 % (24213)Termination phase: Saturation
% 13.94/3.45
% 13.94/3.45 % (24213)Memory used [KB]: 2430
% 13.94/3.45 % (24213)Time elapsed: 0.302 s
% 13.94/3.45 % (24213)Instructions burned: 795 (million)
% 13.94/3.45 % (24213)------------------------------
% 13.94/3.45 % (24213)------------------------------
% 13.94/3.45 % (24219)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_23992 for (2982ds/593Mi)
% 13.94/3.46 % (24220)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_23992 for (2982ds/443Mi)
% 14.73/3.63 % (24220)Instruction limit reached!
% 14.73/3.63 % (24220)------------------------------
% 14.73/3.63 % (24220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/3.63 % (24220)Termination reason: Unknown
% 14.73/3.63 % (24220)Termination phase: Saturation
% 14.73/3.63
% 14.73/3.63 % (24220)Memory used [KB]: 6396
% 14.73/3.63 % (24220)Time elapsed: 0.172 s
% 14.73/3.63 % (24220)Instructions burned: 444 (million)
% 14.73/3.63 % (24220)------------------------------
% 14.73/3.63 % (24220)------------------------------
% 14.73/3.65 % (24221)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_23992 for (2980ds/594Mi)
% 14.73/3.67 % (24219)Instruction limit reached!
% 14.73/3.67 % (24219)------------------------------
% 14.73/3.67 % (24219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/3.67 % (24219)Termination reason: Unknown
% 14.73/3.67 % (24219)Termination phase: Saturation
% 14.73/3.67
% 14.73/3.67 % (24219)Memory used [KB]: 7675
% 14.73/3.67 % (24219)Time elapsed: 0.220 s
% 14.73/3.67 % (24219)Instructions burned: 593 (million)
% 14.73/3.67 % (24219)------------------------------
% 14.73/3.67 % (24219)------------------------------
% 14.73/3.67 % (24221)Refutation not found, incomplete strategy
% 14.73/3.67 % (24221)------------------------------
% 14.73/3.67 % (24221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/3.67 % (24221)Termination reason: Refutation not found, incomplete strategy
% 14.73/3.67
% 14.73/3.67
% 14.73/3.67 % (24221)Memory used [KB]: 5756
% 14.73/3.67 % (24221)Time elapsed: 0.023 s
% 14.73/3.67 % (24221)Instructions burned: 56 (million)
% 14.73/3.67 % (24221)------------------------------
% 14.73/3.67 % (24221)------------------------------
% 14.73/3.69 % (24222)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_23992 for (2980ds/327Mi)
% 14.73/3.69 % (24223)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_23992 for (2980ds/5411Mi)
% 15.39/3.71 % (24223)Refutation not found, incomplete strategy
% 15.39/3.71 % (24223)------------------------------
% 15.39/3.71 % (24223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.71 % (24223)Termination reason: Refutation not found, incomplete strategy
% 15.39/3.71
% 15.39/3.71
% 15.39/3.71 % (24223)Memory used [KB]: 5756
% 15.39/3.71 % (24223)Time elapsed: 0.023 s
% 15.39/3.71 % (24223)Instructions burned: 54 (million)
% 15.39/3.71 % (24223)------------------------------
% 15.39/3.71 % (24223)------------------------------
% 15.39/3.73 % (24224)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_23992 for (2979ds/1762Mi)
% 15.39/3.73 % (24216)Instruction limit reached!
% 15.39/3.73 % (24216)------------------------------
% 15.39/3.73 % (24216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.73 % (24216)Termination reason: Unknown
% 15.39/3.73 % (24216)Termination phase: Saturation
% 15.39/3.73
% 15.39/3.73 % (24216)Memory used [KB]: 7036
% 15.39/3.73 % (24216)Time elapsed: 0.351 s
% 15.39/3.73 % (24216)Instructions burned: 906 (million)
% 15.39/3.73 % (24216)------------------------------
% 15.39/3.73 % (24216)------------------------------
% 15.39/3.75 % (24225)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_23992 for (2979ds/96Mi)
% 15.39/3.79 % (24206)Instruction limit reached!
% 15.39/3.79 % (24206)------------------------------
% 15.39/3.79 % (24206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.79 % (24206)Termination reason: Unknown
% 15.39/3.79 % (24206)Termination phase: Saturation
% 15.39/3.79
% 15.39/3.79 % (24206)Memory used [KB]: 8443
% 15.39/3.79 % (24206)Time elapsed: 0.845 s
% 15.39/3.79 % (24206)Instructions burned: 1827 (million)
% 15.39/3.79 % (24206)------------------------------
% 15.39/3.79 % (24206)------------------------------
% 15.39/3.79 % (24225)Instruction limit reached!
% 15.39/3.79 % (24225)------------------------------
% 15.39/3.79 % (24225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.79 % (24225)Termination reason: Unknown
% 15.39/3.79 % (24225)Termination phase: Property scanning
% 15.39/3.79
% 15.39/3.79 % (24225)Memory used [KB]: 1407
% 15.39/3.79 % (24225)Time elapsed: 0.041 s
% 15.39/3.79 % (24225)Instructions burned: 96 (million)
% 15.39/3.79 % (24225)------------------------------
% 15.39/3.79 % (24225)------------------------------
% 16.05/3.80 % (24226)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_23992 for (2978ds/503Mi)
% 16.05/3.81 % (24227)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_23992 for (2978ds/90Mi)
% 16.05/3.82 % (24226)Refutation not found, incomplete strategy
% 16.05/3.82 % (24226)------------------------------
% 16.05/3.82 % (24226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.82 % (24226)Termination reason: Refutation not found, incomplete strategy
% 16.05/3.82
% 16.05/3.82
% 16.05/3.82 % (24226)Memory used [KB]: 5756
% 16.05/3.82 % (24226)Time elapsed: 0.023 s
% 16.05/3.82 % (24226)Instructions burned: 54 (million)
% 16.05/3.82 % (24226)------------------------------
% 16.05/3.82 % (24226)------------------------------
% 16.05/3.83 % (24222)Instruction limit reached!
% 16.05/3.83 % (24222)------------------------------
% 16.05/3.83 % (24222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.83 % (24222)Termination reason: Unknown
% 16.05/3.83 % (24222)Termination phase: Saturation
% 16.05/3.83
% 16.05/3.83 % (24222)Memory used [KB]: 6780
% 16.05/3.83 % (24222)Time elapsed: 0.147 s
% 16.05/3.83 % (24222)Instructions burned: 329 (million)
% 16.05/3.83 % (24222)------------------------------
% 16.05/3.83 % (24222)------------------------------
% 16.05/3.84 % (24228)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_23992 for (2978ds/593Mi)
% 16.05/3.84 % (24227)Instruction limit reached!
% 16.05/3.84 % (24227)------------------------------
% 16.05/3.84 % (24227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.84 % (24227)Termination reason: Unknown
% 16.05/3.84 % (24227)Termination phase: Property scanning
% 16.05/3.84
% 16.05/3.84 % (24227)Memory used [KB]: 1407
% 16.05/3.84 % (24227)Time elapsed: 0.037 s
% 16.05/3.84 % (24227)Instructions burned: 90 (million)
% 16.05/3.84 % (24227)------------------------------
% 16.05/3.84 % (24227)------------------------------
% 16.05/3.85 % (24229)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_23992 for (2978ds/1512Mi)
% 16.05/3.86 % (24230)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_23992 for (2978ds/569Mi)
% 16.05/3.89 % (24215)Instruction limit reached!
% 16.05/3.89 % (24215)------------------------------
% 16.05/3.89 % (24215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.89 % (24215)Termination reason: Unknown
% 16.05/3.89 % (24215)Termination phase: Saturation
% 16.05/3.89
% 16.05/3.89 % (24215)Memory used [KB]: 8059
% 16.05/3.89 % (24215)Time elapsed: 0.584 s
% 16.05/3.89 % (24215)Instructions burned: 1376 (million)
% 16.05/3.89 % (24215)------------------------------
% 16.05/3.89 % (24215)------------------------------
% 16.05/3.89 % (24229)Refutation not found, incomplete strategy
% 16.05/3.89 % (24229)------------------------------
% 16.05/3.89 % (24229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.89 % (24229)Termination reason: Refutation not found, incomplete strategy
% 16.05/3.89
% 16.05/3.89
% 16.05/3.89 % (24229)Memory used [KB]: 6140
% 16.05/3.89 % (24229)Time elapsed: 0.040 s
% 16.05/3.89 % (24229)Instructions burned: 90 (million)
% 16.05/3.89 % (24229)------------------------------
% 16.05/3.89 % (24229)------------------------------
% 17.05/3.90 % (24231)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_23992 for (2977ds/501Mi)
% 17.05/3.90 % (24232)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_23992 for (2977ds/562Mi)
% 17.05/3.91 % (24232)Refutation not found, incomplete strategy
% 17.05/3.91 % (24232)------------------------------
% 17.05/3.91 % (24232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.91 % (24232)Termination reason: Refutation not found, incomplete strategy
% 17.05/3.91
% 17.05/3.91
% 17.05/3.91 % (24232)Memory used [KB]: 5756
% 17.05/3.91 % (24232)Time elapsed: 0.011 s
% 17.05/3.91 % (24232)Instructions burned: 23 (million)
% 17.05/3.91 % (24232)------------------------------
% 17.05/3.91 % (24232)------------------------------
% 17.05/3.93 % (24233)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23992 for (2977ds/406Mi)
% 18.99/4.07 % (24228)Instruction limit reached!
% 18.99/4.07 % (24228)------------------------------
% 18.99/4.07 % (24228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.99/4.07 % (24228)Termination reason: Unknown
% 18.99/4.07 % (24228)Termination phase: Saturation
% 18.99/4.07
% 18.99/4.07 % (24228)Memory used [KB]: 6780
% 18.99/4.07 % (24228)Time elapsed: 0.231 s
% 18.99/4.07 % (24228)Instructions burned: 593 (million)
% 18.99/4.07 % (24228)------------------------------
% 18.99/4.07 % (24228)------------------------------
% 18.99/4.07 % (24230)Instruction limit reached!
% 18.99/4.07 % (24230)------------------------------
% 18.99/4.07 % (24230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.99/4.07 % (24230)Termination reason: Unknown
% 18.99/4.07 % (24230)Termination phase: Saturation
% 18.99/4.07
% 18.99/4.07 % (24230)Memory used [KB]: 7675
% 18.99/4.07 % (24230)Time elapsed: 0.216 s
% 18.99/4.07 % (24230)Instructions burned: 569 (million)
% 18.99/4.07 % (24230)------------------------------
% 18.99/4.07 % (24230)------------------------------
% 18.99/4.08 % (24231)Refutation not found, incomplete strategy
% 18.99/4.08 % (24231)------------------------------
% 18.99/4.08 % (24231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.99/4.08 % (24231)Termination reason: Refutation not found, incomplete strategy
% 18.99/4.08
% 18.99/4.08
% 18.99/4.08 % (24231)Memory used [KB]: 7547
% 18.99/4.08 % (24231)Time elapsed: 0.175 s
% 18.99/4.08 % (24231)Instructions burned: 473 (million)
% 18.99/4.08 % (24231)------------------------------
% 18.99/4.08 % (24231)------------------------------
% 18.99/4.09 % (24234)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_23992 for (2976ds/582Mi)
% 18.99/4.09 % (24235)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_23992 for (2976ds/456Mi)
% 18.99/4.09 % (24236)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_23992 for (2976ds/393Mi)
% 18.99/4.12 % (24233)Instruction limit reached!
% 18.99/4.12 % (24233)------------------------------
% 18.99/4.12 % (24233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.99/4.12 % (24233)Termination reason: Unknown
% 18.99/4.12 % (24233)Termination phase: Saturation
% 18.99/4.12
% 18.99/4.12 % (24233)Memory used [KB]: 7291
% 18.99/4.12 % (24233)Time elapsed: 0.186 s
% 18.99/4.12 % (24233)Instructions burned: 407 (million)
% 18.99/4.12 % (24233)------------------------------
% 18.99/4.12 % (24233)------------------------------
% 19.57/4.13 % (24237)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_23992 for (2975ds/1335Mi)
% 19.57/4.14 % (24237)Refutation not found, incomplete strategy
% 19.57/4.14 % (24237)------------------------------
% 19.57/4.14 % (24237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.57/4.14 % (24237)Termination reason: Refutation not found, incomplete strategy
% 19.57/4.14
% 19.57/4.14
% 19.57/4.14 % (24237)Memory used [KB]: 5756
% 19.57/4.14 % (24237)Time elapsed: 0.013 s
% 19.57/4.14 % (24237)Instructions burned: 28 (million)
% 19.57/4.14 % (24237)------------------------------
% 19.57/4.14 % (24237)------------------------------
% 19.57/4.16 % (24238)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_23992 for (2975ds/3373Mi)
% 19.80/4.24 % (24236)Instruction limit reached!
% 19.80/4.24 % (24236)------------------------------
% 19.80/4.24 % (24236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.80/4.24 % (24236)Termination reason: Unknown
% 19.80/4.24 % (24236)Termination phase: Saturation
% 19.80/4.24
% 19.80/4.24 % (24236)Memory used [KB]: 7419
% 19.80/4.24 % (24236)Time elapsed: 0.146 s
% 19.80/4.24 % (24236)Instructions burned: 394 (million)
% 19.80/4.24 % (24236)------------------------------
% 19.80/4.24 % (24236)------------------------------
% 19.80/4.25 % (24235)Instruction limit reached!
% 19.80/4.25 % (24235)------------------------------
% 19.80/4.25 % (24235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.80/4.25 % (24235)Termination reason: Unknown
% 19.80/4.25 % (24235)Termination phase: Saturation
% 19.80/4.25
% 19.80/4.25 % (24235)Memory used [KB]: 3070
% 19.80/4.25 % (24235)Time elapsed: 0.169 s
% 19.80/4.25 % (24235)Instructions burned: 458 (million)
% 19.80/4.25 % (24235)------------------------------
% 19.80/4.25 % (24235)------------------------------
% 19.80/4.26 % (24239)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_23992 for (2974ds/474Mi)
% 19.80/4.27 % (24240)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_23992 for (2974ds/157Mi)
% 20.46/4.31 % (24234)Instruction limit reached!
% 20.46/4.31 % (24234)------------------------------
% 20.46/4.31 % (24234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.46/4.31 % (24234)Termination reason: Unknown
% 20.46/4.31 % (24234)Termination phase: Saturation
% 20.46/4.31
% 20.46/4.31 % (24234)Memory used [KB]: 6780
% 20.46/4.31 % (24234)Time elapsed: 0.224 s
% 20.46/4.31 % (24234)Instructions burned: 582 (million)
% 20.46/4.31 % (24234)------------------------------
% 20.46/4.31 % (24234)------------------------------
% 20.46/4.33 % (24241)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_23992 for (2973ds/590Mi)
% 20.46/4.33 % (24240)Instruction limit reached!
% 20.46/4.33 % (24240)------------------------------
% 20.46/4.33 % (24240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.46/4.33 % (24240)Termination reason: Unknown
% 20.46/4.33 % (24240)Termination phase: Saturation
% 20.46/4.33
% 20.46/4.33 % (24240)Memory used [KB]: 6140
% 20.46/4.33 % (24240)Time elapsed: 0.064 s
% 20.46/4.33 % (24240)Instructions burned: 158 (million)
% 20.46/4.33 % (24240)------------------------------
% 20.46/4.33 % (24240)------------------------------
% 20.46/4.35 % (24241)Refutation not found, incomplete strategy
% 20.46/4.35 % (24241)------------------------------
% 20.46/4.35 % (24241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.46/4.35 % (24241)Termination reason: Refutation not found, incomplete strategy
% 20.46/4.35
% 20.46/4.35
% 20.46/4.35 % (24241)Memory used [KB]: 5756
% 20.46/4.35 % (24241)Time elapsed: 0.025 s
% 20.46/4.35 % (24241)Instructions burned: 60 (million)
% 20.46/4.35 % (24241)------------------------------
% 20.46/4.35 % (24241)------------------------------
% 20.46/4.35 % (24242)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_23992 for (2973ds/104Mi)
% 20.46/4.37 % (24243)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_23992 for (2973ds/414Mi)
% 20.46/4.39 % (24242)Instruction limit reached!
% 20.46/4.39 % (24242)------------------------------
% 20.46/4.39 % (24242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.46/4.39 % (24242)Termination reason: Unknown
% 20.46/4.39 % (24242)Termination phase: Property scanning
% 20.46/4.39
% 20.46/4.39 % (24242)Memory used [KB]: 1407
% 20.46/4.39 % (24242)Time elapsed: 0.043 s
% 20.46/4.39 % (24242)Instructions burned: 105 (million)
% 20.46/4.39 % (24242)------------------------------
% 20.46/4.39 % (24242)------------------------------
% 21.17/4.41 % (24244)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_23992 for (2972ds/715Mi)
% 21.17/4.43 % (24239)Instruction limit reached!
% 21.17/4.43 % (24239)------------------------------
% 21.17/4.43 % (24239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.43 % (24239)Termination reason: Unknown
% 21.17/4.43 % (24239)Termination phase: Saturation
% 21.17/4.43
% 21.17/4.43 % (24239)Memory used [KB]: 7675
% 21.17/4.43 % (24239)Time elapsed: 0.176 s
% 21.17/4.43 % (24239)Instructions burned: 476 (million)
% 21.17/4.43 % (24239)------------------------------
% 21.17/4.43 % (24239)------------------------------
% 21.17/4.44 % (24224)Instruction limit reached!
% 21.17/4.44 % (24224)------------------------------
% 21.17/4.44 % (24224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.17/4.44 % (24224)Termination reason: Unknown
% 21.17/4.44 % (24224)Termination phase: Saturation
% 21.17/4.44
% 21.17/4.44 % (24224)Memory used [KB]: 8443
% 21.17/4.44 % (24224)Time elapsed: 0.715 s
% 21.17/4.44 % (24224)Instructions burned: 1764 (million)
% 21.17/4.44 % (24224)------------------------------
% 21.17/4.44 % (24224)------------------------------
% 21.17/4.45 % (24245)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_23992 for (2972ds/961Mi)
% 21.17/4.46 % (24246)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_23992 for (2972ds/1213Mi)
% 21.62/4.52 % (24243)Instruction limit reached!
% 21.62/4.52 % (24243)------------------------------
% 21.62/4.52 % (24243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.62/4.52 % (24243)Termination reason: Unknown
% 21.62/4.52 % (24243)Termination phase: Saturation
% 21.62/4.52
% 21.62/4.52 % (24243)Memory used [KB]: 7419
% 21.62/4.52 % (24243)Time elapsed: 0.155 s
% 21.62/4.52 % (24243)Instructions burned: 415 (million)
% 21.62/4.52 % (24243)------------------------------
% 21.62/4.52 % (24243)------------------------------
% 21.62/4.54 % (24247)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_23992 for (2971ds/1979Mi)
% 21.99/4.65 % (24245)Refutation not found, incomplete strategy
% 21.99/4.65 % (24245)------------------------------
% 21.99/4.65 % (24245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.99/4.65 % (24245)Termination reason: Refutation not found, incomplete strategy
% 21.99/4.65
% 21.99/4.65
% 21.99/4.65 % (24245)Memory used [KB]: 7547
% 21.99/4.65 % (24245)Time elapsed: 0.223 s
% 21.99/4.65 % (24245)Instructions burned: 523 (million)
% 21.99/4.65 % (24245)------------------------------
% 21.99/4.65 % (24245)------------------------------
% 21.99/4.65 % (24188)Instruction limit reached!
% 21.99/4.65 % (24188)------------------------------
% 21.99/4.65 % (24188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.99/4.65 % (24188)Termination reason: Unknown
% 21.99/4.65 % (24188)Termination phase: Saturation
% 21.99/4.65
% 21.99/4.65 % (24188)Memory used [KB]: 9210
% 21.99/4.65 % (24188)Time elapsed: 2.083 s
% 21.99/4.65 % (24188)Instructions burned: 5207 (million)
% 21.99/4.65 % (24188)------------------------------
% 21.99/4.65 % (24188)------------------------------
% 21.99/4.66 % (24248)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_23992 for (2970ds/481Mi)
% 21.99/4.67 % (24249)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_23992 for (2970ds/783Mi)
% 21.99/4.68 % (24244)Instruction limit reached!
% 21.99/4.68 % (24244)------------------------------
% 21.99/4.68 % (24244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.99/4.68 % (24244)Termination reason: Unknown
% 21.99/4.68 % (24244)Termination phase: Saturation
% 21.99/4.68
% 21.99/4.68 % (24244)Memory used [KB]: 2430
% 21.99/4.68 % (24244)Time elapsed: 0.275 s
% 21.99/4.68 % (24244)Instructions burned: 716 (million)
% 21.99/4.68 % (24244)------------------------------
% 21.99/4.68 % (24244)------------------------------
% 21.99/4.69 % (24249)Refutation not found, incomplete strategy
% 21.99/4.69 % (24249)------------------------------
% 21.99/4.69 % (24249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.99/4.69 % (24249)Termination reason: Refutation not found, incomplete strategy
% 21.99/4.69
% 21.99/4.69
% 21.99/4.69 % (24249)Memory used [KB]: 5756
% 21.99/4.69 % (24249)Time elapsed: 0.023 s
% 21.99/4.69 % (24249)Instructions burned: 55 (million)
% 21.99/4.69 % (24249)------------------------------
% 21.99/4.69 % (24249)------------------------------
% 22.70/4.70 % (24250)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_23992 for (2969ds/432Mi)
% 22.70/4.71 % (24251)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_23992 for (2969ds/1670Mi)
% 22.70/4.72 % (24250)Refutation not found, incomplete strategy
% 22.70/4.72 % (24250)------------------------------
% 22.70/4.72 % (24250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.70/4.72 % (24250)Termination reason: Refutation not found, incomplete strategy
% 22.70/4.72
% 22.70/4.72
% 22.70/4.72 % (24250)Memory used [KB]: 5756
% 22.70/4.72 % (24250)Time elapsed: 0.023 s
% 22.70/4.72 % (24250)Instructions burned: 53 (million)
% 22.70/4.72 % (24250)------------------------------
% 22.70/4.72 % (24250)------------------------------
% 22.70/4.74 % (24252)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_23992 for (2969ds/90Mi)
% 22.70/4.77 % (24252)Instruction limit reached!
% 22.70/4.77 % (24252)------------------------------
% 22.70/4.77 % (24252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.70/4.77 % (24252)Termination reason: Unknown
% 22.70/4.77 % (24252)Termination phase: Property scanning
% 22.70/4.77
% 22.70/4.77 % (24252)Memory used [KB]: 1407
% 22.70/4.77 % (24252)Time elapsed: 0.037 s
% 22.70/4.77 % (24252)Instructions burned: 90 (million)
% 22.70/4.77 % (24252)------------------------------
% 22.70/4.77 % (24252)------------------------------
% 22.70/4.79 % (24253)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_23992 for (2968ds/346Mi)
% 22.88/4.84 % (24248)Instruction limit reached!
% 22.88/4.84 % (24248)------------------------------
% 22.88/4.84 % (24248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.84 % (24248)Termination reason: Unknown
% 22.88/4.84 % (24248)Termination phase: Saturation
% 22.88/4.84
% 22.88/4.84 % (24248)Memory used [KB]: 7675
% 22.88/4.84 % (24248)Time elapsed: 0.182 s
% 22.88/4.84 % (24248)Instructions burned: 482 (million)
% 22.88/4.84 % (24248)------------------------------
% 22.88/4.84 % (24248)------------------------------
% 22.88/4.86 % (24254)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_23992 for (2968ds/401Mi)
% 23.19/4.91 % (24253)Instruction limit reached!
% 23.19/4.91 % (24253)------------------------------
% 23.19/4.91 % (24253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.19/4.91 % (24253)Termination reason: Unknown
% 23.19/4.91 % (24253)Termination phase: Saturation
% 23.19/4.91
% 23.19/4.91 % (24253)Memory used [KB]: 6780
% 23.19/4.91 % (24253)Time elapsed: 0.129 s
% 23.19/4.91 % (24253)Instructions burned: 348 (million)
% 23.19/4.91 % (24253)------------------------------
% 23.19/4.91 % (24253)------------------------------
% 23.19/4.93 % (24255)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_23992 for (2967ds/6454Mi)
% 23.19/5.01 % (24254)Instruction limit reached!
% 23.19/5.01 % (24254)------------------------------
% 23.19/5.01 % (24254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.19/5.01 % (24254)Termination reason: Unknown
% 23.19/5.01 % (24254)Termination phase: Saturation
% 23.19/5.01
% 23.19/5.01 % (24254)Memory used [KB]: 7419
% 23.19/5.01 % (24254)Time elapsed: 0.148 s
% 23.19/5.01 % (24254)Instructions burned: 401 (million)
% 23.19/5.01 % (24254)------------------------------
% 23.19/5.01 % (24254)------------------------------
% 23.19/5.02 % (24256)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_23992 for (2966ds/283Mi)
% 25.96/5.04 % (24246)Instruction limit reached!
% 25.96/5.04 % (24246)------------------------------
% 25.96/5.04 % (24246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.96/5.04 % (24246)Termination reason: Unknown
% 25.96/5.04 % (24246)Termination phase: Saturation
% 25.96/5.04
% 25.96/5.04 % (24246)Memory used [KB]: 7547
% 25.96/5.04 % (24246)Time elapsed: 0.611 s
% 25.96/5.04 % (24246)Instructions burned: 1213 (million)
% 25.96/5.04 % (24246)------------------------------
% 25.96/5.04 % (24246)------------------------------
% 25.96/5.06 % (24257)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_23992 for (2966ds/865Mi)
% 26.50/5.13 % (24256)Instruction limit reached!
% 26.50/5.13 % (24256)------------------------------
% 26.50/5.13 % (24256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.50/5.13 % (24256)Termination reason: Unknown
% 26.50/5.13 % (24256)Termination phase: Saturation
% 26.50/5.13
% 26.50/5.13 % (24256)Memory used [KB]: 6268
% 26.50/5.13 % (24256)Time elapsed: 0.113 s
% 26.50/5.13 % (24256)Instructions burned: 284 (million)
% 26.50/5.13 % (24256)------------------------------
% 26.50/5.13 % (24256)------------------------------
% 26.50/5.15 % (24258)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_23992 for (2965ds/4528Mi)
% 26.50/5.17 % (24258)Refutation not found, incomplete strategy
% 26.50/5.17 % (24258)------------------------------
% 26.50/5.17 % (24258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.50/5.17 % (24258)Termination reason: Refutation not found, incomplete strategy
% 26.50/5.17
% 26.50/5.17
% 26.50/5.17 % (24258)Memory used [KB]: 1279
% 26.50/5.17 % (24258)Time elapsed: 0.023 s
% 26.50/5.17 % (24258)Instructions burned: 54 (million)
% 26.50/5.17 % (24258)------------------------------
% 26.50/5.17 % (24258)------------------------------
% 26.50/5.19 % (24259)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_23992 for (2964ds/1001Mi)
% 27.01/5.22 % (24257)Refutation not found, incomplete strategy
% 27.01/5.22 % (24257)------------------------------
% 27.01/5.22 % (24257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.01/5.22 % (24257)Termination reason: Refutation not found, incomplete strategy
% 27.01/5.22
% 27.01/5.22
% 27.01/5.22 % (24257)Memory used [KB]: 7675
% 27.01/5.22 % (24257)Time elapsed: 0.168 s
% 27.01/5.22 % (24257)Instructions burned: 455 (million)
% 27.01/5.22 % (24257)------------------------------
% 27.01/5.22 % (24257)------------------------------
% 27.01/5.24 % (24260)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_23992 for (2964ds/102Mi)
% 27.01/5.29 % (24260)Instruction limit reached!
% 27.01/5.29 % (24260)------------------------------
% 27.01/5.29 % (24260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.01/5.29 % (24260)Termination reason: Unknown
% 27.01/5.29 % (24260)Termination phase: Property scanning
% 27.01/5.29
% 27.01/5.29 % (24260)Memory used [KB]: 1407
% 27.01/5.29 % (24260)Time elapsed: 0.045 s
% 27.01/5.29 % (24260)Instructions burned: 104 (million)
% 27.01/5.29 % (24260)------------------------------
% 27.01/5.29 % (24260)------------------------------
% 27.01/5.29 % (24247)Instruction limit reached!
% 27.01/5.29 % (24247)------------------------------
% 27.01/5.29 % (24247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.01/5.29 % (24247)Termination reason: Unknown
% 27.01/5.29 % (24247)Termination phase: Saturation
% 27.01/5.29
% 27.01/5.29 % (24247)Memory used [KB]: 8827
% 27.01/5.29 % (24247)Time elapsed: 0.757 s
% 27.01/5.29 % (24247)Instructions burned: 1980 (million)
% 27.01/5.29 % (24247)------------------------------
% 27.01/5.29 % (24247)------------------------------
% 27.76/5.30 % (24261)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_23992 for (2963ds/952Mi)
% 27.76/5.31 % (24262)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_23992 for (2963ds/578Mi)
% 27.76/5.35 % (24251)Instruction limit reached!
% 27.76/5.35 % (24251)------------------------------
% 27.76/5.35 % (24251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.76/5.35 % (24251)Termination reason: Unknown
% 27.76/5.35 % (24251)Termination phase: Saturation
% 27.76/5.35
% 27.76/5.36 % (24251)Memory used [KB]: 8699
% 27.76/5.36 % (24251)Time elapsed: 0.647 s
% 27.76/5.36 % (24251)Instructions burned: 1672 (million)
% 27.76/5.36 % (24251)------------------------------
% 27.76/5.36 % (24251)------------------------------
% 27.76/5.37 % (24263)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_23992 for (2963ds/643Mi)
% 28.14/5.43 % (24238)Instruction limit reached!
% 28.14/5.43 % (24238)------------------------------
% 28.14/5.43 % (24238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.14/5.43 % (24238)Termination reason: Unknown
% 28.14/5.43 % (24238)Termination phase: Saturation
% 28.14/5.43
% 28.14/5.43 % (24238)Memory used [KB]: 9850
% 28.14/5.43 % (24238)Time elapsed: 1.268 s
% 28.14/5.43 % (24238)Instructions burned: 3373 (million)
% 28.14/5.43 % (24238)------------------------------
% 28.14/5.43 % (24238)------------------------------
% 28.14/5.44 % (24264)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_23992 for (2962ds/865Mi)
% 28.38/5.58 % (24259)Instruction limit reached!
% 28.38/5.58 % (24259)------------------------------
% 28.38/5.58 % (24259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.38/5.58 % (24259)Termination reason: Unknown
% 28.38/5.58 % (24259)Termination phase: Saturation
% 28.38/5.58
% 28.38/5.58 % (24259)Memory used [KB]: 7164
% 28.38/5.58 % (24259)Time elapsed: 0.388 s
% 28.38/5.58 % (24259)Instructions burned: 1003 (million)
% 28.38/5.58 % (24259)------------------------------
% 28.38/5.58 % (24259)------------------------------
% 28.38/5.59 % (24262)Instruction limit reached!
% 28.38/5.59 % (24262)------------------------------
% 28.38/5.59 % (24262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.38/5.59 % (24262)Termination reason: Unknown
% 28.38/5.59 % (24262)Termination phase: Saturation
% 28.38/5.59
% 28.38/5.59 % (24262)Memory used [KB]: 7164
% 28.38/5.59 % (24262)Time elapsed: 0.281 s
% 28.38/5.59 % (24262)Instructions burned: 579 (million)
% 28.38/5.59 % (24262)------------------------------
% 28.38/5.59 % (24262)------------------------------
% 28.38/5.59 % (24265)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_23992 for (2960ds/1174Mi)
% 29.28/5.60 % (24266)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_23992 for (2960ds/644Mi)
% 29.28/5.61 % (24263)Instruction limit reached!
% 29.28/5.61 % (24263)------------------------------
% 29.28/5.61 % (24263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.28/5.61 % (24263)Termination reason: Unknown
% 29.28/5.61 % (24263)Termination phase: Saturation
% 29.28/5.61
% 29.28/5.61 % (24263)Memory used [KB]: 7675
% 29.28/5.61 % (24263)Time elapsed: 0.243 s
% 29.28/5.61 % (24263)Instructions burned: 643 (million)
% 29.28/5.61 % (24263)------------------------------
% 29.28/5.61 % (24263)------------------------------
% 29.28/5.63 % (24267)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_23992 for (2960ds/1201Mi)
% 29.28/5.67 % (24261)Instruction limit reached!
% 29.28/5.67 % (24261)------------------------------
% 29.28/5.67 % (24261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.28/5.67 % (24261)Termination reason: Unknown
% 29.28/5.67 % (24261)Termination phase: Saturation
% 29.28/5.67
% 29.28/5.67 % (24261)Memory used [KB]: 7164
% 29.28/5.67 % (24261)Time elapsed: 0.369 s
% 29.28/5.67 % (24261)Instructions burned: 953 (million)
% 29.28/5.67 % (24261)------------------------------
% 29.28/5.67 % (24261)------------------------------
% 29.28/5.69 % (24268)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_23992 for (2960ds/1046Mi)
% 30.12/5.77 % (24265)Refutation not found, incomplete strategy
% 30.12/5.77 % (24265)------------------------------
% 30.12/5.77 % (24265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.12/5.77 % (24265)Termination reason: Refutation not found, incomplete strategy
% 30.12/5.77
% 30.12/5.77
% 30.12/5.77 % (24265)Memory used [KB]: 7547
% 30.12/5.77 % (24265)Time elapsed: 0.179 s
% 30.12/5.77 % (24265)Instructions burned: 482 (million)
% 30.12/5.77 % (24265)------------------------------
% 30.12/5.77 % (24265)------------------------------
% 30.12/5.77 % (24266)Refutation not found, incomplete strategy
% 30.12/5.77 % (24266)------------------------------
% 30.12/5.77 % (24266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.12/5.77 % (24266)Termination reason: Refutation not found, incomplete strategy
% 30.12/5.77
% 30.12/5.77
% 30.12/5.77 % (24266)Memory used [KB]: 7675
% 30.12/5.77 % (24266)Time elapsed: 0.168 s
% 30.12/5.77 % (24266)Instructions burned: 454 (million)
% 30.12/5.77 % (24266)------------------------------
% 30.12/5.77 % (24266)------------------------------
% 30.12/5.79 % (24264)Instruction limit reached!
% 30.12/5.79 % (24264)------------------------------
% 30.12/5.79 % (24264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.12/5.79 % (24264)Termination reason: Unknown
% 30.12/5.79 % (24264)Termination phase: Saturation
% 30.12/5.79
% 30.12/5.79 % (24264)Memory used [KB]: 7675
% 30.12/5.79 % (24264)Time elapsed: 0.344 s
% 30.12/5.79 % (24264)Instructions burned: 866 (million)
% 30.12/5.79 % (24264)------------------------------
% 30.12/5.79 % (24264)------------------------------
% 30.12/5.79 % (24269)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_23992 for (2959ds/222Mi)
% 30.12/5.79 % (24270)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_23992 for (2959ds/68Mi)
% 31.07/5.80 % (24271)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_23992 for (2958ds/454Mi)
% 31.07/5.81 % (24270)Instruction limit reached!
% 31.07/5.81 % (24270)------------------------------
% 31.07/5.81 % (24270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.07/5.81 % (24270)Termination reason: Unknown
% 31.07/5.81 % (24270)Termination phase: Function definition elimination
% 31.07/5.81
% 31.07/5.81 % (24270)Memory used [KB]: 1279
% 31.07/5.81 % (24270)Time elapsed: 0.029 s
% 31.07/5.81 % (24270)Instructions burned: 70 (million)
% 31.07/5.81 % (24270)------------------------------
% 31.07/5.81 % (24270)------------------------------
% 31.07/5.83 % (24272)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_23992 for (2958ds/360Mi)
% 31.07/5.87 % (24269)Instruction limit reached!
% 31.07/5.87 % (24269)------------------------------
% 31.07/5.87 % (24269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.07/5.87 % (24269)Termination reason: Unknown
% 31.07/5.87 % (24269)Termination phase: Saturation
% 31.07/5.87
% 31.07/5.87 % (24269)Memory used [KB]: 6524
% 31.07/5.87 % (24269)Time elapsed: 0.087 s
% 31.07/5.87 % (24269)Instructions burned: 222 (million)
% 31.07/5.87 % (24269)------------------------------
% 31.07/5.87 % (24269)------------------------------
% 31.07/5.89 % (24273)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_23992 for (2958ds/157Mi)
% 31.41/5.95 % (24273)Instruction limit reached!
% 31.41/5.95 % (24273)------------------------------
% 31.41/5.95 % (24273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.41/5.95 % (24273)Termination reason: Unknown
% 31.41/5.95 % (24273)Termination phase: Saturation
% 31.41/5.95
% 31.41/5.95 % (24273)Memory used [KB]: 6140
% 31.41/5.95 % (24273)Time elapsed: 0.065 s
% 31.41/5.95 % (24273)Instructions burned: 158 (million)
% 31.41/5.95 % (24273)------------------------------
% 31.41/5.95 % (24273)------------------------------
% 31.41/5.96 % (24272)Instruction limit reached!
% 31.41/5.96 % (24272)------------------------------
% 31.41/5.96 % (24272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.41/5.96 % (24272)Termination reason: Unknown
% 31.41/5.96 % (24272)Termination phase: Saturation
% 31.41/5.96
% 31.41/5.96 % (24272)Memory used [KB]: 6780
% 31.41/5.96 % (24272)Time elapsed: 0.134 s
% 31.41/5.96 % (24272)Instructions burned: 360 (million)
% 31.41/5.96 % (24272)------------------------------
% 31.41/5.96 % (24272)------------------------------
% 31.41/5.97 % (24274)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_23992 for (2957ds/5061Mi)
% 31.41/5.97 % (24271)Instruction limit reached!
% 31.41/5.97 % (24271)------------------------------
% 31.41/5.97 % (24271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.41/5.97 % (24271)Termination reason: Unknown
% 31.41/5.97 % (24271)Termination phase: Saturation
% 31.41/5.97
% 31.41/5.97 % (24271)Memory used [KB]: 12153
% 31.41/5.97 % (24271)Time elapsed: 0.169 s
% 31.41/5.97 % (24271)Instructions burned: 454 (million)
% 31.41/5.97 % (24271)------------------------------
% 31.41/5.97 % (24271)------------------------------
% 31.41/5.98 % (24275)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_23992 for (2957ds/2401Mi)
% 31.41/5.99 % (24276)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_23992 for (2957ds/5798Mi)
% 32.96/6.10 % (24268)Instruction limit reached!
% 32.96/6.10 % (24268)------------------------------
% 32.96/6.10 % (24268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.96/6.10 % (24268)Termination reason: Unknown
% 32.96/6.10 % (24268)Termination phase: Saturation
% 32.96/6.10
% 32.96/6.10 % (24268)Memory used [KB]: 7931
% 32.96/6.10 % (24268)Time elapsed: 0.410 s
% 32.96/6.10 % (24268)Instructions burned: 1047 (million)
% 32.96/6.10 % (24268)------------------------------
% 32.96/6.10 % (24268)------------------------------
% 32.96/6.12 % (24277)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_23992 for (2955ds/346Mi)
% 33.67/6.19 % (24267)Instruction limit reached!
% 33.67/6.19 % (24267)------------------------------
% 33.67/6.19 % (24267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.67/6.19 % (24267)Termination reason: Unknown
% 33.67/6.19 % (24267)Termination phase: Saturation
% 33.67/6.19
% 33.67/6.19 % (24267)Memory used [KB]: 7931
% 33.67/6.19 % (24267)Time elapsed: 0.560 s
% 33.67/6.19 % (24267)Instructions burned: 1202 (million)
% 33.67/6.19 % (24267)------------------------------
% 33.67/6.19 % (24267)------------------------------
% 34.09/6.21 % (24278)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_23992 for (2954ds/1321Mi)
% 34.09/6.25 % (24277)Instruction limit reached!
% 34.09/6.25 % (24277)------------------------------
% 34.09/6.25 % (24277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.25 % (24277)Termination reason: Unknown
% 34.09/6.25 % (24277)Termination phase: Saturation
% 34.09/6.25
% 34.09/6.25 % (24277)Memory used [KB]: 6780
% 34.09/6.25 % (24277)Time elapsed: 0.131 s
% 34.09/6.25 % (24277)Instructions burned: 346 (million)
% 34.09/6.25 % (24277)------------------------------
% 34.09/6.25 % (24277)------------------------------
% 34.09/6.26 % (24278)Refutation not found, incomplete strategy
% 34.09/6.26 % (24278)------------------------------
% 34.09/6.26 % (24278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.26 % (24278)Termination reason: Refutation not found, incomplete strategy
% 34.09/6.26
% 34.09/6.26
% 34.09/6.26 % (24278)Memory used [KB]: 2174
% 34.09/6.26 % (24278)Time elapsed: 0.060 s
% 34.09/6.26 % (24278)Instructions burned: 134 (million)
% 34.09/6.26 % (24278)------------------------------
% 34.09/6.26 % (24278)------------------------------
% 34.09/6.27 % (24279)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_23992 for (2954ds/1312Mi)
% 34.09/6.28 % (24280)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_23992 for (2954ds/672Mi)
% 34.81/6.30 % (24280)Refutation not found, incomplete strategy
% 34.81/6.30 % (24280)------------------------------
% 34.81/6.30 % (24280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.81/6.30 % (24280)Termination reason: Refutation not found, incomplete strategy
% 34.81/6.30
% 34.81/6.30
% 34.81/6.30 % (24280)Memory used [KB]: 5756
% 34.81/6.30 % (24280)Time elapsed: 0.023 s
% 34.81/6.30 % (24280)Instructions burned: 55 (million)
% 34.81/6.30 % (24280)------------------------------
% 34.81/6.30 % (24280)------------------------------
% 34.81/6.32 % (24281)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_23992 for (2953ds/1897Mi)
% 34.81/6.34 % (24281)Refutation not found, incomplete strategy
% 34.81/6.34 % (24281)------------------------------
% 34.81/6.34 % (24281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.81/6.34 % (24281)Termination reason: Refutation not found, incomplete strategy
% 34.81/6.34
% 34.81/6.34
% 34.81/6.34 % (24281)Memory used [KB]: 5756
% 34.81/6.34 % (24281)Time elapsed: 0.023 s
% 34.81/6.34 % (24281)Instructions burned: 55 (million)
% 34.81/6.34 % (24281)------------------------------
% 34.81/6.34 % (24281)------------------------------
% 34.81/6.36 % (24282)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_23992 for (2953ds/1202Mi)
% 37.39/6.80 % (24211)Instruction limit reached!
% 37.39/6.80 % (24211)------------------------------
% 37.39/6.80 % (24211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.80 % (24211)Termination reason: Unknown
% 37.39/6.80 % (24211)Termination phase: Saturation
% 37.39/6.80
% 37.39/6.80 % (24211)Memory used [KB]: 11257
% 37.39/6.80 % (24211)Time elapsed: 3.655 s
% 37.39/6.80 % (24211)Instructions burned: 8251 (million)
% 37.39/6.80 % (24211)------------------------------
% 37.39/6.80 % (24211)------------------------------
% 37.39/6.80 % (24279)Instruction limit reached!
% 37.39/6.80 % (24279)------------------------------
% 37.39/6.80 % (24279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.80 % (24279)Termination reason: Unknown
% 37.39/6.80 % (24279)Termination phase: Saturation
% 37.39/6.80
% 37.39/6.80 % (24279)Memory used [KB]: 7803
% 37.39/6.80 % (24279)Time elapsed: 0.541 s
% 37.39/6.80 % (24279)Instructions burned: 1312 (million)
% 37.39/6.80 % (24279)------------------------------
% 37.39/6.80 % (24279)------------------------------
% 37.39/6.82 % (24284)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_23992 for (2948ds/7679Mi)
% 37.39/6.82 % (24283)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_23992 for (2948ds/1493Mi)
% 37.39/6.83 % (24283)Refutation not found, incomplete strategy
% 37.39/6.83 % (24283)------------------------------
% 37.39/6.83 % (24283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.83 % (24283)Termination reason: Refutation not found, incomplete strategy
% 37.39/6.83
% 37.39/6.83
% 37.39/6.83 % (24283)Memory used [KB]: 5756
% 37.39/6.83 % (24283)Time elapsed: 0.012 s
% 37.39/6.83 % (24283)Instructions burned: 24 (million)
% 37.39/6.83 % (24283)------------------------------
% 37.39/6.83 % (24283)------------------------------
% 37.39/6.84 % (24284)Refutation not found, incomplete strategy
% 37.39/6.84 % (24284)------------------------------
% 37.39/6.84 % (24284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.84 % (24284)Termination reason: Refutation not found, incomplete strategy
% 37.39/6.84
% 37.39/6.84
% 37.39/6.84 % (24284)Memory used [KB]: 1279
% 37.39/6.84 % (24284)Time elapsed: 0.024 s
% 37.39/6.84 % (24284)Instructions burned: 57 (million)
% 37.39/6.84 % (24284)------------------------------
% 37.39/6.84 % (24284)------------------------------
% 37.39/6.85 % (24285)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_23992 for (2948ds/340Mi)
% 37.39/6.86 % (24286)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_23992 for (2948ds/3672Mi)
% 37.39/6.88 % (24286)Refutation not found, incomplete strategy
% 37.39/6.88 % (24286)------------------------------
% 37.39/6.88 % (24286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.88 % (24286)Termination reason: Refutation not found, incomplete strategy
% 37.39/6.88
% 37.39/6.88
% 37.39/6.88 % (24286)Memory used [KB]: 5756
% 37.39/6.88 % (24286)Time elapsed: 0.023 s
% 37.39/6.88 % (24286)Instructions burned: 56 (million)
% 37.39/6.88 % (24286)------------------------------
% 37.39/6.88 % (24286)------------------------------
% 37.39/6.89 % (24275)Instruction limit reached!
% 37.39/6.89 % (24275)------------------------------
% 37.39/6.89 % (24275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.89 % (24275)Termination reason: Unknown
% 37.39/6.89 % (24275)Termination phase: Saturation
% 37.39/6.89
% 37.39/6.89 % (24275)Memory used [KB]: 4989
% 37.39/6.89 % (24275)Time elapsed: 0.912 s
% 37.39/6.89 % (24275)Instructions burned: 2401 (million)
% 37.39/6.89 % (24275)------------------------------
% 37.39/6.89 % (24275)------------------------------
% 38.47/6.90 % (24287)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_23992 for (2948ds/1535Mi)
% 38.47/6.91 % (24288)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_23992 for (2947ds/4637Mi)
% 38.47/6.93 % (24282)Instruction limit reached!
% 38.47/6.93 % (24282)------------------------------
% 38.47/6.93 % (24282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.47/6.93 % (24282)Termination reason: Unknown
% 38.47/6.93 % (24282)Termination phase: Saturation
% 38.47/6.93
% 38.47/6.93 % (24282)Memory used [KB]: 3837
% 38.47/6.93 % (24282)Time elapsed: 0.578 s
% 38.47/6.93 % (24282)Instructions burned: 1202 (million)
% 38.47/6.93 % (24282)------------------------------
% 38.47/6.93 % (24282)------------------------------
% 38.47/6.95 % (24289)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_23992 for (2947ds/3174Mi)
% 38.47/6.97 % (24285)Instruction limit reached!
% 38.47/6.97 % (24285)------------------------------
% 38.47/6.97 % (24285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.47/6.97 % (24285)Termination reason: Unknown
% 38.47/6.97 % (24285)Termination phase: Saturation
% 38.47/6.97
% 38.47/6.97 % (24285)Memory used [KB]: 6652
% 38.47/6.97 % (24285)Time elapsed: 0.127 s
% 38.47/6.97 % (24285)Instructions burned: 340 (million)
% 38.47/6.97 % (24285)------------------------------
% 38.47/6.97 % (24285)------------------------------
% 38.47/6.99 % (24290)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_23992 for (2946ds/307Mi)
% 39.96/7.10 % (24290)Instruction limit reached!
% 39.96/7.10 % (24290)------------------------------
% 39.96/7.10 % (24290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.96/7.10 % (24290)Termination reason: Unknown
% 39.96/7.10 % (24290)Termination phase: Saturation
% 39.96/7.10
% 39.96/7.10 % (24290)Memory used [KB]: 6652
% 39.96/7.10 % (24290)Time elapsed: 0.115 s
% 39.96/7.10 % (24290)Instructions burned: 307 (million)
% 39.96/7.10 % (24290)------------------------------
% 39.96/7.10 % (24290)------------------------------
% 39.96/7.12 % (24291)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_23992 for (2945ds/3619Mi)
% 40.65/7.15 % (24291)Refutation not found, incomplete strategy
% 40.65/7.15 % (24291)------------------------------
% 40.65/7.15 % (24291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.65/7.15 % (24291)Termination reason: Refutation not found, incomplete strategy
% 40.65/7.15
% 40.65/7.15
% 40.65/7.15 % (24291)Memory used [KB]: 5884
% 40.65/7.15 % (24291)Time elapsed: 0.033 s
% 40.65/7.15 % (24291)Instructions burned: 76 (million)
% 40.65/7.15 % (24291)------------------------------
% 40.65/7.15 % (24291)------------------------------
% 40.65/7.17 % (24292)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_23992 for (2945ds/2325Mi)
% 41.72/7.39 % (24255)Refutation not found, non-redundant clauses discarded% (24255)------------------------------
% 41.72/7.39 % (24255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.72/7.39 % (24255)Termination reason: Refutation not found, non-redundant clauses discarded
% 41.72/7.39
% 41.72/7.39 % (24255)Memory used [KB]: 9722
% 41.72/7.39 % (24255)Time elapsed: 2.462 s
% 41.72/7.39 % (24255)Instructions burned: 5753 (million)
% 41.72/7.39 % (24255)------------------------------
% 41.72/7.39 % (24255)------------------------------
% 42.34/7.41 % (24293)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_23992 for (2942ds/2341Mi)
% 42.34/7.43 % (24293)Refutation not found, incomplete strategy
% 42.34/7.43 % (24293)------------------------------
% 42.34/7.43 % (24293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.34/7.43 % (24293)Termination reason: Refutation not found, incomplete strategy
% 42.34/7.43
% 42.34/7.43
% 42.34/7.43 % (24293)Memory used [KB]: 5756
% 42.34/7.43 % (24293)Time elapsed: 0.025 s
% 42.34/7.43 % (24293)Instructions burned: 60 (million)
% 42.34/7.43 % (24293)------------------------------
% 42.34/7.43 % (24293)------------------------------
% 42.34/7.45 % (24294)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_23992 for (2942ds/7257Mi)
% 42.34/7.47 % (24294)Refutation not found, incomplete strategy
% 42.34/7.47 % (24294)------------------------------
% 42.34/7.47 % (24294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.34/7.47 % (24294)Termination reason: Refutation not found, incomplete strategy
% 42.34/7.47
% 42.34/7.47
% 42.34/7.47 % (24294)Memory used [KB]: 5756
% 42.34/7.47 % (24294)Time elapsed: 0.023 s
% 42.34/7.47 % (24294)Instructions burned: 55 (million)
% 42.34/7.47 % (24294)------------------------------
% 42.34/7.47 % (24294)------------------------------
% 42.34/7.48 % (24287)Instruction limit reached!
% 42.34/7.48 % (24287)------------------------------
% 42.34/7.48 % (24287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.34/7.48 % (24287)Termination reason: Unknown
% 42.34/7.48 % (24287)Termination phase: Saturation
% 42.34/7.48
% 42.34/7.48 % (24287)Memory used [KB]: 8443
% 42.34/7.48 % (24287)Time elapsed: 0.584 s
% 42.34/7.48 % (24287)Instructions burned: 1535 (million)
% 42.34/7.48 % (24287)------------------------------
% 42.34/7.48 % (24287)------------------------------
% 42.34/7.49 % (24295)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_23992 for (2942ds/3710Mi)
% 42.91/7.50 % (24296)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_23992 for (2941ds/326Mi)
% 42.91/7.52 % (24296)Refutation not found, incomplete strategy
% 42.91/7.52 % (24296)------------------------------
% 42.91/7.52 % (24296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.91/7.52 % (24296)Termination reason: Refutation not found, incomplete strategy
% 42.91/7.52
% 42.91/7.52
% 42.91/7.52 % (24296)Memory used [KB]: 5756
% 42.91/7.52 % (24296)Time elapsed: 0.023 s
% 42.91/7.52 % (24296)Instructions burned: 54 (million)
% 42.91/7.52 % (24296)------------------------------
% 42.91/7.52 % (24296)------------------------------
% 42.91/7.54 % (24297)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_23992 for (2941ds/1100Mi)
% 43.74/7.79 % (24274)Instruction limit reached!
% 43.74/7.79 % (24274)------------------------------
% 43.74/7.79 % (24274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.74/7.79 % (24274)Termination reason: Unknown
% 43.74/7.79 % (24274)Termination phase: Saturation
% 43.74/7.79
% 43.74/7.79 % (24274)Memory used [KB]: 11001
% 43.74/7.79 % (24274)Time elapsed: 1.819 s
% 43.74/7.79 % (24274)Instructions burned: 5061 (million)
% 43.74/7.79 % (24274)------------------------------
% 43.74/7.79 % (24274)------------------------------
% 44.15/7.80 % (24298)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23992 for (2938ds/406Mi)
% 44.45/7.96 % (24297)Instruction limit reached!
% 44.45/7.96 % (24297)------------------------------
% 44.45/7.96 % (24297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.45/7.96 % (24297)Termination reason: Unknown
% 44.45/7.96 % (24297)Termination phase: Saturation
% 44.45/7.96
% 44.45/7.96 % (24297)Memory used [KB]: 7931
% 44.45/7.96 % (24297)Time elapsed: 0.426 s
% 44.45/7.96 % (24297)Instructions burned: 1101 (million)
% 44.45/7.96 % (24297)------------------------------
% 44.45/7.96 % (24297)------------------------------
% 44.45/7.98 % (24299)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_23992 for (2937ds/1871Mi)
% 44.45/7.99 % (24298)Instruction limit reached!
% 44.45/7.99 % (24298)------------------------------
% 44.45/7.99 % (24298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.45/7.99 % (24298)Termination reason: Unknown
% 44.45/7.99 % (24298)Termination phase: Saturation
% 44.45/7.99
% 44.45/7.99 % (24298)Memory used [KB]: 7419
% 44.45/7.99 % (24298)Time elapsed: 0.186 s
% 44.45/7.99 % (24298)Instructions burned: 406 (million)
% 44.45/7.99 % (24298)------------------------------
% 44.45/7.99 % (24298)------------------------------
% 44.45/8.00 % (24300)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_23992 for (2936ds/1194Mi)
% 47.67/8.17 % (24276)Instruction limit reached!
% 47.67/8.17 % (24276)------------------------------
% 47.67/8.17 % (24276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.67/8.17 % (24276)Termination reason: Unknown
% 47.67/8.17 % (24276)Termination phase: Saturation
% 47.67/8.17
% 47.67/8.17 % (24276)Memory used [KB]: 5884
% 47.67/8.17 % (24276)Time elapsed: 2.182 s
% 47.67/8.17 % (24276)Instructions burned: 5799 (million)
% 47.67/8.17 % (24276)------------------------------
% 47.67/8.17 % (24276)------------------------------
% 47.67/8.18 % (24301)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_23992 for (2935ds/474Mi)
% 47.67/8.20 % (24292)Instruction limit reached!
% 47.67/8.20 % (24292)------------------------------
% 47.67/8.20 % (24292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.67/8.20 % (24292)Termination reason: Unknown
% 47.67/8.20 % (24292)Termination phase: Saturation
% 47.67/8.20
% 47.67/8.20 % (24292)Memory used [KB]: 8955
% 47.67/8.20 % (24292)Time elapsed: 1.028 s
% 47.67/8.20 % (24292)Instructions burned: 2327 (million)
% 47.67/8.20 % (24292)------------------------------
% 47.67/8.20 % (24292)------------------------------
% 48.16/8.21 % (24303)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_23992 for (2934ds/3115Mi)
% 48.67/8.36 % (24289)Instruction limit reached!
% 48.67/8.36 % (24289)------------------------------
% 48.67/8.36 % (24289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.67/8.36 % (24289)Termination reason: Unknown
% 48.67/8.36 % (24289)Termination phase: Saturation
% 48.67/8.36
% 48.67/8.36 % (24289)Memory used [KB]: 10362
% 48.67/8.36 % (24289)Time elapsed: 1.428 s
% 48.67/8.36 % (24289)Instructions burned: 3175 (million)
% 48.67/8.36 % (24289)------------------------------
% 48.67/8.36 % (24289)------------------------------
% 48.67/8.36 % (24301)Instruction limit reached!
% 48.67/8.36 % (24301)------------------------------
% 48.67/8.36 % (24301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.67/8.36 % (24301)Termination reason: Unknown
% 48.67/8.36 % (24301)Termination phase: Saturation
% 48.67/8.36
% 48.67/8.36 % (24301)Memory used [KB]: 7675
% 48.67/8.36 % (24301)Time elapsed: 0.177 s
% 48.67/8.36 % (24301)Instructions burned: 474 (million)
% 48.67/8.36 % (24301)------------------------------
% 48.67/8.36 % (24301)------------------------------
% 48.67/8.37 % (24304)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_23992 for (2933ds/831Mi)
% 48.67/8.38 % (24305)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_23992 for (2933ds/1188Mi)
% 49.32/8.46 % (24300)Instruction limit reached!
% 49.32/8.46 % (24300)------------------------------
% 49.32/8.46 % (24300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.32/8.46 % (24300)Termination reason: Unknown
% 49.32/8.46 % (24300)Termination phase: Saturation
% 49.32/8.46
% 49.32/8.46 % (24300)Memory used [KB]: 7291
% 49.32/8.46 % (24300)Time elapsed: 0.459 s
% 49.32/8.46 % (24300)Instructions burned: 1194 (million)
% 49.32/8.46 % (24300)------------------------------
% 49.32/8.46 % (24300)------------------------------
% 49.32/8.48 % (24306)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_23992 for (2932ds/2868Mi)
% 49.69/8.55 % (24304)Refutation not found, incomplete strategy
% 49.69/8.55 % (24304)------------------------------
% 49.69/8.55 % (24304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.55 % (24304)Termination reason: Refutation not found, incomplete strategy
% 49.69/8.55
% 49.69/8.55
% 49.69/8.55 % (24304)Memory used [KB]: 7675
% 49.69/8.55 % (24304)Time elapsed: 0.178 s
% 49.69/8.55 % (24304)Instructions burned: 477 (million)
% 49.69/8.55 % (24304)------------------------------
% 49.69/8.55 % (24304)------------------------------
% 49.69/8.57 % (24307)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_23992 for (2931ds/1516Mi)
% 49.69/8.59 % (24307)Refutation not found, incomplete strategy
% 49.69/8.59 % (24307)------------------------------
% 49.69/8.59 % (24307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.59 % (24307)Termination reason: Refutation not found, incomplete strategy
% 49.69/8.59
% 49.69/8.59
% 49.69/8.59 % (24307)Memory used [KB]: 5756
% 49.69/8.59 % (24307)Time elapsed: 0.023 s
% 49.69/8.59 % (24307)Instructions burned: 54 (million)
% 49.69/8.59 % (24307)------------------------------
% 49.69/8.59 % (24307)------------------------------
% 50.23/8.61 % (24308)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_23992 for (2930ds/2321Mi)
% 50.23/8.64 % (24306)Refutation not found, incomplete strategy
% 50.23/8.64 % (24306)------------------------------
% 50.23/8.64 % (24306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.23/8.64 % (24306)Termination reason: Refutation not found, incomplete strategy
% 50.23/8.64
% 50.23/8.64
% 50.23/8.64 % (24306)Memory used [KB]: 7675
% 50.23/8.64 % (24306)Time elapsed: 0.165 s
% 50.23/8.64 % (24306)Instructions burned: 446 (million)
% 50.23/8.64 % (24306)------------------------------
% 50.23/8.64 % (24306)------------------------------
% 50.23/8.66 % (24309)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_23992 for (2930ds/2812Mi)
% 50.71/8.77 % (24308)Refutation not found, incomplete strategy
% 50.71/8.77 % (24308)------------------------------
% 50.71/8.77 % (24308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.71/8.77 % (24308)Termination reason: Refutation not found, incomplete strategy
% 50.71/8.77
% 50.71/8.77
% 50.71/8.77 % (24308)Memory used [KB]: 7547
% 50.71/8.77 % (24308)Time elapsed: 0.165 s
% 50.71/8.77 % (24308)Instructions burned: 444 (million)
% 50.71/8.77 % (24308)------------------------------
% 50.71/8.77 % (24308)------------------------------
% 50.71/8.79 % (24310)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_23992 for (2929ds/4604Mi)
% 50.71/8.79 % (24288)Instruction limit reached!
% 50.71/8.79 % (24288)------------------------------
% 50.71/8.79 % (24288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.71/8.79 % (24288)Termination reason: Unknown
% 50.71/8.79 % (24288)Termination phase: Saturation
% 50.71/8.79
% 50.71/8.79 % (24288)Memory used [KB]: 10874
% 50.71/8.79 % (24288)Time elapsed: 1.905 s
% 50.71/8.79 % (24288)Instructions burned: 4637 (million)
% 50.71/8.79 % (24288)------------------------------
% 50.71/8.79 % (24288)------------------------------
% 51.19/8.81 % (24311)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_23992 for (2928ds/2678Mi)
% 51.19/8.83 % (24299)Instruction limit reached!
% 51.19/8.83 % (24299)------------------------------
% 51.19/8.83 % (24299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.19/8.83 % (24299)Termination reason: Unknown
% 51.19/8.83 % (24299)Termination phase: Saturation
% 51.19/8.83
% 51.19/8.83 % (24299)Memory used [KB]: 8699
% 51.19/8.83 % (24299)Time elapsed: 0.858 s
% 51.19/8.83 % (24299)Instructions burned: 1871 (million)
% 51.19/8.83 % (24299)------------------------------
% 51.19/8.83 % (24299)------------------------------
% 51.19/8.85 % (24312)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_23992 for (2928ds/643Mi)
% 51.19/8.87 % (24305)Instruction limit reached!
% 51.19/8.87 % (24305)------------------------------
% 51.19/8.87 % (24305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.19/8.87 % (24305)Termination reason: Unknown
% 51.19/8.87 % (24305)Termination phase: Saturation
% 51.19/8.87
% 51.19/8.87 % (24305)Memory used [KB]: 8059
% 51.19/8.87 % (24305)Time elapsed: 0.498 s
% 51.19/8.87 % (24305)Instructions burned: 1190 (million)
% 51.19/8.87 % (24305)------------------------------
% 51.19/8.87 % (24305)------------------------------
% 51.19/8.89 % (24313)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_23992 for (2928ds/458Mi)
% 53.98/9.05 % (24313)Instruction limit reached!
% 53.98/9.05 % (24313)------------------------------
% 53.98/9.05 % (24313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.98/9.05 % (24313)Termination reason: Unknown
% 53.98/9.05 % (24313)Termination phase: Saturation
% 53.98/9.05
% 53.98/9.05 % (24313)Memory used [KB]: 7547
% 53.98/9.05 % (24313)Time elapsed: 0.168 s
% 53.98/9.05 % (24313)Instructions burned: 459 (million)
% 53.98/9.05 % (24313)------------------------------
% 53.98/9.05 % (24313)------------------------------
% 53.98/9.07 % (24314)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_23992 for (2926ds/2546Mi)
% 53.98/9.10 % (24312)Instruction limit reached!
% 53.98/9.10 % (24312)------------------------------
% 53.98/9.10 % (24312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.98/9.10 % (24312)Termination reason: Unknown
% 53.98/9.10 % (24312)Termination phase: Saturation
% 53.98/9.10
% 53.98/9.10 % (24312)Memory used [KB]: 7675
% 53.98/9.10 % (24312)Time elapsed: 0.243 s
% 53.98/9.10 % (24312)Instructions burned: 643 (million)
% 53.98/9.10 % (24312)------------------------------
% 53.98/9.10 % (24312)------------------------------
% 53.98/9.11 % (24295)Instruction limit reached!
% 53.98/9.11 % (24295)------------------------------
% 53.98/9.11 % (24295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.98/9.11 % (24295)Termination reason: Unknown
% 53.98/9.11 % (24295)Termination phase: Saturation
% 53.98/9.11
% 53.98/9.11 % (24295)Memory used [KB]: 8443
% 53.98/9.11 % (24295)Time elapsed: 1.623 s
% 53.98/9.11 % (24295)Instructions burned: 3710 (million)
% 53.98/9.11 % (24295)------------------------------
% 53.98/9.11 % (24295)------------------------------
% 53.98/9.12 % (24315)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_23992 for (2925ds/1432Mi)
% 53.98/9.13 % (24316)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_23992 for (2925ds/386Mi)
% 54.88/9.27 % (24316)Instruction limit reached!
% 54.88/9.27 % (24316)------------------------------
% 54.88/9.27 % (24316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.88/9.27 % (24316)Termination reason: Unknown
% 54.88/9.27 % (24316)Termination phase: Saturation
% 54.88/9.27
% 54.88/9.27 % (24316)Memory used [KB]: 7419
% 54.88/9.27 % (24316)Time elapsed: 0.146 s
% 54.88/9.27 % (24316)Instructions burned: 388 (million)
% 54.88/9.27 % (24316)------------------------------
% 54.88/9.27 % (24316)------------------------------
% 54.88/9.29 % (24317)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_23992 for (2924ds/360Mi)
% 55.83/9.42 % (24317)Instruction limit reached!
% 55.83/9.42 % (24317)------------------------------
% 55.83/9.42 % (24317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.83/9.42 % (24317)Termination reason: Unknown
% 55.83/9.42 % (24317)Termination phase: Saturation
% 55.83/9.42
% 55.83/9.42 % (24317)Memory used [KB]: 7419
% 55.83/9.42 % (24317)Time elapsed: 0.136 s
% 55.83/9.42 % (24317)Instructions burned: 361 (million)
% 55.83/9.42 % (24317)------------------------------
% 55.83/9.42 % (24317)------------------------------
% 55.83/9.44 % (24318)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_23992 for (2922ds/5446Mi)
% 55.83/9.45 % (24303)Instruction limit reached!
% 55.83/9.45 % (24303)------------------------------
% 55.83/9.45 % (24303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.83/9.45 % (24303)Termination reason: Unknown
% 55.83/9.45 % (24303)Termination phase: Saturation
% 55.83/9.45
% 55.83/9.45 % (24303)Memory used [KB]: 8571
% 55.83/9.45 % (24303)Time elapsed: 1.244 s
% 55.83/9.45 % (24303)Instructions burned: 3116 (million)
% 55.83/9.45 % (24303)------------------------------
% 55.83/9.45 % (24303)------------------------------
% 55.83/9.47 % (24319)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_23992 for (2922ds/2573Mi)
% 56.35/9.58 % (24315)Instruction limit reached!
% 56.35/9.58 % (24315)------------------------------
% 56.35/9.58 % (24315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.35/9.58 % (24315)Termination reason: Unknown
% 56.35/9.58 % (24315)Termination phase: Saturation
% 56.35/9.58
% 56.35/9.58 % (24315)Memory used [KB]: 11513
% 56.35/9.58 % (24315)Time elapsed: 0.463 s
% 56.35/9.58 % (24315)Instructions burned: 1433 (million)
% 56.35/9.58 % (24315)------------------------------
% 56.35/9.58 % (24315)------------------------------
% 56.35/9.59 % (24320)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_23992 for (2921ds/2655Mi)
% 57.43/9.74 % (24309)Instruction limit reached!
% 57.43/9.74 % (24309)------------------------------
% 57.43/9.74 % (24309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.43/9.74 % (24309)Termination reason: Unknown
% 57.43/9.74 % (24309)Termination phase: Saturation
% 57.43/9.74
% 57.43/9.74 % (24309)Memory used [KB]: 9722
% 57.43/9.74 % (24309)Time elapsed: 1.080 s
% 57.43/9.74 % (24309)Instructions burned: 2812 (million)
% 57.43/9.74 % (24309)------------------------------
% 57.43/9.74 % (24309)------------------------------
% 57.43/9.76 % (24321)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_23992 for (2919ds/2781Mi)
% 57.69/9.84 % (24311)Instruction limit reached!
% 57.69/9.84 % (24311)------------------------------
% 57.69/9.84 % (24311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.69/9.84 % (24311)Termination reason: Unknown
% 57.69/9.84 % (24311)Termination phase: Saturation
% 57.69/9.84
% 57.69/9.84 % (24311)Memory used [KB]: 8315
% 57.69/9.84 % (24311)Time elapsed: 1.038 s
% 57.69/9.84 % (24311)Instructions burned: 2680 (million)
% 57.69/9.84 % (24311)------------------------------
% 57.69/9.84 % (24311)------------------------------
% 57.69/9.86 % (24322)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_23992 for (2918ds/307Mi)
% 57.84/9.97 % (24322)Instruction limit reached!
% 57.84/9.97 % (24322)------------------------------
% 57.84/9.97 % (24322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.84/9.97 % (24322)Termination reason: Unknown
% 57.84/9.97 % (24322)Termination phase: Saturation
% 57.84/9.97
% 57.84/9.97 % (24322)Memory used [KB]: 6652
% 57.84/9.97 % (24322)Time elapsed: 0.117 s
% 57.84/9.97 % (24322)Instructions burned: 308 (million)
% 57.84/9.97 % (24322)------------------------------
% 57.84/9.97 % (24322)------------------------------
% 57.84/9.99 % (24323)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_23992 for (2916ds/1548Mi)
% 57.84/10.01 % (24323)Refutation not found, incomplete strategy
% 57.84/10.01 % (24323)------------------------------
% 57.84/10.01 % (24323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.84/10.01 % (24323)Termination reason: Refutation not found, incomplete strategy
% 57.84/10.01
% 57.84/10.01
% 57.84/10.01 % (24323)Memory used [KB]: 5756
% 57.84/10.01 % (24323)Time elapsed: 0.023 s
% 57.84/10.01 % (24323)Instructions burned: 54 (million)
% 57.84/10.01 % (24323)------------------------------
% 57.84/10.01 % (24323)------------------------------
% 57.84/10.03 % (24325)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_23992 for (2916ds/5214Mi)
% 60.96/10.08 % (24314)Instruction limit reached!
% 60.96/10.08 % (24314)------------------------------
% 60.96/10.08 % (24314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.96/10.08 % (24314)Termination reason: Unknown
% 60.96/10.08 % (24314)Termination phase: Saturation
% 60.96/10.08
% 60.96/10.08 % (24314)Memory used [KB]: 8827
% 60.96/10.08 % (24314)Time elapsed: 1.015 s
% 60.96/10.08 % (24314)Instructions burned: 2546 (million)
% 60.96/10.08 % (24314)------------------------------
% 60.96/10.08 % (24314)------------------------------
% 60.96/10.10 % (24326)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_23992 for (2915ds/3201Mi)
% 63.87/10.61 % (24319)Instruction limit reached!
% 63.87/10.61 % (24319)------------------------------
% 63.87/10.61 % (24319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.87/10.61 % (24319)Termination reason: Unknown
% 63.87/10.61 % (24319)Termination phase: Saturation
% 63.87/10.61
% 63.87/10.61 % (24319)Memory used [KB]: 8187
% 63.87/10.61 % (24319)Time elapsed: 1.156 s
% 63.87/10.61 % (24319)Instructions burned: 2573 (million)
% 63.87/10.61 % (24319)------------------------------
% 63.87/10.61 % (24319)------------------------------
% 63.87/10.63 % (24327)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_23992 for (2910ds/454Mi)
% 64.29/10.74 % (24320)Instruction limit reached!
% 64.29/10.74 % (24320)------------------------------
% 64.29/10.74 % (24320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.29/10.74 % (24320)Termination reason: Unknown
% 64.29/10.74 % (24320)Termination phase: Saturation
% 64.29/10.74
% 64.29/10.74 % (24320)Memory used [KB]: 3709
% 64.29/10.74 % (24320)Time elapsed: 1.171 s
% 64.29/10.74 % (24320)Instructions burned: 2655 (million)
% 64.29/10.74 % (24320)------------------------------
% 64.29/10.74 % (24320)------------------------------
% 64.29/10.76 % (24328)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_23992 for (2909ds/3049Mi)
% 64.29/10.80 % (24327)Instruction limit reached!
% 64.29/10.80 % (24327)------------------------------
% 64.29/10.80 % (24327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.29/10.80 % (24327)Termination reason: Unknown
% 64.29/10.80 % (24327)Termination phase: Saturation
% 64.29/10.80
% 64.29/10.80 % (24327)Memory used [KB]: 12025
% 64.29/10.80 % (24327)Time elapsed: 0.168 s
% 64.29/10.80 % (24327)Instructions burned: 454 (million)
% 64.29/10.80 % (24327)------------------------------
% 64.29/10.80 % (24327)------------------------------
% 64.83/10.81 % (24329)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_23992 for (2908ds/7311Mi)
% 64.83/10.83 % (24329)Refutation not found, incomplete strategy
% 64.83/10.83 % (24329)------------------------------
% 64.83/10.83 % (24329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.83/10.83 % (24329)Termination reason: Refutation not found, incomplete strategy
% 64.83/10.83
% 64.83/10.83
% 64.83/10.83 % (24329)Memory used [KB]: 5756
% 64.83/10.83 % (24329)Time elapsed: 0.023 s
% 64.83/10.83 % (24329)Instructions burned: 54 (million)
% 64.83/10.83 % (24329)------------------------------
% 64.83/10.83 % (24329)------------------------------
% 64.83/10.85 % (24310)Instruction limit reached!
% 64.83/10.85 % (24310)------------------------------
% 64.83/10.85 % (24310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.83/10.85 % (24310)Termination reason: Unknown
% 64.83/10.85 % (24310)Termination phase: Saturation
% 64.83/10.85
% 64.83/10.85 % (24310)Memory used [KB]: 12537
% 64.83/10.85 % (24310)Time elapsed: 2.065 s
% 64.83/10.85 % (24310)Instructions burned: 4604 (million)
% 64.83/10.85 % (24310)------------------------------
% 64.83/10.85 % (24310)------------------------------
% 64.83/10.85 % (24330)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_23992 for (2908ds/6804Mi)
% 64.83/10.86 % (24321)Instruction limit reached!
% 64.83/10.86 % (24321)------------------------------
% 64.83/10.86 % (24321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.83/10.86 % (24321)Termination reason: Unknown
% 64.83/10.86 % (24321)Termination phase: Saturation
% 64.83/10.86
% 64.83/10.86 % (24321)Memory used [KB]: 3837
% 64.83/10.86 % (24321)Time elapsed: 1.128 s
% 64.83/10.86 % (24321)Instructions burned: 2781 (million)
% 64.83/10.86 % (24321)------------------------------
% 64.83/10.86 % (24321)------------------------------
% 64.83/10.87 % (24331)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_23992 for (2908ds/1683Mi)
% 64.83/10.88 % (24332)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_23992 for (2908ds/4688Mi)
% 64.83/10.89 % (24330)Refutation not found, incomplete strategy
% 64.83/10.89 % (24330)------------------------------
% 64.83/10.89 % (24330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.83/10.89 % (24330)Termination reason: Refutation not found, incomplete strategy
% 64.83/10.89
% 64.83/10.89
% 64.83/10.89 % (24330)Memory used [KB]: 6012
% 64.83/10.89 % (24330)Time elapsed: 0.037 s
% 64.83/10.89 % (24330)Instructions burned: 87 (million)
% 64.83/10.89 % (24330)------------------------------
% 64.83/10.89 % (24330)------------------------------
% 65.16/10.90 % (24333)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_23992 for (2907ds/2207Mi)
% 69.15/11.24 % (24318)Instruction limit reached!
% 69.15/11.24 % (24318)------------------------------
% 69.15/11.24 % (24318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.15/11.24 % (24318)Termination reason: Unknown
% 69.15/11.24 % (24318)Termination phase: Saturation
% 69.15/11.24
% 69.15/11.24 % (24318)Memory used [KB]: 9978
% 69.15/11.24 % (24318)Time elapsed: 1.805 s
% 69.15/11.24 % (24318)Instructions burned: 5449 (million)
% 69.15/11.24 % (24318)------------------------------
% 69.15/11.24 % (24318)------------------------------
% 69.15/11.26 % (24334)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_23992 for (2904ds/8216Mi)
% 69.15/11.27 % (24334)Refutation not found, incomplete strategy
% 69.15/11.27 % (24334)------------------------------
% 69.15/11.27 % (24334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.15/11.27 % (24334)Termination reason: Refutation not found, incomplete strategy
% 69.15/11.27
% 69.15/11.27
% 69.15/11.27 % (24334)Memory used [KB]: 5756
% 69.15/11.27 % (24334)Time elapsed: 0.015 s
% 69.15/11.27 % (24334)Instructions burned: 33 (million)
% 69.15/11.27 % (24334)------------------------------
% 69.15/11.27 % (24334)------------------------------
% 69.15/11.29 % (24335)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_23992 for (2903ds/430Mi)
% 69.83/11.34 % (24326)Instruction limit reached!
% 69.83/11.34 % (24326)------------------------------
% 69.83/11.34 % (24326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.83/11.34 % (24326)Termination reason: Unknown
% 69.83/11.34 % (24326)Termination phase: Saturation
% 69.83/11.34
% 69.83/11.34 % (24326)Memory used [KB]: 9978
% 69.83/11.34 % (24326)Time elapsed: 1.239 s
% 69.83/11.34 % (24326)Instructions burned: 3201 (million)
% 69.83/11.34 % (24326)------------------------------
% 69.83/11.34 % (24326)------------------------------
% 69.83/11.36 % (24336)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_23992 for (2903ds/2012Mi)
% 70.39/11.45 % (24335)Instruction limit reached!
% 70.39/11.45 % (24335)------------------------------
% 70.39/11.45 % (24335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.39/11.45 % (24335)Termination reason: Unknown
% 70.39/11.45 % (24335)Termination phase: Saturation
% 70.39/11.45
% 70.39/11.45 % (24335)Memory used [KB]: 7547
% 70.39/11.45 % (24335)Time elapsed: 0.159 s
% 70.39/11.45 % (24335)Instructions burned: 430 (million)
% 70.39/11.45 % (24335)------------------------------
% 70.39/11.45 % (24335)------------------------------
% 70.39/11.46 % (24337)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_23992 for (2902ds/631Mi)
% 71.55/11.62 % (24331)Instruction limit reached!
% 71.55/11.62 % (24331)------------------------------
% 71.55/11.62 % (24331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.55/11.62 % (24331)Termination reason: Unknown
% 71.55/11.62 % (24331)Termination phase: Saturation
% 71.55/11.62
% 71.55/11.62 % (24331)Memory used [KB]: 7803
% 71.55/11.62 % (24331)Time elapsed: 0.759 s
% 71.55/11.62 % (24331)Instructions burned: 1684 (million)
% 71.55/11.62 % (24331)------------------------------
% 71.55/11.62 % (24331)------------------------------
% 71.55/11.63 % (24337)Refutation not found, incomplete strategy
% 71.55/11.63 % (24337)------------------------------
% 71.55/11.63 % (24337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.55/11.63 % (24337)Termination reason: Refutation not found, incomplete strategy
% 71.55/11.63
% 71.55/11.63
% 71.55/11.63 % (24337)Memory used [KB]: 7675
% 71.55/11.63 % (24337)Time elapsed: 0.170 s
% 71.55/11.63 % (24337)Instructions burned: 455 (million)
% 71.55/11.63 % (24337)------------------------------
% 71.55/11.63 % (24337)------------------------------
% 71.55/11.64 % (24338)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_23992 for (2900ds/8785Mi)
% 71.55/11.65 % (24339)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_23992 for (2900ds/739Mi)
% 72.17/11.75 % (24333)Instruction limit reached!
% 72.17/11.75 % (24333)------------------------------
% 72.17/11.75 % (24333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.17/11.75 % (24333)Termination reason: Unknown
% 72.17/11.75 % (24333)Termination phase: Saturation
% 72.17/11.75
% 72.17/11.75 % (24333)Memory used [KB]: 9083
% 72.17/11.75 % (24333)Time elapsed: 0.844 s
% 72.17/11.75 % (24333)Instructions burned: 2209 (million)
% 72.17/11.75 % (24333)------------------------------
% 72.17/11.75 % (24333)------------------------------
% 72.17/11.76 % (24340)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_23992 for (2899ds/5473Mi)
% 72.82/11.93 % (24328)Instruction limit reached!
% 72.82/11.93 % (24328)------------------------------
% 72.82/11.93 % (24328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.82/11.93 % (24328)Termination reason: Unknown
% 72.82/11.93 % (24328)Termination phase: Saturation
% 72.82/11.93
% 72.82/11.93 % (24328)Memory used [KB]: 9722
% 72.82/11.93 % (24328)Time elapsed: 1.171 s
% 72.82/11.93 % (24328)Instructions burned: 3050 (million)
% 72.82/11.93 % (24328)------------------------------
% 72.82/11.93 % (24328)------------------------------
% 72.82/11.95 % (24341)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_23992 for (2897ds/43570Mi)
% 72.82/11.97 % (24341)Refutation not found, incomplete strategy
% 72.82/11.97 % (24341)------------------------------
% 72.82/11.97 % (24341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.82/11.97 % (24341)Termination reason: Refutation not found, incomplete strategy
% 72.82/11.97
% 72.82/11.97
% 72.82/11.97 % (24341)Memory used [KB]: 5756
% 72.82/11.97 % (24341)Time elapsed: 0.023 s
% 72.82/11.97 % (24341)Instructions burned: 54 (million)
% 72.82/11.97 % (24341)------------------------------
% 72.82/11.97 % (24341)------------------------------
% 72.82/11.98 % (24342)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_23992 for (2897ds/8382Mi)
% 72.82/12.00 % (24339)Instruction limit reached!
% 72.82/12.00 % (24339)------------------------------
% 72.82/12.00 % (24339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.82/12.00 % (24339)Termination reason: Unknown
% 72.82/12.00 % (24339)Termination phase: Saturation
% 72.82/12.00
% 72.82/12.00 % (24339)Memory used [KB]: 7419
% 72.82/12.00 % (24339)Time elapsed: 0.356 s
% 72.82/12.00 % (24339)Instructions burned: 739 (million)
% 72.82/12.00 % (24339)------------------------------
% 72.82/12.00 % (24339)------------------------------
% 72.82/12.02 % (24343)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_23992 for (2896ds/407Mi)
% 74.92/12.06 % (24325)Instruction limit reached!
% 74.92/12.06 % (24325)------------------------------
% 74.92/12.06 % (24325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.92/12.06 % (24325)Termination reason: Unknown
% 74.92/12.06 % (24325)Termination phase: Saturation
% 74.92/12.06
% 74.92/12.06 % (24325)Memory used [KB]: 10490
% 74.92/12.06 % (24325)Time elapsed: 2.037 s
% 74.92/12.06 % (24325)Instructions burned: 5216 (million)
% 74.92/12.06 % (24325)------------------------------
% 74.92/12.06 % (24325)------------------------------
% 74.92/12.08 % (24344)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_23992 for (2896ds/2971Mi)
% 75.47/12.18 % (24343)Instruction limit reached!
% 75.47/12.18 % (24343)------------------------------
% 75.47/12.18 % (24343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.47/12.18 % (24343)Termination reason: Unknown
% 75.47/12.18 % (24343)Termination phase: Saturation
% 75.47/12.18
% 75.47/12.18 % (24343)Memory used [KB]: 6396
% 75.47/12.18 % (24343)Time elapsed: 0.162 s
% 75.47/12.18 % (24343)Instructions burned: 409 (million)
% 75.47/12.18 % (24343)------------------------------
% 75.47/12.18 % (24343)------------------------------
% 76.00/12.20 % (24345)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_23992 for (2894ds/9822Mi)
% 76.00/12.22 % (24336)Instruction limit reached!
% 76.00/12.22 % (24336)------------------------------
% 76.00/12.22 % (24336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.00/12.22 % (24336)Termination reason: Unknown
% 76.00/12.22 % (24336)Termination phase: Saturation
% 76.00/12.22
% 76.00/12.22 % (24336)Memory used [KB]: 12792
% 76.00/12.22 % (24336)Time elapsed: 0.866 s
% 76.00/12.22 % (24336)Instructions burned: 2013 (million)
% 76.00/12.22 % (24336)------------------------------
% 76.00/12.22 % (24336)------------------------------
% 76.00/12.24 % (24346)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_23992 for (2894ds/8425Mi)
% 76.00/12.25 % (24344)Refutation not found, incomplete strategy
% 76.00/12.25 % (24344)------------------------------
% 76.00/12.25 % (24344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.00/12.25 % (24344)Termination reason: Refutation not found, incomplete strategy
% 76.00/12.25
% 76.00/12.25
% 76.00/12.25 % (24344)Memory used [KB]: 7675
% 76.00/12.25 % (24344)Time elapsed: 0.166 s
% 76.00/12.25 % (24344)Instructions burned: 450 (million)
% 76.00/12.25 % (24344)------------------------------
% 76.00/12.25 % (24344)------------------------------
% 76.00/12.25 % (24345)Refutation not found, incomplete strategy
% 76.00/12.25 % (24345)------------------------------
% 76.00/12.25 % (24345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.00/12.25 % (24345)Termination reason: Refutation not found, incomplete strategy
% 76.00/12.25
% 76.00/12.25
% 76.00/12.25 % (24345)Memory used [KB]: 6780
% 76.00/12.25 % (24345)Time elapsed: 0.056 s
% 76.00/12.25 % (24345)Instructions burned: 122 (million)
% 76.00/12.25 % (24345)------------------------------
% 76.00/12.25 % (24345)------------------------------
% 76.00/12.26 % (24347)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_23992 for (2894ds/3107Mi)
% 76.00/12.27 % (24348)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_23992 for (2894ds/7967Mi)
% 77.10/12.43 % (24348)Refutation not found, incomplete strategy
% 77.10/12.43 % (24348)------------------------------
% 77.10/12.43 % (24348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.10/12.43 % (24348)Termination reason: Refutation not found, incomplete strategy
% 77.10/12.43
% 77.10/12.43
% 77.10/12.43 % (24348)Memory used [KB]: 7547
% 77.10/12.43 % (24348)Time elapsed: 0.164 s
% 77.10/12.43 % (24348)Instructions burned: 447 (million)
% 77.10/12.43 % (24348)------------------------------
% 77.10/12.43 % (24348)------------------------------
% 77.10/12.44 % (24347)Refutation not found, incomplete strategy
% 77.10/12.44 % (24347)------------------------------
% 77.10/12.44 % (24347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.10/12.44 % (24347)Termination reason: Refutation not found, incomplete strategy
% 77.10/12.44
% 77.10/12.44
% 77.10/12.44 % (24347)Memory used [KB]: 7547
% 77.10/12.44 % (24347)Time elapsed: 0.174 s
% 77.10/12.44 % (24347)Instructions burned: 475 (million)
% 77.10/12.44 % (24347)------------------------------
% 77.10/12.44 % (24347)------------------------------
% 77.10/12.45 % (24349)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_23992 for (2892ds/3629Mi)
% 77.10/12.45 % (24350)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_23992 for (2892ds/939Mi)
% 79.07/12.81 % (24350)Instruction limit reached!
% 79.07/12.81 % (24350)------------------------------
% 79.07/12.81 % (24350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.07/12.81 % (24350)Termination reason: Unknown
% 79.07/12.81 % (24350)Termination phase: Saturation
% 79.07/12.81
% 79.07/12.81 % (24350)Memory used [KB]: 7164
% 79.07/12.81 % (24350)Time elapsed: 0.363 s
% 79.07/12.81 % (24350)Instructions burned: 939 (million)
% 79.07/12.81 % (24350)------------------------------
% 79.07/12.81 % (24350)------------------------------
% 79.07/12.83 % (24351)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_23992 for (2888ds/1188Mi)
% 81.90/13.09 % (24332)Instruction limit reached!
% 81.90/13.09 % (24332)------------------------------
% 81.90/13.09 % (24332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.90/13.09 % (24332)Termination reason: Unknown
% 81.90/13.09 % (24332)Termination phase: Saturation
% 81.90/13.09
% 81.90/13.09 % (24332)Memory used [KB]: 10106
% 81.90/13.09 % (24332)Time elapsed: 2.214 s
% 81.90/13.09 % (24332)Instructions burned: 4688 (million)
% 81.90/13.09 % (24332)------------------------------
% 81.90/13.09 % (24332)------------------------------
% 81.90/13.11 % (24352)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_23992 for (2885ds/3205Mi)
% 83.64/13.32 % (24351)Instruction limit reached!
% 83.64/13.32 % (24351)------------------------------
% 83.64/13.32 % (24351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.64/13.32 % (24351)Termination reason: Unknown
% 83.64/13.32 % (24351)Termination phase: Saturation
% 83.64/13.32
% 83.64/13.32 % (24351)Memory used [KB]: 7931
% 83.64/13.32 % (24351)Time elapsed: 0.495 s
% 83.64/13.32 % (24351)Instructions burned: 1189 (million)
% 83.64/13.32 % (24351)------------------------------
% 83.64/13.32 % (24351)------------------------------
% 83.64/13.34 % (24353)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_23992 for (2883ds/865Mi)
% 85.16/13.68 % (24353)Instruction limit reached!
% 85.16/13.68 % (24353)------------------------------
% 85.16/13.68 % (24353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.16/13.68 % (24353)Termination reason: Unknown
% 85.16/13.68 % (24353)Termination phase: Saturation
% 85.16/13.68
% 85.16/13.68 % (24353)Memory used [KB]: 7675
% 85.16/13.68 % (24353)Time elapsed: 0.340 s
% 85.16/13.68 % (24353)Instructions burned: 866 (million)
% 85.16/13.68 % (24353)------------------------------
% 85.16/13.68 % (24353)------------------------------
% 86.01/13.70 % (24354)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_23992 for (2880ds/7469Mi)
% 87.00/13.98 % (24340)Instruction limit reached!
% 87.00/13.98 % (24340)------------------------------
% 87.00/13.98 % (24340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.00/13.98 % (24340)Termination reason: Unknown
% 87.00/13.98 % (24340)Termination phase: Saturation
% 87.00/13.98
% 87.00/13.98 % (24340)Memory used [KB]: 11129
% 87.00/13.98 % (24340)Time elapsed: 2.209 s
% 87.00/13.98 % (24340)Instructions burned: 5474 (million)
% 87.00/13.98 % (24340)------------------------------
% 87.00/13.98 % (24340)------------------------------
% 88.84/14.02 % (24355)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_23992 for (2877ds/4165Mi)
% 89.54/14.18 % (24349)Instruction limit reached!
% 89.54/14.18 % (24349)------------------------------
% 89.54/14.18 % (24349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.54/14.18 % (24349)Termination reason: Unknown
% 89.54/14.18 % (24349)Termination phase: Saturation
% 89.54/14.18
% 89.54/14.18 % (24349)Memory used [KB]: 16502
% 89.54/14.18 % (24349)Time elapsed: 1.731 s
% 89.54/14.18 % (24349)Instructions burned: 3630 (million)
% 89.54/14.18 % (24349)------------------------------
% 89.54/14.18 % (24349)------------------------------
% 89.54/14.20 % (24356)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_23992 for (2875ds/13468Mi)
% 90.09/14.21 % (24356)Refutation not found, incomplete strategy
% 90.09/14.21 % (24356)------------------------------
% 90.09/14.21 % (24356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.09/14.21 % (24356)Termination reason: Refutation not found, incomplete strategy
% 90.09/14.21
% 90.09/14.21
% 90.09/14.21 % (24356)Memory used [KB]: 5756
% 90.09/14.21 % (24356)Time elapsed: 0.013 s
% 90.09/14.21 % (24356)Instructions burned: 26 (million)
% 90.09/14.21 % (24356)------------------------------
% 90.09/14.21 % (24356)------------------------------
% 90.09/14.22 % (24357)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_23992 for (2874ds/2635Mi)
% 90.71/14.37 % (24352)Instruction limit reached!
% 90.71/14.37 % (24352)------------------------------
% 90.71/14.37 % (24352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.71/14.37 % (24352)Termination reason: Unknown
% 90.71/14.37 % (24352)Termination phase: Saturation
% 90.71/14.37
% 90.71/14.37 % (24352)Memory used [KB]: 9850
% 90.71/14.37 % (24352)Time elapsed: 1.260 s
% 90.71/14.37 % (24352)Instructions burned: 3206 (million)
% 90.71/14.37 % (24352)------------------------------
% 90.71/14.37 % (24352)------------------------------
% 90.71/14.38 % (24358)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_23992 for (2873ds/631Mi)
% 91.28/14.40 % (24357)Refutation not found, incomplete strategy
% 91.28/14.40 % (24357)------------------------------
% 91.28/14.40 % (24357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.28/14.40 % (24357)Termination reason: Refutation not found, incomplete strategy
% 91.28/14.40
% 91.28/14.40
% 91.28/14.40 % (24357)Memory used [KB]: 7675
% 91.28/14.40 % (24357)Time elapsed: 0.180 s
% 91.28/14.40 % (24357)Instructions burned: 482 (million)
% 91.28/14.40 % (24357)------------------------------
% 91.28/14.40 % (24357)------------------------------
% 91.28/14.42 % (24359)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_23992 for (2872ds/15557Mi)
% 91.97/14.53 % (24342)Instruction limit reached!
% 91.97/14.53 % (24342)------------------------------
% 91.97/14.53 % (24342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.97/14.53 % (24342)Termination reason: Unknown
% 91.97/14.53 % (24342)Termination phase: Saturation
% 91.97/14.53
% 91.97/14.53 % (24342)Memory used [KB]: 9850
% 91.97/14.53 % (24342)Time elapsed: 2.552 s
% 91.97/14.53 % (24342)Instructions burned: 8382 (million)
% 91.97/14.53 % (24342)------------------------------
% 91.97/14.53 % (24342)------------------------------
% 91.97/14.55 % (24360)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_23992 for (2871ds/2142Mi)
% 91.97/14.58 % (24360)Refutation not found, incomplete strategy
% 91.97/14.58 % (24360)------------------------------
% 91.97/14.58 % (24360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.97/14.58 % (24360)Termination reason: Refutation not found, incomplete strategy
% 91.97/14.58
% 91.97/14.58
% 91.97/14.58 % (24360)Memory used [KB]: 5756
% 91.97/14.58 % (24360)Time elapsed: 0.025 s
% 91.97/14.58 % (24360)Instructions burned: 60 (million)
% 91.97/14.58 % (24360)------------------------------
% 91.97/14.58 % (24360)------------------------------
% 91.97/14.59 % (24361)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_23992 for (2871ds/5624Mi)
% 92.46/14.60 % (24361)Refutation not found, incomplete strategy
% 92.46/14.60 % (24361)------------------------------
% 92.46/14.60 % (24361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.46/14.60 % (24361)Termination reason: Refutation not found, incomplete strategy
% 92.46/14.60
% 92.46/14.60
% 92.46/14.60 % (24361)Memory used [KB]: 5756
% 92.46/14.60 % (24361)Time elapsed: 0.011 s
% 92.46/14.60 % (24361)Instructions burned: 23 (million)
% 92.46/14.60 % (24361)------------------------------
% 92.46/14.60 % (24361)------------------------------
% 92.46/14.62 % (24362)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_23992 for (2870ds/1665Mi)
% 92.46/14.62 % (24358)Instruction limit reached!
% 92.46/14.62 % (24358)------------------------------
% 92.46/14.62 % (24358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.46/14.62 % (24358)Termination reason: Unknown
% 92.46/14.62 % (24358)Termination phase: Saturation
% 92.46/14.62
% 92.46/14.62 % (24358)Memory used [KB]: 7675
% 92.46/14.62 % (24358)Time elapsed: 0.241 s
% 92.46/14.62 % (24358)Instructions burned: 633 (million)
% 92.46/14.62 % (24358)------------------------------
% 92.46/14.62 % (24358)------------------------------
% 92.46/14.64 % (24363)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_23992 for (2870ds/64912Mi)
% 92.46/14.66 % (24363)Refutation not found, incomplete strategy
% 92.46/14.66 % (24363)------------------------------
% 92.46/14.66 % (24363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.46/14.66 % (24363)Termination reason: Refutation not found, incomplete strategy
% 92.46/14.66
% 92.46/14.66
% 92.46/14.66 % (24363)Memory used [KB]: 1279
% 92.46/14.66 % (24363)Time elapsed: 0.023 s
% 92.46/14.66 % (24363)Instructions burned: 54 (million)
% 92.46/14.66 % (24363)------------------------------
% 92.46/14.66 % (24363)------------------------------
% 92.46/14.68 % (24364)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_23992 for (2870ds/7801Mi)
% 93.99/14.95 % (24346)Instruction limit reached!
% 93.99/14.95 % (24346)------------------------------
% 93.99/14.95 % (24346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.99/14.95 % (24346)Termination reason: Unknown
% 93.99/14.95 % (24346)Termination phase: Saturation
% 93.99/14.95
% 93.99/14.95 % (24346)Memory used [KB]: 5884
% 93.99/14.95 % (24346)Time elapsed: 2.712 s
% 93.99/14.95 % (24346)Instructions burned: 8426 (million)
% 93.99/14.95 % (24346)------------------------------
% 93.99/14.95 % (24346)------------------------------
% 93.99/14.97 % (24365)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_23992 for (2867ds/15194Mi)
% 96.57/15.17 % (24365)Refutation not found, incomplete strategy
% 96.57/15.17 % (24365)------------------------------
% 96.57/15.17 % (24365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.57/15.17 % (24365)Termination reason: Refutation not found, incomplete strategy
% 96.57/15.17
% 96.57/15.17
% 96.57/15.17 % (24365)Memory used [KB]: 7675
% 96.57/15.17 % (24365)Time elapsed: 0.228 s
% 96.57/15.17 % (24365)Instructions burned: 519 (million)
% 96.57/15.17 % (24365)------------------------------
% 96.57/15.17 % (24365)------------------------------
% 96.57/15.19 % (24366)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_23992 for (2864ds/6753Mi)
% 97.06/15.23 % (24366)Refutation not found, incomplete strategy
% 97.06/15.23 % (24366)------------------------------
% 97.06/15.23 % (24366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.06/15.23 % (24366)Termination reason: Refutation not found, incomplete strategy
% 97.06/15.23
% 97.06/15.23
% 97.06/15.23 % (24366)Memory used [KB]: 6140
% 97.06/15.23 % (24366)Time elapsed: 0.040 s
% 97.06/15.23 % (24366)Instructions burned: 90 (million)
% 97.06/15.23 % (24366)------------------------------
% 97.06/15.23 % (24366)------------------------------
% 97.06/15.24 % (24338)Instruction limit reached!
% 97.06/15.24 % (24338)------------------------------
% 97.06/15.24 % (24338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.06/15.24 % (24338)Termination reason: Unknown
% 97.06/15.24 % (24338)Termination phase: Saturation
% 97.06/15.24
% 97.06/15.24 % (24338)Memory used [KB]: 12281
% 97.06/15.24 % (24338)Time elapsed: 3.600 s
% 97.06/15.24 % (24338)Instructions burned: 8787 (million)
% 97.06/15.24 % (24338)------------------------------
% 97.06/15.24 % (24338)------------------------------
% 97.06/15.25 % (24367)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_23992 for (2864ds/1003Mi)
% 97.06/15.26 % (24368)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_23992 for (2864ds/13018Mi)
% 97.06/15.26 % (24362)Instruction limit reached!
% 97.06/15.26 % (24362)------------------------------
% 97.06/15.26 % (24362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.06/15.26 % (24362)Termination reason: Unknown
% 97.06/15.26 % (24362)Termination phase: Saturation
% 97.06/15.26
% 97.06/15.26 % (24362)Memory used [KB]: 8059
% 97.06/15.26 % (24362)Time elapsed: 0.645 s
% 97.06/15.26 % (24362)Instructions burned: 1665 (million)
% 97.06/15.26 % (24362)------------------------------
% 97.06/15.26 % (24362)------------------------------
% 97.06/15.28 % (24369)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_23992 for (2864ds/1267Mi)
% 97.64/15.30 % (24369)Refutation not found, incomplete strategy
% 97.64/15.30 % (24369)------------------------------
% 97.64/15.30 % (24369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.64/15.30 % (24369)Termination reason: Refutation not found, incomplete strategy
% 97.64/15.30
% 97.64/15.30
% 97.64/15.30 % (24369)Memory used [KB]: 5756
% 97.64/15.30 % (24369)Time elapsed: 0.023 s
% 97.64/15.30 % (24369)Instructions burned: 53 (million)
% 97.64/15.30 % (24369)------------------------------
% 97.64/15.30 % (24369)------------------------------
% 97.64/15.32 % (24370)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_23992 for (2863ds/2570Mi)
% 98.89/15.63 % (24367)Instruction limit reached!
% 98.89/15.63 % (24367)------------------------------
% 98.89/15.63 % (24367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.89/15.63 % (24367)Termination reason: Unknown
% 98.89/15.63 % (24367)Termination phase: Saturation
% 98.89/15.63
% 98.89/15.63 % (24367)Memory used [KB]: 7803
% 98.89/15.63 % (24367)Time elapsed: 0.389 s
% 98.89/15.63 % (24367)Instructions burned: 1004 (million)
% 98.89/15.63 % (24367)------------------------------
% 98.89/15.63 % (24367)------------------------------
% 98.89/15.65 % (24371)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_23992 for (2860ds/13163Mi)
% 100.49/16.00 % (24355)Instruction limit reached!
% 100.49/16.00 % (24355)------------------------------
% 100.49/16.00 % (24355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.49/16.00 % (24355)Termination reason: Unknown
% 100.49/16.00 % (24355)Termination phase: Saturation
% 100.49/16.00
% 100.49/16.00 % (24355)Memory used [KB]: 9338
% 100.49/16.00 % (24355)Time elapsed: 2.017 s
% 100.49/16.00 % (24355)Instructions burned: 4166 (million)
% 100.49/16.00 % (24355)------------------------------
% 100.49/16.00 % (24355)------------------------------
% 100.49/16.01 % (24372)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_23992 for (2856ds/5087Mi)
% 102.83/16.12 % (24372)Refutation not found, incomplete strategy
% 102.83/16.12 % (24372)------------------------------
% 102.83/16.12 % (24372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.83/16.12 % (24372)Termination reason: Refutation not found, incomplete strategy
% 102.83/16.12
% 102.83/16.12
% 102.83/16.12 % (24372)Memory used [KB]: 6780
% 102.83/16.12 % (24372)Time elapsed: 0.107 s
% 102.83/16.12 % (24372)Instructions burned: 257 (million)
% 102.83/16.12 % (24372)------------------------------
% 102.83/16.12 % (24372)------------------------------
% 103.57/16.14 % (24373)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_23992 for (2855ds/10380Mi)
% 104.01/16.28 % (24373)Refutation not found, incomplete strategy
% 104.01/16.28 % (24373)------------------------------
% 104.01/16.28 % (24373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.01/16.28 % (24373)Termination reason: Refutation not found, incomplete strategy
% 104.01/16.28
% 104.01/16.28
% 104.01/16.28 % (24373)Memory used [KB]: 6396
% 104.01/16.28 % (24373)Time elapsed: 0.146 s
% 104.01/16.28 % (24373)Instructions burned: 388 (million)
% 104.01/16.28 % (24373)------------------------------
% 104.01/16.28 % (24373)------------------------------
% 104.77/16.30 % (24374)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_23992 for (2853ds/4218Mi)
% 104.77/16.34 % (24374)Refutation not found, incomplete strategy
% 104.77/16.34 % (24374)------------------------------
% 104.77/16.34 % (24374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.77/16.34 % (24374)Termination reason: Refutation not found, incomplete strategy
% 104.77/16.34
% 104.77/16.34
% 104.77/16.34 % (24374)Memory used [KB]: 5884
% 104.77/16.34 % (24374)Time elapsed: 0.043 s
% 104.77/16.34 % (24374)Instructions burned: 110 (million)
% 104.77/16.34 % (24374)------------------------------
% 104.77/16.34 % (24374)------------------------------
% 104.77/16.36 % (24375)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_23992 for (2853ds/3971Mi)
% 104.77/16.37 % (24370)Instruction limit reached!
% 104.77/16.37 % (24370)------------------------------
% 104.77/16.37 % (24370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.77/16.37 % (24370)Termination reason: Unknown
% 104.77/16.37 % (24370)Termination phase: Saturation
% 104.77/16.37
% 104.77/16.37 % (24370)Memory used [KB]: 8699
% 104.77/16.37 % (24370)Time elapsed: 1.053 s
% 104.77/16.37 % (24370)Instructions burned: 2571 (million)
% 104.77/16.37 % (24370)------------------------------
% 104.77/16.37 % (24370)------------------------------
% 104.77/16.38 % (24376)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_23992 for (2853ds/14014Mi)
% 105.41/16.41 % (24376)Refutation not found, incomplete strategy
% 105.41/16.41 % (24376)------------------------------
% 105.41/16.41 % (24376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.41/16.41 % (24376)Termination reason: Refutation not found, incomplete strategy
% 105.41/16.41
% 105.41/16.41
% 105.41/16.41 % (24376)Memory used [KB]: 5756
% 105.41/16.41 % (24376)Time elapsed: 0.024 s
% 105.41/16.41 % (24376)Instructions burned: 56 (million)
% 105.41/16.41 % (24376)------------------------------
% 105.41/16.41 % (24376)------------------------------
% 105.41/16.42 % (24377)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_23992 for (2852ds/8517Mi)
% 105.41/16.45 % (24377)Refutation not found, incomplete strategy
% 105.41/16.45 % (24377)------------------------------
% 105.41/16.45 % (24377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.41/16.45 % (24377)Termination reason: Refutation not found, incomplete strategy
% 105.41/16.45
% 105.41/16.45
% 105.41/16.45 % (24377)Memory used [KB]: 5756
% 105.41/16.45 % (24377)Time elapsed: 0.024 s
% 105.41/16.45 % (24377)Instructions burned: 55 (million)
% 105.41/16.45 % (24377)------------------------------
% 105.41/16.45 % (24377)------------------------------
% 105.41/16.46 % (24378)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_23992 for (2852ds/10148Mi)
% 106.00/16.56 % (24354)Instruction limit reached!
% 106.00/16.56 % (24354)------------------------------
% 106.00/16.56 % (24354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.00/16.56 % (24354)Termination reason: Unknown
% 106.00/16.56 % (24354)Termination phase: Saturation
% 106.00/16.56
% 106.00/16.56 % (24354)Memory used [KB]: 9338
% 106.00/16.56 % (24354)Time elapsed: 2.862 s
% 106.00/16.56 % (24354)Instructions burned: 7470 (million)
% 106.00/16.56 % (24354)------------------------------
% 106.00/16.56 % (24354)------------------------------
% 106.00/16.58 % (24379)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_23992 for (2851ds/9078Mi)
% 106.47/16.60 % (24379)Refutation not found, incomplete strategy
% 106.47/16.60 % (24379)------------------------------
% 106.47/16.60 % (24379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.47/16.60 % (24379)Termination reason: Refutation not found, incomplete strategy
% 106.47/16.60
% 106.47/16.60
% 106.47/16.60 % (24379)Memory used [KB]: 5756
% 106.47/16.60 % (24379)Time elapsed: 0.022 s
% 106.47/16.60 % (24379)Instructions burned: 53 (million)
% 106.47/16.60 % (24379)------------------------------
% 106.47/16.60 % (24379)------------------------------
% 106.47/16.61 % (24380)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_23992 for (2850ds/16164Mi)
% 106.47/16.62 % (24380)Refutation not found, incomplete strategy
% 106.47/16.62 % (24380)------------------------------
% 106.47/16.62 % (24380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.47/16.62 % (24380)Termination reason: Refutation not found, incomplete strategy
% 106.47/16.62
% 106.47/16.63
% 106.47/16.63 % (24380)Memory used [KB]: 5756
% 106.47/16.63 % (24380)Time elapsed: 0.012 s
% 106.47/16.63 % (24380)Instructions burned: 23 (million)
% 106.47/16.63 % (24380)------------------------------
% 106.47/16.63 % (24380)------------------------------
% 106.47/16.64 % (24381)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_23992 for (2850ds/6102Mi)
% 115.25/17.90 % (24375)Instruction limit reached!
% 115.25/17.90 % (24375)------------------------------
% 115.25/17.90 % (24375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.25/17.90 % (24375)Termination reason: Unknown
% 115.25/17.90 % (24375)Termination phase: Saturation
% 115.25/17.90
% 115.25/17.90 % (24375)Memory used [KB]: 10106
% 115.25/17.90 % (24375)Time elapsed: 1.540 s
% 115.25/17.90 % (24375)Instructions burned: 3971 (million)
% 115.25/17.90 % (24375)------------------------------
% 115.25/17.90 % (24375)------------------------------
% 114.41/17.91 % (24382)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_23992 for (2837ds/10308Mi)
% 114.41/17.95 % (24382)Refutation not found, incomplete strategy
% 114.41/17.95 % (24382)------------------------------
% 114.41/17.95 % (24382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.41/17.95 % (24382)Termination reason: Refutation not found, incomplete strategy
% 114.41/17.95
% 114.41/17.95
% 114.41/17.95 % (24382)Memory used [KB]: 6012
% 114.41/17.95 % (24382)Time elapsed: 0.039 s
% 114.41/17.95 % (24382)Instructions burned: 91 (million)
% 114.41/17.95 % (24382)------------------------------
% 114.41/17.95 % (24382)------------------------------
% 114.41/17.97 % (24383)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_23992 for (2837ds/4041Mi)
% 114.41/17.99 % (24383)Refutation not found, incomplete strategy
% 114.41/17.99 % (24383)------------------------------
% 114.41/17.99 % (24383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.41/17.99 % (24383)Termination reason: Refutation not found, incomplete strategy
% 114.41/17.99
% 114.41/17.99
% 114.41/17.99 % (24383)Memory used [KB]: 5756
% 114.41/17.99 % (24383)Time elapsed: 0.023 s
% 114.41/17.99 % (24383)Instructions burned: 55 (million)
% 114.41/17.99 % (24383)------------------------------
% 114.41/17.99 % (24383)------------------------------
% 114.41/18.01 % (24384)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on DTF2THF_23992 for (2836ds/6901Mi)
% 116.86/18.03 % (24384)Refutation not found, incomplete strategy
% 116.86/18.03 % (24384)------------------------------
% 116.86/18.03 % (24384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.86/18.03 % (24384)Termination reason: Refutation not found, incomplete strategy
% 116.86/18.03
% 116.86/18.03
% 116.86/18.03 % (24384)Memory used [KB]: 5756
% 116.86/18.03 % (24384)Time elapsed: 0.023 s
% 116.86/18.03 % (24384)Instructions burned: 56 (million)
% 116.86/18.03 % (24384)------------------------------
% 116.86/18.03 % (24384)------------------------------
% 116.86/18.05 % (24385)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_23992 for (2836ds/5576Mi)
% 119.11/18.45 % (24364)Instruction limit reached!
% 119.11/18.45 % (24364)------------------------------
% 119.11/18.45 % (24364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.11/18.45 % (24364)Termination reason: Unknown
% 119.11/18.45 % (24364)Termination phase: Saturation
% 119.11/18.45
% 119.11/18.45 % (24364)Memory used [KB]: 13304
% 119.11/18.45 % (24364)Time elapsed: 3.796 s
% 119.11/18.45 % (24364)Instructions burned: 7801 (million)
% 119.11/18.45 % (24364)------------------------------
% 119.11/18.45 % (24364)------------------------------
% 119.11/18.47 % (24386)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_23992 for (2832ds/2014Mi)
% 124.18/19.14 % (24371)Instruction limit reached!
% 124.18/19.14 % (24371)------------------------------
% 124.18/19.14 % (24371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.18/19.14 % (24371)Termination reason: Unknown
% 124.18/19.14 % (24371)Termination phase: Saturation
% 124.18/19.14
% 124.18/19.14 % (24371)Memory used [KB]: 6396
% 124.18/19.14 % (24371)Time elapsed: 3.491 s
% 124.18/19.14 % (24371)Instructions burned: 13166 (million)
% 124.18/19.14 % (24371)------------------------------
% 124.18/19.14 % (24371)------------------------------
% 124.18/19.16 % (24387)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on DTF2THF_23992 for (2825ds/5115Mi)
% 125.24/19.31 % (24386)Instruction limit reached!
% 125.24/19.31 % (24386)------------------------------
% 125.24/19.31 % (24386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.24/19.31 % (24386)Termination reason: Unknown
% 125.24/19.31 % (24386)Termination phase: Saturation
% 125.24/19.31
% 125.24/19.31 % (24386)Memory used [KB]: 8955
% 125.24/19.31 % (24386)Time elapsed: 0.687 s
% 125.24/19.31 % (24386)Instructions burned: 2015 (million)
% 125.24/19.31 % (24386)------------------------------
% 125.24/19.31 % (24386)------------------------------
% 125.24/19.33 % (24388)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_23992 for (2823ds/13001Mi)
% 125.24/19.34 % (24388)Refutation not found, incomplete strategy
% 125.24/19.34 % (24388)------------------------------
% 125.24/19.34 % (24388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.24/19.34 % (24388)Termination reason: Refutation not found, incomplete strategy
% 125.24/19.34
% 125.24/19.34
% 125.24/19.34 % (24388)Memory used [KB]: 5756
% 125.24/19.34 % (24388)Time elapsed: 0.012 s
% 125.24/19.34 % (24388)Instructions burned: 23 (million)
% 125.24/19.34 % (24388)------------------------------
% 125.24/19.34 % (24388)------------------------------
% 125.24/19.36 % (24389)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on DTF2THF_23992 for (2823ds/11105Mi)
% 126.29/19.54 % (24381)Instruction limit reached!
% 126.29/19.54 % (24381)------------------------------
% 126.29/19.54 % (24381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 126.29/19.54 % (24381)Termination reason: Unknown
% 126.29/19.54 % (24381)Termination phase: Saturation
% 126.29/19.54
% 126.29/19.54 % (24381)Memory used [KB]: 17654
% 126.29/19.54 % (24381)Time elapsed: 2.896 s
% 126.29/19.54 % (24381)Instructions burned: 6102 (million)
% 126.29/19.54 % (24381)------------------------------
% 126.29/19.54 % (24381)------------------------------
% 126.29/19.55 % (24390)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=13832:si=on:rtra=on_0 on DTF2THF_23992 for (2821ds/13832Mi)
% 127.52/19.87 % (24359)First to succeed.
% 130.39/20.03 % (24359)Refutation found. Thanks to Tanya!
% 130.39/20.03 % SZS status Theorem for DTF2THF_23992
% 130.39/20.03 % SZS output start Proof for DTF2THF_23992
% 130.39/20.03 thf(type_def_5, type, mworld: $tType).
% 130.39/20.03 thf(func_def_0, type, mworld: $tType).
% 130.39/20.03 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 130.39/20.03 thf(func_def_2, type, mactual: mworld).
% 130.39/20.03 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 130.39/20.03 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 130.39/20.03 thf(func_def_12, type, v1: mworld > $o).
% 130.39/20.03 thf(func_def_13, type, v2: mworld > $o).
% 130.39/20.03 thf(func_def_14, type, v3: mworld > $o).
% 130.39/20.03 thf(func_def_15, type, v4: mworld > $o).
% 130.39/20.03 thf(func_def_16, type, v5: mworld > $o).
% 130.39/20.03 thf(func_def_17, type, v6: mworld > $o).
% 130.39/20.03 thf(func_def_18, type, v7: mworld > $o).
% 130.39/20.03 thf(func_def_19, type, v8: mworld > $o).
% 130.39/20.03 thf(func_def_20, type, v9: mworld > $o).
% 130.39/20.03 thf(func_def_21, type, v10: mworld > $o).
% 130.39/20.03 thf(func_def_22, type, v12: mworld > $o).
% 130.39/20.03 thf(func_def_23, type, v11: mworld > $o).
% 130.39/20.03 thf(func_def_24, type, v14: mworld > $o).
% 130.39/20.03 thf(func_def_25, type, v13: mworld > $o).
% 130.39/20.03 thf(func_def_26, type, v16: mworld > $o).
% 130.39/20.03 thf(func_def_27, type, v15: mworld > $o).
% 130.39/20.03 thf(func_def_28, type, v18: mworld > $o).
% 130.39/20.03 thf(func_def_29, type, v17: mworld > $o).
% 130.39/20.03 thf(func_def_30, type, v19: mworld > $o).
% 130.39/20.03 thf(func_def_31, type, v21: mworld > $o).
% 130.39/20.03 thf(func_def_32, type, v20: mworld > $o).
% 130.39/20.03 thf(func_def_33, type, v23: mworld > $o).
% 130.39/20.03 thf(func_def_34, type, v22: mworld > $o).
% 130.39/20.03 thf(func_def_35, type, v25: mworld > $o).
% 130.39/20.03 thf(func_def_36, type, v24: mworld > $o).
% 130.39/20.03 thf(func_def_37, type, v27: mworld > $o).
% 130.39/20.03 thf(func_def_38, type, v26: mworld > $o).
% 130.39/20.03 thf(func_def_39, type, v28: mworld > $o).
% 130.39/20.03 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 130.39/20.03 thf(func_def_55, type, sK2: mworld).
% 130.39/20.03 thf(func_def_56, type, sK3: mworld > mworld).
% 130.39/20.03 thf(func_def_57, type, sK4: mworld > mworld).
% 130.39/20.03 thf(func_def_58, type, sK5: mworld > mworld).
% 130.39/20.03 thf(func_def_59, type, sK6: mworld > mworld).
% 130.39/20.03 thf(func_def_60, type, sK7: mworld > mworld).
% 130.39/20.03 thf(func_def_61, type, sK8: mworld > mworld).
% 130.39/20.03 thf(func_def_62, type, sK9: mworld > mworld).
% 130.39/20.03 thf(func_def_63, type, sK10: mworld > mworld).
% 130.39/20.03 thf(func_def_64, type, sK11: mworld > mworld).
% 130.39/20.03 thf(func_def_65, type, sK12: mworld > mworld).
% 130.39/20.03 thf(func_def_66, type, sK13: mworld > mworld).
% 130.39/20.03 thf(func_def_67, type, sK14: mworld > mworld).
% 130.39/20.03 thf(func_def_68, type, sK15: mworld > mworld).
% 130.39/20.03 thf(func_def_69, type, sK16: mworld > mworld).
% 130.39/20.03 thf(func_def_70, type, sK17: mworld > mworld).
% 130.39/20.03 thf(func_def_71, type, sK18: mworld > mworld).
% 130.39/20.03 thf(func_def_72, type, sK19: mworld > mworld).
% 130.39/20.03 thf(func_def_73, type, sK20: mworld > mworld).
% 130.39/20.03 thf(func_def_74, type, sK21: mworld > mworld).
% 130.39/20.03 thf(func_def_75, type, sK22: mworld > mworld).
% 130.39/20.03 thf(func_def_76, type, sK23: mworld > mworld).
% 130.39/20.03 thf(func_def_77, type, sK24: mworld > mworld).
% 130.39/20.03 thf(func_def_78, type, sK25: mworld > mworld).
% 130.39/20.03 thf(func_def_79, type, sK26: mworld > mworld).
% 130.39/20.03 thf(func_def_80, type, sK27: mworld > mworld).
% 130.39/20.03 thf(f4811,plain,(
% 130.39/20.03 $false),
% 130.39/20.03 inference(avatar_sat_refutation,[status(thm)],[f1048,f2396,f2551,f2927,f2990,f3111,f3142,f3401,f3930,f4004,f4079,f4218,f4483,f4484,f4616,f4740,f4745,f4810])).
% 130.39/20.03 thf(f4810,plain,(
% 130.39/20.03 ~spl0_14),
% 130.39/20.03 inference(avatar_contradiction_clause,[status(thm)],[f4809])).
% 130.39/20.03 thf(f4809,plain,(
% 130.39/20.03 $false | ~spl0_14),
% 130.39/20.03 inference(trivial_inequality_removal,[status(thm)],[f4806])).
% 130.39/20.03 thf(f4806,plain,(
% 130.39/20.03 ($true = $false) | ~spl0_14),
% 130.39/20.03 inference(superposition,[status(thm)],[f2702,f4798])).
% 130.39/20.03 thf(f4798,plain,(
% 130.39/20.03 ( ! [X17 : mworld] : (((v5 @ X17) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f4797])).
% 130.39/20.03 thf(f4797,plain,(
% 130.39/20.03 ( ! [X17 : mworld] : ((($true => (v5 @ X17)) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f4796,f358])).
% 130.39/20.03 thf(f358,plain,(
% 130.39/20.03 ( ! [X2 : mworld,X1 : mworld] : (((mrel @ X2 @ X1) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f357])).
% 130.39/20.03 thf(f357,plain,(
% 130.39/20.03 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: (mrel @ Y0 @ X1)) @ X2) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f356])).
% 130.39/20.03 thf(f356,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: (mrel @ Y0 @ X1))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f355])).
% 130.39/20.03 thf(f355,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (mrel @ Y1 @ Y0)))) @ X1) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f226])).
% 130.39/20.03 thf(f226,plain,(
% 130.39/20.03 ($true = (!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (mrel @ Y1 @ Y0))))))),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f93])).
% 130.39/20.03 thf(f93,plain,(
% 130.39/20.03 ($true = (!! @ mworld @ (^[Y0 : mworld]: (!! @ mworld @ (^[Y1 : mworld]: (mrel @ Y1 @ Y0))))))),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f92])).
% 130.39/20.03 thf(f92,plain,(
% 130.39/20.03 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 130.39/20.03 inference(rectify,[status(thm)],[f9])).
% 130.39/20.03 thf(f9,axiom,(
% 130.39/20.03 ! [X2 : mworld,X4 : mworld] : (mrel @ X2 @ X4)),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mrel_universal)).
% 130.39/20.03 thf(f4796,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X17 : mworld] : ((((mrel @ X16 @ X17) => (v5 @ X17)) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f4795])).
% 130.39/20.03 thf(f4795,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X17 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (v5 @ Y0))) @ X17))) ) | ~spl0_14),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f4788])).
% 130.39/20.03 thf(f4788,plain,(
% 130.39/20.03 ( ! [X16 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (v5 @ Y0)))) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f4787])).
% 130.39/20.03 thf(f4787,plain,(
% 130.39/20.03 ( ! [X16 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (v5 @ Y0))))) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f4786,f358])).
% 130.39/20.03 thf(f4786,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X15 : mworld] : (($true = ((mrel @ X15 @ X16) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (v5 @ Y0))))))) ) | ~spl0_14),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f4785])).
% 130.39/20.03 thf(f4785,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v5 @ Y1)))))) @ X16) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f4777])).
% 130.39/20.03 thf(f4777,plain,(
% 130.39/20.03 ( ! [X15 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v5 @ Y1))))))) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f4776])).
% 130.39/20.03 thf(f4776,plain,(
% 130.39/20.03 ( ! [X15 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v5 @ Y1)))))))) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f4775,f358])).
% 130.39/20.03 thf(f4775,plain,(
% 130.39/20.03 ( ! [X14 : mworld,X15 : mworld] : (($true = ((mrel @ X14 @ X15) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v5 @ Y1)))))))))) ) | ~spl0_14),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f4774])).
% 130.39/20.03 thf(f4774,plain,(
% 130.39/20.03 ( ! [X14 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v5 @ Y2))))))))) @ X15) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2124])).
% 130.39/20.03 thf(f2124,plain,(
% 130.39/20.03 ( ! [X14 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v5 @ Y2)))))))))) = $true)) ) | ~spl0_14),
% 130.39/20.03 inference(avatar_component_clause,[status(thm)],[f2123])).
% 130.39/20.03 thf(f2123,definition,(
% 130.39/20.03 spl0_14 <=> ! [X14 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v5 @ Y2)))))))))) = $true)),
% 130.39/20.03 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 130.39/20.03 thf(f2702,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : (($false = (v5 @ (sK27 @ X23)))) )),
% 130.39/20.03 inference(not_proxy_clausification,[status(thm)],[f2695])).
% 130.39/20.03 thf(f2695,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : (((~ (v5 @ (sK27 @ X23))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2694])).
% 130.39/20.03 thf(f2694,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : (($true = ((~ (v5 @ (sK27 @ X23))) & $true))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2693,f358])).
% 130.39/20.03 thf(f2693,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : (($true = ((~ (v5 @ (sK27 @ X23))) & (mrel @ X23 @ (sK27 @ X23))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2692])).
% 130.39/20.03 thf(f2692,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : ((((^[Y0 : mworld]: ((~ (v5 @ Y0)) & (mrel @ X23 @ Y0))) @ (sK27 @ X23)) = $true)) )),
% 130.39/20.03 inference(sigma_clausification,[status(thm)],[f2643])).
% 130.39/20.03 thf(f2643,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v5 @ Y0)) & (mrel @ X23 @ Y0)))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2639])).
% 130.39/20.03 thf(f2639,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v5 @ Y0) & (mrel @ X23 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v5 @ Y0)) & (mrel @ X23 @ Y0))))))) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2632])).
% 130.39/20.03 thf(f2632,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (?? @ mworld @ (mrel @ Y3))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v5 @ Y0) & (mrel @ X23 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v5 @ Y0)) & (mrel @ X23 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2631])).
% 130.39/20.03 thf(f2631,plain,(
% 130.39/20.03 ( ! [X23 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (?? @ mworld @ (mrel @ Y3))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v5 @ Y0) & (mrel @ X23 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v5 @ Y0)) & (mrel @ X23 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2630,f358])).
% 130.39/20.03 thf(f2630,plain,(
% 130.39/20.03 ( ! [X22 : mworld,X23 : mworld] : (($true = ((mrel @ X22 @ X23) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (?? @ mworld @ (mrel @ Y3))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v5 @ Y0) & (mrel @ X23 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v5 @ Y0)) & (mrel @ X23 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2629])).
% 130.39/20.03 thf(f2629,plain,(
% 130.39/20.03 ( ! [X22 : mworld,X23 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (?? @ mworld @ (mrel @ Y4))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v5 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v5 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X23) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2534])).
% 130.39/20.03 thf(f2534,plain,(
% 130.39/20.03 ( ! [X22 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (?? @ mworld @ (mrel @ Y4))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v5 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v5 @ Y1)) & (mrel @ Y0 @ Y1))))))))))) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2527])).
% 130.39/20.03 thf(f2527,plain,(
% 130.39/20.03 ( ! [X22 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (?? @ mworld @ (mrel @ Y4))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v5 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v5 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2526])).
% 130.39/20.03 thf(f2526,plain,(
% 130.39/20.03 ( ! [X22 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (?? @ mworld @ (mrel @ Y4))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v5 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v5 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2525,f358])).
% 130.39/20.03 thf(f2525,plain,(
% 130.39/20.03 ( ! [X21 : mworld,X22 : mworld] : (($true = ((mrel @ X21 @ X22) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (?? @ mworld @ (mrel @ Y4))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v5 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v5 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2524])).
% 130.39/20.03 thf(f2524,plain,(
% 130.39/20.03 ( ! [X21 : mworld,X22 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (?? @ mworld @ (mrel @ Y5))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v5 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v5 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v6 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v6 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X22) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2518])).
% 130.39/20.03 thf(f2518,plain,(
% 130.39/20.03 ( ! [X21 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (?? @ mworld @ (mrel @ Y5))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v5 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v5 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v6 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v6 @ Y1)) & (mrel @ Y0 @ Y1))))))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2517])).
% 130.39/20.03 thf(f2517,plain,(
% 130.39/20.03 ( ! [X21 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (?? @ mworld @ (mrel @ Y5))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v5 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v5 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v6 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v6 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true) = $true)) )),
% 130.39/20.03 inference(backward_demodulation,[status(thm)],[f2490,f2515])).
% 130.39/20.03 thf(f2515,plain,(
% 130.39/20.03 ( ! [X21 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v7 @ Y0)) & (mrel @ X21 @ Y0))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2490])).
% 130.39/20.03 thf(f2490,plain,(
% 130.39/20.03 ( ! [X21 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (?? @ mworld @ (mrel @ Y5))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v5 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v5 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v6 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v6 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v7 @ Y0)) & (mrel @ X21 @ Y0)))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2489])).
% 130.39/20.03 thf(f2489,plain,(
% 130.39/20.03 ( ! [X21 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (?? @ mworld @ (mrel @ Y5))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v5 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v5 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v6 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v6 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v7 @ Y0)) & (mrel @ X21 @ Y0))))))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2488,f358])).
% 130.39/20.03 thf(f2488,plain,(
% 130.39/20.03 ( ! [X21 : mworld,X20 : mworld] : ((((mrel @ X20 @ X21) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (?? @ mworld @ (mrel @ Y5))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v5 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v5 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v6 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v6 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v7 @ Y0)) & (mrel @ X21 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2487])).
% 130.39/20.03 thf(f2487,plain,(
% 130.39/20.03 ( ! [X21 : mworld,X20 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X21))) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2482])).
% 130.39/20.03 thf(f2482,plain,(
% 130.39/20.03 ( ! [X20 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2481])).
% 130.39/20.03 thf(f2481,plain,(
% 130.39/20.03 ( ! [X20 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true) = $true)) )),
% 130.39/20.03 inference(backward_demodulation,[status(thm)],[f2474,f2479])).
% 130.39/20.03 thf(f2479,plain,(
% 130.39/20.03 ( ! [X20 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2474])).
% 130.39/20.03 thf(f2474,plain,(
% 130.39/20.03 ( ! [X20 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0)))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2473])).
% 130.39/20.03 thf(f2473,plain,(
% 130.39/20.03 ( ! [X20 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2472,f358])).
% 130.39/20.03 thf(f2472,plain,(
% 130.39/20.03 ( ! [X19 : mworld,X20 : mworld] : (($true = ((mrel @ X19 @ X20) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (?? @ mworld @ (mrel @ Y6))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v5 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v5 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v6 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v6 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v7 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v7 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v8 @ Y0) & (mrel @ X20 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2471])).
% 130.39/20.03 thf(f2471,plain,(
% 130.39/20.03 ( ! [X19 : mworld,X20 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X20) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2466])).
% 130.39/20.03 thf(f2466,plain,(
% 130.39/20.03 ( ! [X19 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1))))))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2465])).
% 130.39/20.03 thf(f2465,plain,(
% 130.39/20.03 ( ! [X19 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2464,f1603])).
% 130.39/20.03 thf(f1603,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : (((?? @ mworld @ (mrel @ X1)) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f1601])).
% 130.39/20.03 thf(f1601,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (?? @ mworld @ (mrel @ Y25))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v5 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v5 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v6 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v6 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v7 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v7 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v8 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v8 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v13 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v13 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v14 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v14 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v15 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v15 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v16 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v16 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v21 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v21 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v22 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v22 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v23 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v23 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v24 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v24 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X1))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1600])).
% 130.39/20.03 thf(f1600,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (?? @ mworld @ (mrel @ Y25))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v5 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v5 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v6 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v6 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v7 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v7 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v8 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v8 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v13 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v13 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v14 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v14 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v15 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v15 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v16 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v16 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v21 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v21 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v22 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v22 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v23 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v23 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v24 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v24 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X1)))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f1599,f358])).
% 130.39/20.03 thf(f1599,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (?? @ mworld @ (mrel @ Y25))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v5 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v5 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v6 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v6 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v7 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v7 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v8 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v8 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v13 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v13 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v14 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v14 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v15 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v15 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v16 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v16 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v21 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v21 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v22 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v22 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v23 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v23 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v24 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v24 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X1)))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f1598])).
% 130.39/20.03 thf(f1598,plain,(
% 130.39/20.03 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (mrel @ Y26))))) & (?? @ mworld @ (mrel @ Y25)))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X1) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f1597])).
% 130.39/20.03 thf(f1597,plain,(
% 130.39/20.03 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (mrel @ Y26))))) & (?? @ mworld @ (mrel @ Y25)))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))))),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1596])).
% 130.39/20.03 thf(f1596,plain,(
% 130.39/20.03 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (mrel @ Y26))))) & (?? @ mworld @ (mrel @ Y25)))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true) = $true)),
% 130.39/20.03 inference(backward_demodulation,[status(thm)],[f353,f1594])).
% 130.39/20.03 thf(f1594,plain,(
% 130.39/20.03 ((?? @ mworld @ (mrel @ mactual)) = $true)),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f353])).
% 130.39/20.03 thf(f353,plain,(
% 130.39/20.03 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (mrel @ Y26))))) & (?? @ mworld @ (mrel @ Y25)))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ mactual))))),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f352])).
% 130.39/20.03 thf(f352,plain,(
% 130.39/20.03 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (^[Y27 : mworld]: (mrel @ Y26 @ Y27)))))) & (?? @ mworld @ (^[Y26 : mworld]: (mrel @ Y25 @ Y26))))))) & (?? @ mworld @ (^[Y25 : mworld]: (mrel @ Y24 @ Y25))))))) & (?? @ mworld @ (^[Y24 : mworld]: (mrel @ Y23 @ Y24))))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (^[Y19 : mworld]: (mrel @ Y18 @ Y19))))))) & (?? @ mworld @ (^[Y18 : mworld]: (mrel @ Y17 @ Y18))))))) & (?? @ mworld @ (^[Y17 : mworld]: (mrel @ Y16 @ Y17))))))) & (?? @ mworld @ (^[Y16 : mworld]: (mrel @ Y15 @ Y16))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (^[Y11 : mworld]: (mrel @ Y10 @ Y11))))))) & (?? @ mworld @ (^[Y10 : mworld]: (mrel @ Y9 @ Y10))))))) & (?? @ mworld @ (^[Y9 : mworld]: (mrel @ Y8 @ Y9))))))) & (?? @ mworld @ (^[Y8 : mworld]: (mrel @ Y7 @ Y8))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (^[Y3 : mworld]: (mrel @ Y2 @ Y3))))))) & (?? @ mworld @ (^[Y2 : mworld]: (mrel @ Y1 @ Y2))))))) & (?? @ mworld @ (^[Y1 : mworld]: (mrel @ Y0 @ Y1))))))) & (?? @ mworld @ (mrel @ mactual))) = $true)),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f351])).
% 130.39/20.03 thf(f351,plain,(
% 130.39/20.03 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (^[Y27 : mworld]: ($true & (mrel @ Y26 @ Y27))))))) & (?? @ mworld @ (^[Y26 : mworld]: ($true & (mrel @ Y25 @ Y26)))))))) & (?? @ mworld @ (^[Y25 : mworld]: ($true & (mrel @ Y24 @ Y25)))))))) & (?? @ mworld @ (^[Y24 : mworld]: ($true & (mrel @ Y23 @ Y24)))))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (^[Y19 : mworld]: ($true & (mrel @ Y18 @ Y19)))))))) & (?? @ mworld @ (^[Y18 : mworld]: ($true & (mrel @ Y17 @ Y18)))))))) & (?? @ mworld @ (^[Y17 : mworld]: ($true & (mrel @ Y16 @ Y17)))))))) & (?? @ mworld @ (^[Y16 : mworld]: ($true & (mrel @ Y15 @ Y16)))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (^[Y11 : mworld]: ($true & (mrel @ Y10 @ Y11)))))))) & (?? @ mworld @ (^[Y10 : mworld]: ($true & (mrel @ Y9 @ Y10)))))))) & (?? @ mworld @ (^[Y9 : mworld]: ($true & (mrel @ Y8 @ Y9)))))))) & (?? @ mworld @ (^[Y8 : mworld]: ($true & (mrel @ Y7 @ Y8)))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (^[Y3 : mworld]: ($true & (mrel @ Y2 @ Y3)))))))) & (?? @ mworld @ (^[Y2 : mworld]: ($true & (mrel @ Y1 @ Y2)))))))) & (?? @ mworld @ (^[Y1 : mworld]: ($true & (mrel @ Y0 @ Y1)))))))) & (?? @ mworld @ (mrel @ mactual))))),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f350])).
% 130.39/20.03 thf(f350,plain,(
% 130.39/20.03 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (^[Y27 : mworld]: ($true & (mrel @ Y26 @ Y27))))))) & (?? @ mworld @ (^[Y26 : mworld]: ($true & (mrel @ Y25 @ Y26)))))))) & (?? @ mworld @ (^[Y25 : mworld]: ($true & (mrel @ Y24 @ Y25)))))))) & (?? @ mworld @ (^[Y24 : mworld]: ($true & (mrel @ Y23 @ Y24)))))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (^[Y19 : mworld]: ($true & (mrel @ Y18 @ Y19)))))))) & (?? @ mworld @ (^[Y18 : mworld]: ($true & (mrel @ Y17 @ Y18)))))))) & (?? @ mworld @ (^[Y17 : mworld]: ($true & (mrel @ Y16 @ Y17)))))))) & (?? @ mworld @ (^[Y16 : mworld]: ($true & (mrel @ Y15 @ Y16)))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (^[Y11 : mworld]: ($true & (mrel @ Y10 @ Y11)))))))) & (?? @ mworld @ (^[Y10 : mworld]: ($true & (mrel @ Y9 @ Y10)))))))) & (?? @ mworld @ (^[Y9 : mworld]: ($true & (mrel @ Y8 @ Y9)))))))) & (?? @ mworld @ (^[Y8 : mworld]: ($true & (mrel @ Y7 @ Y8)))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (^[Y3 : mworld]: ($true & (mrel @ Y2 @ Y3)))))))) & (?? @ mworld @ (^[Y2 : mworld]: ($true & (mrel @ Y1 @ Y2)))))))) & (?? @ mworld @ (^[Y1 : mworld]: ($true & (mrel @ Y0 @ Y1)))))))) & (?? @ mworld @ (^[Y0 : mworld]: (mrel @ mactual @ Y0)))))),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f349])).
% 130.39/20.03 thf(f349,plain,(
% 130.39/20.03 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => ((!! @ mworld @ (^[Y26 : mworld]: ((mrel @ Y25 @ Y26) => (?? @ mworld @ (^[Y27 : mworld]: ($true & (mrel @ Y26 @ Y27))))))) & (?? @ mworld @ (^[Y26 : mworld]: ($true & (mrel @ Y25 @ Y26)))))))) & (?? @ mworld @ (^[Y25 : mworld]: ($true & (mrel @ Y24 @ Y25)))))))) & (?? @ mworld @ (^[Y24 : mworld]: ($true & (mrel @ Y23 @ Y24)))))))) & ((?? @ mworld @ (^[Y23 : mworld]: ((v5 @ Y23) & (mrel @ Y22 @ Y23)))) & (?? @ mworld @ (^[Y23 : mworld]: ((~ (v5 @ Y23)) & (mrel @ Y22 @ Y23))))))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v6 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v6 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v7 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v7 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v8 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v8 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & (?? @ mworld @ (^[Y19 : mworld]: ($true & (mrel @ Y18 @ Y19)))))))) & (?? @ mworld @ (^[Y18 : mworld]: ($true & (mrel @ Y17 @ Y18)))))))) & (?? @ mworld @ (^[Y17 : mworld]: ($true & (mrel @ Y16 @ Y17)))))))) & (?? @ mworld @ (^[Y16 : mworld]: ($true & (mrel @ Y15 @ Y16)))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v13 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v13 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v14 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v14 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v15 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v15 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v16 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v16 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (^[Y11 : mworld]: ($true & (mrel @ Y10 @ Y11)))))))) & (?? @ mworld @ (^[Y10 : mworld]: ($true & (mrel @ Y9 @ Y10)))))))) & (?? @ mworld @ (^[Y9 : mworld]: ($true & (mrel @ Y8 @ Y9)))))))) & (?? @ mworld @ (^[Y8 : mworld]: ($true & (mrel @ Y7 @ Y8)))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v21 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v21 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v22 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v22 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v23 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v23 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v24 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v24 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (^[Y3 : mworld]: ($true & (mrel @ Y2 @ Y3)))))))) & (?? @ mworld @ (^[Y2 : mworld]: ($true & (mrel @ Y1 @ Y2)))))))) & (?? @ mworld @ (^[Y1 : mworld]: ($true & (mrel @ Y0 @ Y1)))))))) & (?? @ mworld @ (^[Y0 : mworld]: ($true & (mrel @ mactual @ Y0))))) = $true)),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f295])).
% 130.39/20.03 thf(f295,plain,(
% 130.39/20.03 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true)))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v5) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v5))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v6) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v6))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v7) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v7))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v8) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v8))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v13) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v13))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v14) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v14))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v15) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v15))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v16) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v16))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v21) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v21))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v22) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v22))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v23) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v23))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ v24) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v24))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))) @ (^[Y0 : mworld]: ($true))))) = $true)),
% 130.39/20.03 inference(definition_unfolding,[status(thm)],[f243,f207,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f198,f201,f209,f209,f209,f209,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f209,f209,f209,f209,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f209,f209,f209,f209,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f198,f209,f209,f208,f209,f209,f209,f209])).
% 130.39/20.03 thf(f208,plain,(
% 130.39/20.03 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f110])).
% 130.39/20.03 thf(f110,plain,(
% 130.39/20.03 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f109])).
% 130.39/20.03 thf(f109,plain,(
% 130.39/20.03 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 130.39/20.03 inference(rectify,[status(thm)],[f2])).
% 130.39/20.03 thf(f2,axiom,(
% 130.39/20.03 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mnot_def)).
% 130.39/20.03 thf(f209,plain,(
% 130.39/20.03 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f184])).
% 130.39/20.03 thf(f184,plain,(
% 130.39/20.03 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f183])).
% 130.39/20.03 thf(f183,plain,(
% 130.39/20.03 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))))),
% 130.39/20.03 inference(rectify,[status(thm)],[f8])).
% 130.39/20.03 thf(f8,axiom,(
% 130.39/20.03 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))))),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mdia_def)).
% 130.39/20.03 thf(f201,plain,(
% 130.39/20.03 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f178])).
% 130.39/20.03 thf(f178,plain,(
% 130.39/20.03 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f177])).
% 130.39/20.03 thf(f177,plain,(
% 130.39/20.03 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 130.39/20.03 inference(rectify,[status(thm)],[f7])).
% 130.39/20.03 thf(f7,axiom,(
% 130.39/20.03 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mbox_def)).
% 130.39/20.03 thf(f198,plain,(
% 130.39/20.03 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f168])).
% 130.39/20.03 thf(f168,plain,(
% 130.39/20.03 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f167])).
% 130.39/20.03 thf(f167,plain,(
% 130.39/20.03 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 130.39/20.03 inference(rectify,[status(thm)],[f3])).
% 130.39/20.03 thf(f3,axiom,(
% 130.39/20.03 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mand_def)).
% 130.39/20.03 thf(f207,plain,(
% 130.39/20.03 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f94])).
% 130.39/20.03 thf(f94,plain,(
% 130.39/20.03 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f1])).
% 130.39/20.03 thf(f1,axiom,(
% 130.39/20.03 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mlocal_def)).
% 130.39/20.03 thf(f243,plain,(
% 130.39/20.03 ((mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[Y0 : mworld]: ($true)))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mand @ (mdia @ v5) @ (mdia @ (mnot @ v5))))) @ (mand @ (mdia @ v6) @ (mdia @ (mnot @ v6))))) @ (mand @ (mdia @ v7) @ (mdia @ (mnot @ v7))))) @ (mand @ (mdia @ v8) @ (mdia @ (mnot @ v8))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mand @ (mdia @ v13) @ (mdia @ (mnot @ v13))))) @ (mand @ (mdia @ v14) @ (mdia @ (mnot @ v14))))) @ (mand @ (mdia @ v15) @ (mdia @ (mnot @ v15))))) @ (mand @ (mdia @ v16) @ (mdia @ (mnot @ v16))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mand @ (mdia @ v21) @ (mdia @ (mnot @ v21))))) @ (mand @ (mdia @ v22) @ (mdia @ (mnot @ v22))))) @ (mand @ (mdia @ v23) @ (mdia @ (mnot @ v23))))) @ (mand @ (mdia @ v24) @ (mdia @ (mnot @ v24))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) = $true)),
% 130.39/20.03 inference(cnf_transformation,[status(thm)],[f116])).
% 130.39/20.03 thf(f116,plain,(
% 130.39/20.03 ((mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[Y0 : mworld]: ($true)))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mand @ (mdia @ v5) @ (mdia @ (mnot @ v5))))) @ (mand @ (mdia @ v6) @ (mdia @ (mnot @ v6))))) @ (mand @ (mdia @ v7) @ (mdia @ (mnot @ v7))))) @ (mand @ (mdia @ v8) @ (mdia @ (mnot @ v8))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mand @ (mdia @ v13) @ (mdia @ (mnot @ v13))))) @ (mand @ (mdia @ v14) @ (mdia @ (mnot @ v14))))) @ (mand @ (mdia @ v15) @ (mdia @ (mnot @ v15))))) @ (mand @ (mdia @ v16) @ (mdia @ (mnot @ v16))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mand @ (mdia @ v21) @ (mdia @ (mnot @ v21))))) @ (mand @ (mdia @ v22) @ (mdia @ (mnot @ v22))))) @ (mand @ (mdia @ v23) @ (mdia @ (mnot @ v23))))) @ (mand @ (mdia @ v24) @ (mdia @ (mnot @ v24))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) @ (mdia @ (^[Y0 : mworld]: ($true))))) = $true)),
% 130.39/20.03 inference(fool_elimination,[status(thm)],[f115])).
% 130.39/20.03 thf(f115,plain,(
% 130.39/20.03 (mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[X0 : mworld] : ($true)))) @ (mdia @ (^[X1 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X3 : mworld] : ($true))))) @ (mand @ (mdia @ v5) @ (mdia @ (mnot @ v5))))) @ (mand @ (mdia @ v6) @ (mdia @ (mnot @ v6))))) @ (mand @ (mdia @ v7) @ (mdia @ (mnot @ v7))))) @ (mand @ (mdia @ v8) @ (mdia @ (mnot @ v8))))) @ (mdia @ (^[X4 : mworld] : ($true))))) @ (mdia @ (^[X5 : mworld] : ($true))))) @ (mdia @ (^[X6 : mworld] : ($true))))) @ (mdia @ (^[X7 : mworld] : ($true))))) @ (mand @ (mdia @ v13) @ (mdia @ (mnot @ v13))))) @ (mand @ (mdia @ v14) @ (mdia @ (mnot @ v14))))) @ (mand @ (mdia @ v15) @ (mdia @ (mnot @ v15))))) @ (mand @ (mdia @ v16) @ (mdia @ (mnot @ v16))))) @ (mdia @ (^[X8 : mworld] : ($true))))) @ (mdia @ (^[X9 : mworld] : ($true))))) @ (mdia @ (^[X10 : mworld] : ($true))))) @ (mdia @ (^[X11 : mworld] : ($true))))) @ (mand @ (mdia @ v21) @ (mdia @ (mnot @ v21))))) @ (mand @ (mdia @ v22) @ (mdia @ (mnot @ v22))))) @ (mand @ (mdia @ v23) @ (mdia @ (mnot @ v23))))) @ (mand @ (mdia @ v24) @ (mdia @ (mnot @ v24))))) @ (mdia @ (^[X12 : mworld] : ($true))))) @ (mdia @ (^[X13 : mworld] : ($true))))) @ (mdia @ (^[X14 : mworld] : ($true))))) @ (mdia @ (^[X15 : mworld] : ($true)))))),
% 130.39/20.03 inference(rectify,[status(thm)],[f60])).
% 130.39/20.03 thf(f60,axiom,(
% 130.39/20.03 (mlocal @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mand @ (mbox @ (mdia @ (^[X2 : mworld] : ($true)))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mand @ (mdia @ v5) @ (mdia @ (mnot @ v5))))) @ (mand @ (mdia @ v6) @ (mdia @ (mnot @ v6))))) @ (mand @ (mdia @ v7) @ (mdia @ (mnot @ v7))))) @ (mand @ (mdia @ v8) @ (mdia @ (mnot @ v8))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mand @ (mdia @ v13) @ (mdia @ (mnot @ v13))))) @ (mand @ (mdia @ v14) @ (mdia @ (mnot @ v14))))) @ (mand @ (mdia @ v15) @ (mdia @ (mnot @ v15))))) @ (mand @ (mdia @ v16) @ (mdia @ (mnot @ v16))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mand @ (mdia @ v21) @ (mdia @ (mnot @ v21))))) @ (mand @ (mdia @ v22) @ (mdia @ (mnot @ v22))))) @ (mand @ (mdia @ v23) @ (mdia @ (mnot @ v23))))) @ (mand @ (mdia @ v24) @ (mdia @ (mnot @ v24))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true))))) @ (mdia @ (^[X2 : mworld] : ($true)))))),
% 130.39/20.03 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',alt1)).
% 130.39/20.03 thf(f2464,plain,(
% 130.39/20.03 ( ! [X19 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X19))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2463])).
% 130.39/20.03 thf(f2463,plain,(
% 130.39/20.03 ( ! [X19 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X19)))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2462,f358])).
% 130.39/20.03 thf(f2462,plain,(
% 130.39/20.03 ( ! [X18 : mworld,X19 : mworld] : (($true = ((mrel @ X18 @ X19) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (?? @ mworld @ (mrel @ Y7))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v5 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v5 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v6 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v6 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v7 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v7 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v8 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v8 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X19)))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2461])).
% 130.39/20.03 thf(f2461,plain,(
% 130.39/20.03 ( ! [X18 : mworld,X19 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (?? @ mworld @ (mrel @ Y8))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v5 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v5 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v6 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v6 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v7 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v7 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v8 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v8 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0))))) @ X19) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2454])).
% 130.39/20.03 thf(f2454,plain,(
% 130.39/20.03 ( ! [X18 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (?? @ mworld @ (mrel @ Y8))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v5 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v5 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v6 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v6 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v7 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v7 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v8 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v8 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2453])).
% 130.39/20.03 thf(f2453,plain,(
% 130.39/20.03 ( ! [X18 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (?? @ mworld @ (mrel @ Y8))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v5 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v5 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v6 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v6 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v7 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v7 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v8 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v8 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2452,f1603])).
% 130.39/20.03 thf(f2452,plain,(
% 130.39/20.03 ( ! [X18 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (?? @ mworld @ (mrel @ Y8))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v5 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v5 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v6 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v6 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v7 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v7 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v8 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v8 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X18))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2451])).
% 130.39/20.03 thf(f2451,plain,(
% 130.39/20.03 ( ! [X18 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (?? @ mworld @ (mrel @ Y8))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v5 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v5 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v6 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v6 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v7 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v7 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v8 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v8 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X18)))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2450,f358])).
% 130.39/20.03 thf(f2450,plain,(
% 130.39/20.03 ( ! [X18 : mworld,X17 : mworld] : (($true = ((mrel @ X17 @ X18) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (?? @ mworld @ (mrel @ Y8))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v5 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v5 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v6 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v6 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v7 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v7 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v8 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v8 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X18)))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2449])).
% 130.39/20.03 thf(f2449,plain,(
% 130.39/20.03 ( ! [X18 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X17 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (?? @ mworld @ (mrel @ Y9))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v5 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v5 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v6 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v6 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v7 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v7 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v8 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v8 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X18) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2447])).
% 130.39/20.03 thf(f2447,plain,(
% 130.39/20.03 ( ! [X17 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (?? @ mworld @ (mrel @ Y9))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v5 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v5 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v6 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v6 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v7 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v7 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v8 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v8 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2446])).
% 130.39/20.03 thf(f2446,plain,(
% 130.39/20.03 ( ! [X17 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (?? @ mworld @ (mrel @ Y9))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v5 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v5 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v6 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v6 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v7 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v7 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v8 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v8 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2445,f1603])).
% 130.39/20.03 thf(f2445,plain,(
% 130.39/20.03 ( ! [X17 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (?? @ mworld @ (mrel @ Y9))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v5 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v5 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v6 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v6 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v7 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v7 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v8 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v8 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X17))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2444])).
% 130.39/20.03 thf(f2444,plain,(
% 130.39/20.03 ( ! [X17 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (?? @ mworld @ (mrel @ Y9))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v5 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v5 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v6 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v6 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v7 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v7 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v8 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v8 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X17)))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2443,f358])).
% 130.39/20.03 thf(f2443,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X17 : mworld] : ((((mrel @ X16 @ X17) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (?? @ mworld @ (mrel @ Y9))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v5 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v5 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v6 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v6 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v7 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v7 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v8 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v8 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X17)))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2442])).
% 130.39/20.03 thf(f2442,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X17 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (?? @ mworld @ (mrel @ Y10))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v5 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v5 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v6 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v6 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v7 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v7 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v8 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v8 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X17))) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2437])).
% 130.39/20.03 thf(f2437,plain,(
% 130.39/20.03 ( ! [X16 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (?? @ mworld @ (mrel @ Y10))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v5 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v5 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v6 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v6 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v7 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v7 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v8 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v8 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2436])).
% 130.39/20.03 thf(f2436,plain,(
% 130.39/20.03 ( ! [X16 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (?? @ mworld @ (mrel @ Y10))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v5 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v5 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v6 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v6 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v7 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v7 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v8 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v8 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2435,f1603])).
% 130.39/20.03 thf(f2435,plain,(
% 130.39/20.03 ( ! [X16 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (?? @ mworld @ (mrel @ Y10))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v5 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v5 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v6 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v6 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v7 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v7 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v8 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v8 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X16))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2434])).
% 130.39/20.03 thf(f2434,plain,(
% 130.39/20.03 ( ! [X16 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (?? @ mworld @ (mrel @ Y10))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v5 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v5 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v6 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v6 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v7 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v7 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v8 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v8 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X16)))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2433,f358])).
% 130.39/20.03 thf(f2433,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X15 : mworld] : (($true = ((mrel @ X15 @ X16) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (?? @ mworld @ (mrel @ Y10))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v5 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v5 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v6 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v6 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v7 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v7 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v8 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v8 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X16)))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2432])).
% 130.39/20.03 thf(f2432,plain,(
% 130.39/20.03 ( ! [X16 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X15 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (?? @ mworld @ (mrel @ Y11))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v5 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v5 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v6 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v6 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v7 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v7 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v8 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v8 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X16) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2294])).
% 130.39/20.03 thf(f2294,plain,(
% 130.39/20.03 ( ! [X15 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (?? @ mworld @ (mrel @ Y11))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v5 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v5 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v6 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v6 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v7 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v7 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v8 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v8 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2288])).
% 130.39/20.03 thf(f2288,plain,(
% 130.39/20.03 ( ! [X15 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (?? @ mworld @ (mrel @ Y11))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v5 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v5 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v6 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v6 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v7 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v7 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v8 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v8 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2287])).
% 130.39/20.03 thf(f2287,plain,(
% 130.39/20.03 ( ! [X15 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (?? @ mworld @ (mrel @ Y11))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v5 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v5 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v6 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v6 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v7 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v7 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v8 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v8 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2286,f358])).
% 130.39/20.03 thf(f2286,plain,(
% 130.39/20.03 ( ! [X14 : mworld,X15 : mworld] : (($true = ((mrel @ X14 @ X15) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (?? @ mworld @ (mrel @ Y11))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v5 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v5 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v6 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v6 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v7 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v7 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v8 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v8 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2285])).
% 130.39/20.03 thf(f2285,plain,(
% 130.39/20.03 ( ! [X14 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (?? @ mworld @ (mrel @ Y12))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v5 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v5 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v6 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v6 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v7 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v7 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v8 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v8 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v13 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v13 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X15) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2257])).
% 130.39/20.03 thf(f2257,plain,(
% 130.39/20.03 ( ! [X14 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (?? @ mworld @ (mrel @ Y12))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v5 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v5 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v6 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v6 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v7 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v7 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v8 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v8 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v13 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v13 @ Y1)) & (mrel @ Y0 @ Y1))))))))))) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2177])).
% 130.39/20.03 thf(f2177,plain,(
% 130.39/20.03 ( ! [X14 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (?? @ mworld @ (mrel @ Y12))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v5 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v5 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v6 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v6 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v7 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v7 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v8 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v8 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v13 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v13 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2176])).
% 130.39/20.03 thf(f2176,plain,(
% 130.39/20.03 ( ! [X14 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (?? @ mworld @ (mrel @ Y12))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v5 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v5 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v6 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v6 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v7 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v7 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v8 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v8 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v13 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v13 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2175,f358])).
% 130.39/20.03 thf(f2175,plain,(
% 130.39/20.03 ( ! [X14 : mworld,X13 : mworld] : (($true = ((mrel @ X13 @ X14) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (?? @ mworld @ (mrel @ Y12))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v5 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v5 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v6 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v6 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v7 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v7 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v8 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v8 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v13 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v13 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2174])).
% 130.39/20.03 thf(f2174,plain,(
% 130.39/20.03 ( ! [X14 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (?? @ mworld @ (mrel @ Y13))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v5 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v5 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v6 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v6 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v7 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v7 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v8 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v8 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v13 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v13 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v14 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v14 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X14) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2169])).
% 130.39/20.03 thf(f2169,plain,(
% 130.39/20.03 ( ! [X13 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (?? @ mworld @ (mrel @ Y13))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v5 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v5 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v6 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v6 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v7 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v7 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v8 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v8 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v13 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v13 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v14 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v14 @ Y1)) & (mrel @ Y0 @ Y1))))))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2168])).
% 130.39/20.03 thf(f2168,plain,(
% 130.39/20.03 ( ! [X13 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (?? @ mworld @ (mrel @ Y13))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v5 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v5 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v6 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v6 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v7 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v7 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v8 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v8 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v13 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v13 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v14 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v14 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true) = $true)) )),
% 130.39/20.03 inference(backward_demodulation,[status(thm)],[f2161,f2166])).
% 130.39/20.03 thf(f2166,plain,(
% 130.39/20.03 ( ! [X13 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v15 @ Y0)) & (mrel @ X13 @ Y0))))))) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2161])).
% 130.39/20.03 thf(f2161,plain,(
% 130.39/20.03 ( ! [X13 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (?? @ mworld @ (mrel @ Y13))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v5 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v5 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v6 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v6 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v7 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v7 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v8 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v8 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v13 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v13 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v14 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v14 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v15 @ Y0)) & (mrel @ X13 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2160])).
% 130.39/20.03 thf(f2160,plain,(
% 130.39/20.03 ( ! [X13 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (?? @ mworld @ (mrel @ Y13))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v5 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v5 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v6 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v6 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v7 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v7 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v8 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v8 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v13 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v13 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v14 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v14 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v15 @ Y0)) & (mrel @ X13 @ Y0))))))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2159,f358])).
% 130.39/20.03 thf(f2159,plain,(
% 130.39/20.03 ( ! [X12 : mworld,X13 : mworld] : (($true = ((mrel @ X12 @ X13) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (?? @ mworld @ (mrel @ Y13))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v5 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v5 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v6 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v6 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v7 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v7 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v8 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v8 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v13 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v13 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v14 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v14 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v15 @ Y0)) & (mrel @ X13 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2158])).
% 130.39/20.03 thf(f2158,plain,(
% 130.39/20.03 ( ! [X12 : mworld,X13 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (?? @ mworld @ (mrel @ Y14))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v5 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v5 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v6 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v6 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v7 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v7 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v8 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v8 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v13 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v13 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v14 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v14 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v15 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v15 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X13))) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2157])).
% 130.39/20.03 thf(f2157,plain,(
% 130.39/20.03 ( ! [X12 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (?? @ mworld @ (mrel @ Y14))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v5 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v5 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v6 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v6 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v7 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v7 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v8 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v8 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v13 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v13 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v14 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v14 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v15 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v15 @ Y1)) & (mrel @ Y0 @ Y1))))))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2156])).
% 130.39/20.03 thf(f2156,plain,(
% 130.39/20.03 ( ! [X12 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (?? @ mworld @ (mrel @ Y14))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v5 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v5 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v6 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v6 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v7 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v7 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v8 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v8 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v13 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v13 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v14 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v14 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v15 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v15 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true) = $true)) )),
% 130.39/20.03 inference(backward_demodulation,[status(thm)],[f2153,f2154])).
% 130.39/20.03 thf(f2154,plain,(
% 130.39/20.03 ( ! [X12 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f2153])).
% 130.39/20.03 thf(f2153,plain,(
% 130.39/20.03 ( ! [X12 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (?? @ mworld @ (mrel @ Y14))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v5 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v5 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v6 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v6 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v7 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v7 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v8 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v8 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v13 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v13 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v14 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v14 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v15 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v15 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2152])).
% 130.39/20.03 thf(f2152,plain,(
% 130.39/20.03 ( ! [X12 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (?? @ mworld @ (mrel @ Y14))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v5 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v5 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v6 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v6 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v7 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v7 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v8 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v8 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v13 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v13 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v14 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v14 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v15 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v15 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2151,f358])).
% 130.39/20.03 thf(f2151,plain,(
% 130.39/20.03 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (?? @ mworld @ (mrel @ Y14))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v5 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v5 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v6 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v6 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v7 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v7 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v8 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v8 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v13 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v13 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v14 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v14 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v15 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v15 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v16 @ Y0)) & (mrel @ X12 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2150])).
% 130.39/20.03 thf(f2150,plain,(
% 130.39/20.03 ( ! [X11 : mworld,X12 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (?? @ mworld @ (mrel @ Y15))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v5 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v5 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v6 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v6 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v7 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v7 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v8 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v8 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v13 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v13 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v14 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v14 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v15 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v15 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v16 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v16 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X12) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2149])).
% 130.39/20.03 thf(f2149,plain,(
% 130.39/20.03 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (?? @ mworld @ (mrel @ Y15))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v5 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v5 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v6 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v6 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v7 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v7 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v8 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v8 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v13 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v13 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v14 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v14 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v15 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v15 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v16 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v16 @ Y1)) & (mrel @ Y0 @ Y1))))))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2148])).
% 130.39/20.03 thf(f2148,plain,(
% 130.39/20.03 ( ! [X11 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (?? @ mworld @ (mrel @ Y15))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v5 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v5 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v6 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v6 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v7 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v7 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v8 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v8 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v13 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v13 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v14 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v14 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v15 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v15 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v16 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v16 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2147,f1603])).
% 130.39/20.03 thf(f2147,plain,(
% 130.39/20.03 ( ! [X11 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (?? @ mworld @ (mrel @ Y15))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v5 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v5 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v6 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v6 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v7 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v7 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v8 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v8 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v13 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v13 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v14 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v14 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v15 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v15 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v16 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v16 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X11))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2146])).
% 130.39/20.03 thf(f2146,plain,(
% 130.39/20.03 ( ! [X11 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (?? @ mworld @ (mrel @ Y15))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v5 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v5 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v6 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v6 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v7 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v7 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v8 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v8 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v13 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v13 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v14 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v14 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v15 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v15 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v16 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v16 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X11)))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2145,f358])).
% 130.39/20.03 thf(f2145,plain,(
% 130.39/20.03 ( ! [X10 : mworld,X11 : mworld] : ((((mrel @ X10 @ X11) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (?? @ mworld @ (mrel @ Y15))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v5 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v5 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v6 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v6 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v7 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v7 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v8 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v8 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v13 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v13 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v14 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v14 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v15 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v15 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v16 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v16 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X11)))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2144])).
% 130.39/20.03 thf(f2144,plain,(
% 130.39/20.03 ( ! [X10 : mworld,X11 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (?? @ mworld @ (mrel @ Y16))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v5 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v5 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v6 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v6 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v7 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v7 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v8 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v8 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v13 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v13 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v14 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v14 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v15 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v15 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v16 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v16 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0))))) @ X11) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2112])).
% 130.39/20.03 thf(f2112,plain,(
% 130.39/20.03 ( ! [X10 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (?? @ mworld @ (mrel @ Y16))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v5 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v5 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v6 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v6 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v7 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v7 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v8 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v8 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v13 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v13 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v14 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v14 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v15 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v15 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v16 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v16 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2111])).
% 130.39/20.03 thf(f2111,plain,(
% 130.39/20.03 ( ! [X10 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (?? @ mworld @ (mrel @ Y16))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v5 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v5 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v6 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v6 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v7 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v7 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v8 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v8 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v13 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v13 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v14 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v14 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v15 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v15 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v16 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v16 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2110,f1603])).
% 130.39/20.03 thf(f2110,plain,(
% 130.39/20.03 ( ! [X10 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (?? @ mworld @ (mrel @ Y16))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v5 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v5 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v6 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v6 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v7 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v7 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v8 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v8 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v13 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v13 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v14 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v14 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v15 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v15 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v16 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v16 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X10))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2109])).
% 130.39/20.03 thf(f2109,plain,(
% 130.39/20.03 ( ! [X10 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (?? @ mworld @ (mrel @ Y16))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v5 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v5 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v6 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v6 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v7 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v7 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v8 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v8 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v13 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v13 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v14 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v14 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v15 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v15 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v16 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v16 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X10)))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2108,f358])).
% 130.39/20.03 thf(f2108,plain,(
% 130.39/20.03 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (?? @ mworld @ (mrel @ Y16))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v5 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v5 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v6 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v6 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v7 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v7 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v8 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v8 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v13 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v13 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v14 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v14 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v15 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v15 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v16 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v16 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X10)))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2107])).
% 130.39/20.03 thf(f2107,plain,(
% 130.39/20.03 ( ! [X10 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (?? @ mworld @ (mrel @ Y17))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v5 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v5 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v6 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v6 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v7 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v7 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v8 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v8 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v13 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v13 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v14 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v14 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v15 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v15 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v16 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v16 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X10) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2106])).
% 130.39/20.03 thf(f2106,plain,(
% 130.39/20.03 ( ! [X9 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (?? @ mworld @ (mrel @ Y17))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v5 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v5 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v6 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v6 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v7 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v7 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v8 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v8 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v13 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v13 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v14 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v14 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v15 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v15 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v16 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v16 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2105])).
% 130.39/20.03 thf(f2105,plain,(
% 130.39/20.03 ( ! [X9 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (?? @ mworld @ (mrel @ Y17))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v5 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v5 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v6 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v6 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v7 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v7 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v8 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v8 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v13 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v13 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v14 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v14 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v15 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v15 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v16 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v16 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2104,f1603])).
% 130.39/20.03 thf(f2104,plain,(
% 130.39/20.03 ( ! [X9 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (?? @ mworld @ (mrel @ Y17))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v5 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v5 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v6 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v6 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v7 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v7 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v8 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v8 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v13 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v13 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v14 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v14 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v15 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v15 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v16 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v16 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X9))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2103])).
% 130.39/20.03 thf(f2103,plain,(
% 130.39/20.03 ( ! [X9 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (?? @ mworld @ (mrel @ Y17))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v5 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v5 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v6 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v6 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v7 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v7 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v8 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v8 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v13 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v13 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v14 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v14 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v15 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v15 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v16 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v16 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X9)))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2102,f358])).
% 130.39/20.03 thf(f2102,plain,(
% 130.39/20.03 ( ! [X8 : mworld,X9 : mworld] : ((((mrel @ X8 @ X9) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (?? @ mworld @ (mrel @ Y17))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v5 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v5 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v6 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v6 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v7 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v7 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v8 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v8 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v13 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v13 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v14 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v14 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v15 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v15 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v16 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v16 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X9)))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2101])).
% 130.39/20.03 thf(f2101,plain,(
% 130.39/20.03 ( ! [X8 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (?? @ mworld @ (mrel @ Y18))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v5 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v5 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v6 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v6 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v7 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v7 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v8 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v8 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v13 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v13 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v14 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v14 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v15 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v15 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v16 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v16 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X9) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f2099])).
% 130.39/20.03 thf(f2099,plain,(
% 130.39/20.03 ( ! [X8 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (?? @ mworld @ (mrel @ Y18))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v5 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v5 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v6 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v6 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v7 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v7 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v8 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v8 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v13 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v13 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v14 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v14 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v15 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v15 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v16 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v16 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2098])).
% 130.39/20.03 thf(f2098,plain,(
% 130.39/20.03 ( ! [X8 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (?? @ mworld @ (mrel @ Y18))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v5 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v5 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v6 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v6 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v7 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v7 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v8 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v8 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v13 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v13 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v14 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v14 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v15 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v15 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v16 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v16 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2097,f1603])).
% 130.39/20.03 thf(f2097,plain,(
% 130.39/20.03 ( ! [X8 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (?? @ mworld @ (mrel @ Y18))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v5 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v5 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v6 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v6 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v7 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v7 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v8 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v8 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v13 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v13 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v14 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v14 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v15 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v15 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v16 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v16 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X8))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f2096])).
% 130.39/20.03 thf(f2096,plain,(
% 130.39/20.03 ( ! [X8 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (?? @ mworld @ (mrel @ Y18))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v5 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v5 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v6 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v6 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v7 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v7 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v8 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v8 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v13 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v13 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v14 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v14 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v15 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v15 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v16 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v16 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X8)))))) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f2095,f358])).
% 130.39/20.03 thf(f2095,plain,(
% 130.39/20.03 ( ! [X8 : mworld,X7 : mworld] : ((((mrel @ X7 @ X8) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (?? @ mworld @ (mrel @ Y18))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v5 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v5 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v6 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v6 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v7 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v7 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v8 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v8 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v13 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v13 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v14 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v14 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v15 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v15 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v16 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v16 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X8)))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f2094])).
% 130.39/20.03 thf(f2094,plain,(
% 130.39/20.03 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (?? @ mworld @ (mrel @ Y19))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v5 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v5 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v6 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v6 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v7 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v7 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v8 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v8 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v13 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v13 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v14 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v14 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v15 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v15 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v16 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v16 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X8) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f1817])).
% 130.39/20.03 thf(f1817,plain,(
% 130.39/20.03 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (?? @ mworld @ (mrel @ Y19))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v5 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v5 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v6 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v6 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v7 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v7 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v8 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v8 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v13 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v13 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v14 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v14 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v15 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v15 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v16 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v16 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f1811])).
% 130.39/20.03 thf(f1811,plain,(
% 130.39/20.03 ( ! [X7 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (?? @ mworld @ (mrel @ Y19))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v5 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v5 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v6 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v6 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v7 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v7 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v8 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v8 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v13 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v13 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v14 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v14 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v15 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v15 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v16 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v16 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1810])).
% 130.39/20.03 thf(f1810,plain,(
% 130.39/20.03 ( ! [X7 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (?? @ mworld @ (mrel @ Y19))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v5 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v5 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v6 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v6 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v7 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v7 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v8 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v8 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v13 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v13 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v14 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v14 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v15 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v15 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v16 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v16 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f1809,f358])).
% 130.39/20.03 thf(f1809,plain,(
% 130.39/20.03 ( ! [X6 : mworld,X7 : mworld] : (($true = ((mrel @ X6 @ X7) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (?? @ mworld @ (mrel @ Y19))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v5 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v5 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v6 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v6 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v7 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v7 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v8 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v8 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v13 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v13 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v14 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v14 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v15 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v15 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v16 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v16 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f1808])).
% 130.39/20.03 thf(f1808,plain,(
% 130.39/20.03 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (?? @ mworld @ (mrel @ Y20))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v5 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v5 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v6 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v6 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v7 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v7 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v8 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v8 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v13 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v13 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v14 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v14 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v15 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v15 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v16 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v16 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v21 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v21 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X7) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f1803])).
% 130.39/20.03 thf(f1803,plain,(
% 130.39/20.03 ( ! [X6 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (?? @ mworld @ (mrel @ Y20))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v5 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v5 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v6 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v6 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v7 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v7 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v8 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v8 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v13 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v13 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v14 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v14 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v15 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v15 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v16 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v16 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v21 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v21 @ Y1)) & (mrel @ Y0 @ Y1))))))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1802])).
% 130.39/20.03 thf(f1802,plain,(
% 130.39/20.03 ( ! [X6 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (?? @ mworld @ (mrel @ Y20))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v5 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v5 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v6 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v6 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v7 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v7 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v8 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v8 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v13 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v13 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v14 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v14 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v15 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v15 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v16 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v16 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v21 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v21 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true))) )),
% 130.39/20.03 inference(backward_demodulation,[status(thm)],[f1793,f1800])).
% 130.39/20.03 thf(f1800,plain,(
% 130.39/20.03 ( ! [X6 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f1793])).
% 130.39/20.03 thf(f1793,plain,(
% 130.39/20.03 ( ! [X6 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (?? @ mworld @ (mrel @ Y20))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v5 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v5 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v6 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v6 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v7 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v7 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v8 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v8 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v13 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v13 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v14 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v14 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v15 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v15 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v16 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v16 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v21 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v21 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1792])).
% 130.39/20.03 thf(f1792,plain,(
% 130.39/20.03 ( ! [X6 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (?? @ mworld @ (mrel @ Y20))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v5 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v5 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v6 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v6 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v7 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v7 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v8 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v8 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v13 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v13 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v14 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v14 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v15 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v15 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v16 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v16 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v21 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v21 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f1791,f358])).
% 130.39/20.03 thf(f1791,plain,(
% 130.39/20.03 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (?? @ mworld @ (mrel @ Y20))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & (?? @ mworld @ (mrel @ Y17)))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v5 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v5 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v6 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v6 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v7 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v7 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v8 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v8 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & (?? @ mworld @ (mrel @ Y9)))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v13 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v13 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v14 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v14 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v15 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v15 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v16 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v16 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & (?? @ mworld @ (mrel @ Y1)))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v21 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v21 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f1790])).
% 130.39/20.03 thf(f1790,plain,(
% 130.39/20.03 ( ! [X6 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (?? @ mworld @ (mrel @ Y21))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v5 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v5 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v6 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v6 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v7 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v7 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v8 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v8 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v13 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v13 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v14 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v14 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v15 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v15 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v16 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v16 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v21 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v21 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v22 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v22 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X6) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f1760])).
% 130.39/20.03 thf(f1760,plain,(
% 130.39/20.03 ( ! [X5 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (?? @ mworld @ (mrel @ Y21))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v5 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v5 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v6 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v6 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v7 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v7 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v8 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v8 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v13 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v13 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v14 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v14 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v15 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v15 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v16 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v16 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v21 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v21 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v22 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v22 @ Y1)) & (mrel @ Y0 @ Y1))))))))) = $true)) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f1758])).
% 130.39/20.03 thf(f1758,plain,(
% 130.39/20.03 ( ! [X5 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (?? @ mworld @ (mrel @ Y21))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v5 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v5 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v6 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v6 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v7 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v7 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v8 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v8 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v13 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v13 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v14 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v14 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v15 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v15 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v16 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v16 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v21 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v21 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v22 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v22 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v23 @ Y0) & (mrel @ X5 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0)))))) = $true)) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1757])).
% 130.39/20.03 thf(f1757,plain,(
% 130.39/20.03 ( ! [X5 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (?? @ mworld @ (mrel @ Y21))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v5 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v5 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v6 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v6 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v7 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v7 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v8 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v8 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v13 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v13 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v14 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v14 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v15 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v15 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v16 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v16 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v21 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v21 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v22 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v22 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v23 @ Y0) & (mrel @ X5 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f1756,f358])).
% 130.39/20.03 thf(f1756,plain,(
% 130.39/20.03 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (?? @ mworld @ (mrel @ Y21))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & (?? @ mworld @ (mrel @ Y18)))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v5 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v5 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v6 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v6 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v7 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v7 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & ((?? @ mworld @ (^[Y15 : mworld]: ((v8 @ Y15) & (mrel @ Y14 @ Y15)))) & (?? @ mworld @ (^[Y15 : mworld]: ((~ (v8 @ Y15)) & (mrel @ Y14 @ Y15))))))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & (?? @ mworld @ (mrel @ Y10)))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v13 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v13 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v14 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v14 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v15 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v15 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & ((?? @ mworld @ (^[Y7 : mworld]: ((v16 @ Y7) & (mrel @ Y6 @ Y7)))) & (?? @ mworld @ (^[Y7 : mworld]: ((~ (v16 @ Y7)) & (mrel @ Y6 @ Y7))))))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & (?? @ mworld @ (mrel @ Y2)))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v21 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v21 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v22 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v22 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v23 @ Y0) & (mrel @ X5 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v23 @ Y0)) & (mrel @ X5 @ Y0))))))))) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f1755])).
% 130.39/20.03 thf(f1755,plain,(
% 130.39/20.03 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (?? @ mworld @ (mrel @ Y22))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v5 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v5 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v6 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v6 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v7 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v7 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v8 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v8 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v13 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v13 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v14 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v14 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v15 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v15 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v16 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v16 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v21 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v21 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v22 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v22 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v23 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v23 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X5) = $true)) )),
% 130.39/20.03 inference(pi_clausification,[status(thm)],[f1627])).
% 130.39/20.03 thf(f1627,plain,(
% 130.39/20.03 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (?? @ mworld @ (mrel @ Y22))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v5 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v5 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v6 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v6 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v7 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v7 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v8 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v8 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v13 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v13 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v14 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v14 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v15 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v15 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v16 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v16 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v21 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v21 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v22 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v22 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v23 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v23 @ Y1)) & (mrel @ Y0 @ Y1))))))))))) )),
% 130.39/20.03 inference(binary_proxy_clausification,[status(thm)],[f1625])).
% 130.39/20.03 thf(f1625,plain,(
% 130.39/20.03 ( ! [X4 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (?? @ mworld @ (mrel @ Y22))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v5 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v5 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v6 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v6 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v7 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v7 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v8 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v8 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v13 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v13 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v14 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v14 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v15 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v15 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v16 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v16 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v21 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v21 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v22 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v22 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v23 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v23 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0)))))))) )),
% 130.39/20.03 inference(boolean_simplification,[status(thm)],[f1624])).
% 130.39/20.03 thf(f1624,plain,(
% 130.39/20.03 ( ! [X4 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (?? @ mworld @ (mrel @ Y22))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v5 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v5 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v6 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v6 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v7 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v7 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v8 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v8 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v13 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v13 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v14 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v14 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v15 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v15 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v16 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v16 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v21 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v21 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v22 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v22 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v23 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v23 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(forward_demodulation,[status(thm)],[f1623,f358])).
% 130.39/20.03 thf(f1623,plain,(
% 130.39/20.03 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (?? @ mworld @ (mrel @ Y22))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & (?? @ mworld @ (mrel @ Y19)))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v5 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v5 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v6 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v6 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v7 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v7 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & ((?? @ mworld @ (^[Y16 : mworld]: ((v8 @ Y16) & (mrel @ Y15 @ Y16)))) & (?? @ mworld @ (^[Y16 : mworld]: ((~ (v8 @ Y16)) & (mrel @ Y15 @ Y16))))))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & (?? @ mworld @ (mrel @ Y11)))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v13 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v13 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v14 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v14 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v15 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v15 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & ((?? @ mworld @ (^[Y8 : mworld]: ((v16 @ Y8) & (mrel @ Y7 @ Y8)))) & (?? @ mworld @ (^[Y8 : mworld]: ((~ (v16 @ Y8)) & (mrel @ Y7 @ Y8))))))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & (?? @ mworld @ (mrel @ Y3)))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v21 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v21 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v22 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v22 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v23 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v23 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & ((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0))))))) = $true)) )),
% 130.39/20.03 inference(beta_eta_normalization,[status(thm)],[f1622])).
% 130.39/20.03 thf(f1622,plain,(
% 130.39/20.03 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (?? @ mworld @ (mrel @ Y23))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v5 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v5 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v6 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v6 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v7 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v7 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v8 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v8 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v13 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v13 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v14 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v14 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v15 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v15 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v16 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v16 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v21 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v21 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v22 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v22 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v23 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v23 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v24 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v24 @ Y1)) & (mrel @ Y0 @ Y1)))))))) @ X4) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1621])).
% 130.39/20.04 thf(f1621,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (?? @ mworld @ (mrel @ Y23))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v5 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v5 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v6 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v6 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v7 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v7 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v8 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v8 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v13 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v13 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v14 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v14 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v15 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v15 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v16 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v16 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v21 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v21 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v22 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v22 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v23 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v23 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v24 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v24 @ Y1)) & (mrel @ Y0 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1620])).
% 130.39/20.04 thf(f1620,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (?? @ mworld @ (mrel @ Y23))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v5 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v5 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v6 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v6 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v7 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v7 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v8 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v8 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v13 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v13 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v14 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v14 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v15 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v15 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v16 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v16 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v21 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v21 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v22 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v22 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v23 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v23 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v24 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v24 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1619,f1603])).
% 130.39/20.04 thf(f1619,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (?? @ mworld @ (mrel @ Y23))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v5 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v5 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v6 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v6 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v7 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v7 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v8 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v8 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v13 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v13 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v14 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v14 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v15 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v15 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v16 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v16 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v21 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v21 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v22 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v22 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v23 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v23 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v24 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v24 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X3))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1618])).
% 130.39/20.04 thf(f1618,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (?? @ mworld @ (mrel @ Y23))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v5 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v5 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v6 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v6 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v7 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v7 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v8 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v8 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v13 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v13 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v14 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v14 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v15 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v15 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v16 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v16 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v21 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v21 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v22 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v22 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v23 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v23 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v24 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v24 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X3)))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1617,f358])).
% 130.39/20.04 thf(f1617,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (?? @ mworld @ (mrel @ Y23))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & (?? @ mworld @ (mrel @ Y20)))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v5 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v5 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v6 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v6 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v7 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v7 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & ((?? @ mworld @ (^[Y17 : mworld]: ((v8 @ Y17) & (mrel @ Y16 @ Y17)))) & (?? @ mworld @ (^[Y17 : mworld]: ((~ (v8 @ Y17)) & (mrel @ Y16 @ Y17))))))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & (?? @ mworld @ (mrel @ Y12)))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v13 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v13 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v14 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v14 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v15 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v15 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & ((?? @ mworld @ (^[Y9 : mworld]: ((v16 @ Y9) & (mrel @ Y8 @ Y9)))) & (?? @ mworld @ (^[Y9 : mworld]: ((~ (v16 @ Y9)) & (mrel @ Y8 @ Y9))))))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & (?? @ mworld @ (mrel @ Y4)))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v21 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v21 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v22 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v22 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v23 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v23 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & ((?? @ mworld @ (^[Y1 : mworld]: ((v24 @ Y1) & (mrel @ Y0 @ Y1)))) & (?? @ mworld @ (^[Y1 : mworld]: ((~ (v24 @ Y1)) & (mrel @ Y0 @ Y1))))))))) & (?? @ mworld @ (mrel @ X3)))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1616])).
% 130.39/20.04 thf(f1616,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (?? @ mworld @ (mrel @ Y24))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v5 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v5 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v6 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v6 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v7 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v7 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v8 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v8 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v13 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v13 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v14 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v14 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v15 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v15 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v16 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v16 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v21 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v21 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v22 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v22 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v23 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v23 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v24 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v24 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0))))) @ X3))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1615])).
% 130.39/20.04 thf(f1615,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (?? @ mworld @ (mrel @ Y24))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v5 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v5 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v6 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v6 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v7 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v7 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v8 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v8 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v13 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v13 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v14 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v14 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v15 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v15 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v16 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v16 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v21 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v21 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v22 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v22 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v23 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v23 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v24 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v24 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1614])).
% 130.39/20.04 thf(f1614,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (?? @ mworld @ (mrel @ Y24))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v5 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v5 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v6 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v6 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v7 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v7 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v8 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v8 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v13 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v13 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v14 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v14 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v15 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v15 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v16 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v16 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v21 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v21 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v22 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v22 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v23 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v23 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v24 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v24 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1613,f1603])).
% 130.39/20.04 thf(f1613,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (?? @ mworld @ (mrel @ Y24))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v5 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v5 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v6 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v6 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v7 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v7 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v8 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v8 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v13 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v13 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v14 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v14 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v15 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v15 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v16 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v16 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v21 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v21 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v22 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v22 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v23 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v23 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v24 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v24 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X2))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1612])).
% 130.39/20.04 thf(f1612,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (?? @ mworld @ (mrel @ Y24))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v5 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v5 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v6 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v6 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v7 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v7 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v8 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v8 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v13 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v13 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v14 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v14 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v15 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v15 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v16 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v16 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v21 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v21 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v22 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v22 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v23 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v23 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v24 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v24 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X2)))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1611,f358])).
% 130.39/20.04 thf(f1611,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (?? @ mworld @ (mrel @ Y24))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & (?? @ mworld @ (mrel @ Y21)))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v5 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v5 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v6 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v6 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v7 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v7 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & ((?? @ mworld @ (^[Y18 : mworld]: ((v8 @ Y18) & (mrel @ Y17 @ Y18)))) & (?? @ mworld @ (^[Y18 : mworld]: ((~ (v8 @ Y18)) & (mrel @ Y17 @ Y18))))))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & (?? @ mworld @ (mrel @ Y13)))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v13 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v13 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v14 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v14 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v15 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v15 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & ((?? @ mworld @ (^[Y10 : mworld]: ((v16 @ Y10) & (mrel @ Y9 @ Y10)))) & (?? @ mworld @ (^[Y10 : mworld]: ((~ (v16 @ Y10)) & (mrel @ Y9 @ Y10))))))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & (?? @ mworld @ (mrel @ Y5)))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v21 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v21 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v22 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v22 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v23 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v23 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & ((?? @ mworld @ (^[Y2 : mworld]: ((v24 @ Y2) & (mrel @ Y1 @ Y2)))) & (?? @ mworld @ (^[Y2 : mworld]: ((~ (v24 @ Y2)) & (mrel @ Y1 @ Y2))))))))) & (?? @ mworld @ (mrel @ Y0)))))) & (?? @ mworld @ (mrel @ X2)))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1610])).
% 130.39/20.04 thf(f1610,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (?? @ mworld @ (mrel @ Y25))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v5 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v5 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v6 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v6 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v7 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v7 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v8 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v8 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v13 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v13 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v14 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v14 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v15 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v15 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v16 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v16 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v21 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v21 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v22 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v22 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v23 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v23 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v24 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v24 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0))))) @ X2))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1608])).
% 130.39/20.04 thf(f1608,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (?? @ mworld @ (mrel @ Y25))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v5 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v5 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v6 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v6 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v7 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v7 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v8 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v8 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v13 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v13 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v14 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v14 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v15 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v15 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v16 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v16 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v21 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v21 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v22 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v22 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v23 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v23 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v24 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v24 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1607])).
% 130.39/20.04 thf(f1607,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => ((!! @ mworld @ (^[Y25 : mworld]: ((mrel @ Y24 @ Y25) => (?? @ mworld @ (mrel @ Y25))))) & (?? @ mworld @ (mrel @ Y24)))))) & (?? @ mworld @ (mrel @ Y23)))))) & (?? @ mworld @ (mrel @ Y22)))))) & ((?? @ mworld @ (^[Y22 : mworld]: ((v5 @ Y22) & (mrel @ Y21 @ Y22)))) & (?? @ mworld @ (^[Y22 : mworld]: ((~ (v5 @ Y22)) & (mrel @ Y21 @ Y22))))))))) & ((?? @ mworld @ (^[Y21 : mworld]: ((v6 @ Y21) & (mrel @ Y20 @ Y21)))) & (?? @ mworld @ (^[Y21 : mworld]: ((~ (v6 @ Y21)) & (mrel @ Y20 @ Y21))))))))) & ((?? @ mworld @ (^[Y20 : mworld]: ((v7 @ Y20) & (mrel @ Y19 @ Y20)))) & (?? @ mworld @ (^[Y20 : mworld]: ((~ (v7 @ Y20)) & (mrel @ Y19 @ Y20))))))))) & ((?? @ mworld @ (^[Y19 : mworld]: ((v8 @ Y19) & (mrel @ Y18 @ Y19)))) & (?? @ mworld @ (^[Y19 : mworld]: ((~ (v8 @ Y19)) & (mrel @ Y18 @ Y19))))))))) & (?? @ mworld @ (mrel @ Y17)))))) & (?? @ mworld @ (mrel @ Y16)))))) & (?? @ mworld @ (mrel @ Y15)))))) & (?? @ mworld @ (mrel @ Y14)))))) & ((?? @ mworld @ (^[Y14 : mworld]: ((v13 @ Y14) & (mrel @ Y13 @ Y14)))) & (?? @ mworld @ (^[Y14 : mworld]: ((~ (v13 @ Y14)) & (mrel @ Y13 @ Y14))))))))) & ((?? @ mworld @ (^[Y13 : mworld]: ((v14 @ Y13) & (mrel @ Y12 @ Y13)))) & (?? @ mworld @ (^[Y13 : mworld]: ((~ (v14 @ Y13)) & (mrel @ Y12 @ Y13))))))))) & ((?? @ mworld @ (^[Y12 : mworld]: ((v15 @ Y12) & (mrel @ Y11 @ Y12)))) & (?? @ mworld @ (^[Y12 : mworld]: ((~ (v15 @ Y12)) & (mrel @ Y11 @ Y12))))))))) & ((?? @ mworld @ (^[Y11 : mworld]: ((v16 @ Y11) & (mrel @ Y10 @ Y11)))) & (?? @ mworld @ (^[Y11 : mworld]: ((~ (v16 @ Y11)) & (mrel @ Y10 @ Y11))))))))) & (?? @ mworld @ (mrel @ Y9)))))) & (?? @ mworld @ (mrel @ Y8)))))) & (?? @ mworld @ (mrel @ Y7)))))) & (?? @ mworld @ (mrel @ Y6)))))) & ((?? @ mworld @ (^[Y6 : mworld]: ((v21 @ Y6) & (mrel @ Y5 @ Y6)))) & (?? @ mworld @ (^[Y6 : mworld]: ((~ (v21 @ Y6)) & (mrel @ Y5 @ Y6))))))))) & ((?? @ mworld @ (^[Y5 : mworld]: ((v22 @ Y5) & (mrel @ Y4 @ Y5)))) & (?? @ mworld @ (^[Y5 : mworld]: ((~ (v22 @ Y5)) & (mrel @ Y4 @ Y5))))))))) & ((?? @ mworld @ (^[Y4 : mworld]: ((v23 @ Y4) & (mrel @ Y3 @ Y4)))) & (?? @ mworld @ (^[Y4 : mworld]: ((~ (v23 @ Y4)) & (mrel @ Y3 @ Y4))))))))) & ((?? @ mworld @ (^[Y3 : mworld]: ((v24 @ Y3) & (mrel @ Y2 @ Y3)))) & (?? @ mworld @ (^[Y3 : mworld]: ((~ (v24 @ Y3)) & (mrel @ Y2 @ Y3))))))))) & (?? @ mworld @ (mrel @ Y1)))))) & (?? @ mworld @ (mrel @ Y0)))))) & $true))) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f1601,f1603])).
% 130.39/20.04 thf(f4745,plain,(
% 130.39/20.04 spl0_21 | ~spl0_6),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f4744,f1046,f2908])).
% 130.39/20.04 thf(f2908,definition,(
% 130.39/20.04 spl0_21 <=> ! [X13 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 130.39/20.04 thf(f1046,definition,(
% 130.39/20.04 spl0_6 <=> ! [X19 : mworld] : ($true = (v10 @ X19))),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 130.39/20.04 thf(f4744,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13))) = $true)) ) | ~spl0_6),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f4743])).
% 130.39/20.04 thf(f4743,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = $false) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13))) = $true)) ) | ~spl0_6),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4742])).
% 130.39/20.04 thf(f4742,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (((~ $true) = $true) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13))) = $true)) ) | ~spl0_6),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3092,f1047])).
% 130.39/20.04 thf(f1047,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : (($true = (v10 @ X19))) ) | ~spl0_6),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f1046])).
% 130.39/20.04 thf(f3092,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13))) = $true) | ($true = (~ (v10 @ X12)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3091])).
% 130.39/20.04 thf(f3091,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : (($true = (~ (v10 @ X12))) | (($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13)))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3089,f358])).
% 130.39/20.04 thf(f3089,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((mrel @ X12 @ X13) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13)))) = $true) | ($true = (~ (v10 @ X12)))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3087])).
% 130.39/20.04 thf(f3087,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : (($true = (~ (v10 @ X12))) | ($true = ((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v5 @ Y4))))))))))))) | (~ (v9 @ Y0))))) @ X13))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2142])).
% 130.39/20.04 thf(f2142,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v5 @ Y4))))))))))))) | (~ (v9 @ Y0)))))) = $true) | ($true = (~ (v10 @ X12)))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2079])).
% 130.39/20.04 thf(f2079,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v5 @ Y4))))))))))))) | (~ (v9 @ Y0)))))) | (~ (v10 @ X12))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2078])).
% 130.39/20.04 thf(f2078,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v5 @ Y4))))))))))))) | (~ (v9 @ Y0)))))) | (~ (v10 @ X12)))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2077,f358])).
% 130.39/20.04 thf(f2077,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v5 @ Y4))))))))))))) | (~ (v9 @ Y0)))))) | (~ (v10 @ X12)))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2076])).
% 130.39/20.04 thf(f2076,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v5 @ Y5))))))))))))) | (~ (v9 @ Y1)))))) | (~ (v10 @ Y0))))) @ X12))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2071])).
% 130.39/20.04 thf(f2071,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v5 @ Y5))))))))))))) | (~ (v9 @ Y1)))))) | (~ (v10 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2070])).
% 130.39/20.04 thf(f2070,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v5 @ Y5))))))))))))) | (~ (v9 @ Y1)))))) | (~ (v10 @ Y0))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2069,f358])).
% 130.39/20.04 thf(f2069,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v5 @ Y5))))))))))))) | (~ (v9 @ Y1)))))) | (~ (v10 @ Y0))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2068])).
% 130.39/20.04 thf(f2068,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v5 @ Y6))))))))))))) | (~ (v9 @ Y2)))))) | (~ (v10 @ Y1)))))))) @ X11) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2063])).
% 130.39/20.04 thf(f2063,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v5 @ Y6))))))))))))) | (~ (v9 @ Y2)))))) | (~ (v10 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2062])).
% 130.39/20.04 thf(f2062,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v5 @ Y6))))))))))))) | (~ (v9 @ Y2)))))) | (~ (v10 @ Y1)))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2061,f358])).
% 130.39/20.04 thf(f2061,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v5 @ Y6))))))))))))) | (~ (v9 @ Y2)))))) | (~ (v10 @ Y1)))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2060])).
% 130.39/20.04 thf(f2060,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v5 @ Y7))))))))))))) | (~ (v9 @ Y3)))))) | (~ (v10 @ Y2))))))))))) @ X10))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2055])).
% 130.39/20.04 thf(f2055,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v5 @ Y7))))))))))))) | (~ (v9 @ Y3)))))) | (~ (v10 @ Y2)))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2054])).
% 130.39/20.04 thf(f2054,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v5 @ Y7))))))))))))) | (~ (v9 @ Y3)))))) | (~ (v10 @ Y2))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2053,f358])).
% 130.39/20.04 thf(f2053,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v5 @ Y7))))))))))))) | (~ (v9 @ Y3)))))) | (~ (v10 @ Y2))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2052])).
% 130.39/20.04 thf(f2052,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v5 @ Y8))))))))))))) | (~ (v9 @ Y4)))))) | (~ (v10 @ Y3)))))))))))))) @ X9) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2047])).
% 130.39/20.04 thf(f2047,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v5 @ Y8))))))))))))) | (~ (v9 @ Y4)))))) | (~ (v10 @ Y3))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2046])).
% 130.39/20.04 thf(f2046,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v5 @ Y8))))))))))))) | (~ (v9 @ Y4)))))) | (~ (v10 @ Y3)))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2045,f358])).
% 130.39/20.04 thf(f2045,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : (($true = ((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v5 @ Y8))))))))))))) | (~ (v9 @ Y4)))))) | (~ (v10 @ Y3)))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2044])).
% 130.39/20.04 thf(f2044,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v5 @ Y9))))))))))))) | (~ (v9 @ Y5)))))) | (~ (v10 @ Y4))))))))))))))))) @ X8) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2039])).
% 130.39/20.04 thf(f2039,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v5 @ Y9))))))))))))) | (~ (v9 @ Y5)))))) | (~ (v10 @ Y4)))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2038])).
% 130.39/20.04 thf(f2038,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v5 @ Y9))))))))))))) | (~ (v9 @ Y5)))))) | (~ (v10 @ Y4))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2037,f358])).
% 130.39/20.04 thf(f2037,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v5 @ Y9))))))))))))) | (~ (v9 @ Y5)))))) | (~ (v10 @ Y4))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2036])).
% 130.39/20.04 thf(f2036,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v5 @ Y10))))))))))))) | (~ (v9 @ Y6)))))) | (~ (v10 @ Y5)))))))))))))))))))) @ X7) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2031])).
% 130.39/20.04 thf(f2031,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v5 @ Y10))))))))))))) | (~ (v9 @ Y6)))))) | (~ (v10 @ Y5))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2030])).
% 130.39/20.04 thf(f2030,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v5 @ Y10))))))))))))) | (~ (v9 @ Y6)))))) | (~ (v10 @ Y5)))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2029,f358])).
% 130.39/20.04 thf(f2029,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v5 @ Y10))))))))))))) | (~ (v9 @ Y6)))))) | (~ (v10 @ Y5)))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2028])).
% 130.39/20.04 thf(f2028,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v5 @ Y11))))))))))))) | (~ (v9 @ Y7)))))) | (~ (v10 @ Y6))))))))))))))))))))))) @ X6))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2021])).
% 130.39/20.04 thf(f2021,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v5 @ Y11))))))))))))) | (~ (v9 @ Y7)))))) | (~ (v10 @ Y6)))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2020])).
% 130.39/20.04 thf(f2020,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v5 @ Y11))))))))))))) | (~ (v9 @ Y7)))))) | (~ (v10 @ Y6))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2019,f358])).
% 130.39/20.04 thf(f2019,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v5 @ Y11))))))))))))) | (~ (v9 @ Y7)))))) | (~ (v10 @ Y6))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2018])).
% 130.39/20.04 thf(f2018,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v5 @ Y12))))))))))))) | (~ (v9 @ Y8)))))) | (~ (v10 @ Y7)))))))))))))))))))))))))) @ X5) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2016])).
% 130.39/20.04 thf(f2016,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v5 @ Y12))))))))))))) | (~ (v9 @ Y8)))))) | (~ (v10 @ Y7))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2015])).
% 130.39/20.04 thf(f2015,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v5 @ Y12))))))))))))) | (~ (v9 @ Y8)))))) | (~ (v10 @ Y7)))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2014,f358])).
% 130.39/20.04 thf(f2014,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v5 @ Y12))))))))))))) | (~ (v9 @ Y8)))))) | (~ (v10 @ Y7)))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2013])).
% 130.39/20.04 thf(f2013,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v5 @ Y13))))))))))))) | (~ (v9 @ Y9)))))) | (~ (v10 @ Y8))))))))))))))))))))))))))))) @ X4) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2008])).
% 130.39/20.04 thf(f2008,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v5 @ Y13))))))))))))) | (~ (v9 @ Y9)))))) | (~ (v10 @ Y8)))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2007])).
% 130.39/20.04 thf(f2007,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v5 @ Y13))))))))))))) | (~ (v9 @ Y9)))))) | (~ (v10 @ Y8))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2006,f358])).
% 130.39/20.04 thf(f2006,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v5 @ Y13))))))))))))) | (~ (v9 @ Y9)))))) | (~ (v10 @ Y8))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2005])).
% 130.39/20.04 thf(f2005,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v5 @ Y14))))))))))))) | (~ (v9 @ Y10)))))) | (~ (v10 @ Y9)))))))))))))))))))))))))))))))) @ X3) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2000])).
% 130.39/20.04 thf(f2000,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v5 @ Y14))))))))))))) | (~ (v9 @ Y10)))))) | (~ (v10 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1999])).
% 130.39/20.04 thf(f1999,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v5 @ Y14))))))))))))) | (~ (v9 @ Y10)))))) | (~ (v10 @ Y9)))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1998,f358])).
% 130.39/20.04 thf(f1998,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v5 @ Y14))))))))))))) | (~ (v9 @ Y10)))))) | (~ (v10 @ Y9)))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1997])).
% 130.39/20.04 thf(f1997,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v5 @ Y15))))))))))))) | (~ (v9 @ Y11)))))) | (~ (v10 @ Y10))))))))))))))))))))))))))))))))))) @ X2) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1992])).
% 130.39/20.04 thf(f1992,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v5 @ Y15))))))))))))) | (~ (v9 @ Y11)))))) | (~ (v10 @ Y10)))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1991])).
% 130.39/20.04 thf(f1991,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v5 @ Y15))))))))))))) | (~ (v9 @ Y11)))))) | (~ (v10 @ Y10))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1990,f358])).
% 130.39/20.04 thf(f1990,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK8 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v5 @ Y15))))))))))))) | (~ (v9 @ Y11)))))) | (~ (v10 @ Y10))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1987])).
% 130.39/20.04 thf(f1987,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK8 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11)))))))))))))))))))))))))))))))))))))) @ X1) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1824])).
% 130.39/20.04 thf(f1824,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK8 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1823])).
% 130.39/20.04 thf(f1823,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK8 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11))))))))))))))))))))))))))))))))))))))) | $false) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1820])).
% 130.39/20.04 thf(f1820,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK8 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11))))))))))))))))))))))))))))))))))))))) | (~ $true)) = $true)) )),
% 130.39/20.04 inference(superposition,[status(thm)],[f888,f1815])).
% 130.39/20.04 thf(f1815,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = (v22 @ (sK8 @ X6)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1814])).
% 130.39/20.04 thf(f1814,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((((v22 @ (sK8 @ X6)) & $true) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1813,f358])).
% 130.39/20.04 thf(f1813,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ((v22 @ (sK8 @ X6)) & (mrel @ X6 @ (sK8 @ X6))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1812])).
% 130.39/20.04 thf(f1812,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ((^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0))) @ (sK8 @ X6)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f1805])).
% 130.39/20.04 thf(f1805,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v22 @ Y0) & (mrel @ X6 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f1800])).
% 130.39/20.04 thf(f888,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ X7))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f887])).
% 130.39/20.04 thf(f887,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ X7)))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f886,f358])).
% 130.39/20.04 thf(f886,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v5 @ Y16))))))))))))) | (~ (v9 @ Y12)))))) | (~ (v10 @ Y11))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ X7)))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f885])).
% 130.39/20.04 thf(f885,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v5 @ Y17))))))))))))) | (~ (v9 @ Y13)))))) | (~ (v10 @ Y12))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y0))))) @ X7) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f884])).
% 130.39/20.04 thf(f884,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v5 @ Y17))))))))))))) | (~ (v9 @ Y13)))))) | (~ (v10 @ Y12))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y0)))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f883])).
% 130.39/20.04 thf(f883,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v5 @ Y17))))))))))))) | (~ (v9 @ Y13)))))) | (~ (v10 @ Y12))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y0))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f882,f358])).
% 130.39/20.04 thf(f882,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v5 @ Y17))))))))))))) | (~ (v9 @ Y13)))))) | (~ (v10 @ Y12))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y0))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f881])).
% 130.39/20.04 thf(f881,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v5 @ Y18))))))))))))) | (~ (v9 @ Y14)))))) | (~ (v10 @ Y13))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y1)))))))) @ X6))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f880])).
% 130.39/20.04 thf(f880,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v5 @ Y18))))))))))))) | (~ (v9 @ Y14)))))) | (~ (v10 @ Y13))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f879])).
% 130.39/20.04 thf(f879,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v5 @ Y18))))))))))))) | (~ (v9 @ Y14)))))) | (~ (v10 @ Y13))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y1)))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f878,f358])).
% 130.39/20.04 thf(f878,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v5 @ Y18))))))))))))) | (~ (v9 @ Y14)))))) | (~ (v10 @ Y13))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y1)))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f877])).
% 130.39/20.04 thf(f877,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v5 @ Y19))))))))))))) | (~ (v9 @ Y15)))))) | (~ (v10 @ Y14))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y2))))))))))) @ X5))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f876])).
% 130.39/20.04 thf(f876,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v5 @ Y19))))))))))))) | (~ (v9 @ Y15)))))) | (~ (v10 @ Y14))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y2)))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f875])).
% 130.39/20.04 thf(f875,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v5 @ Y19))))))))))))) | (~ (v9 @ Y15)))))) | (~ (v10 @ Y14))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y2))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f874,f358])).
% 130.39/20.04 thf(f874,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v5 @ Y19))))))))))))) | (~ (v9 @ Y15)))))) | (~ (v10 @ Y14))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y2))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f873])).
% 130.39/20.04 thf(f873,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v5 @ Y20))))))))))))) | (~ (v9 @ Y16)))))) | (~ (v10 @ Y15))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y3)))))))))))))) @ X4))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f872])).
% 130.39/20.04 thf(f872,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v5 @ Y20))))))))))))) | (~ (v9 @ Y16)))))) | (~ (v10 @ Y15))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y3))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f871])).
% 130.39/20.04 thf(f871,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v5 @ Y20))))))))))))) | (~ (v9 @ Y16)))))) | (~ (v10 @ Y15))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y3)))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f870,f358])).
% 130.39/20.04 thf(f870,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v5 @ Y20))))))))))))) | (~ (v9 @ Y16)))))) | (~ (v10 @ Y15))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y3)))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f869])).
% 130.39/20.04 thf(f869,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v5 @ Y21))))))))))))) | (~ (v9 @ Y17)))))) | (~ (v10 @ Y16))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y4))))))))))))))))) @ X3))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f868])).
% 130.39/20.04 thf(f868,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v5 @ Y21))))))))))))) | (~ (v9 @ Y17)))))) | (~ (v10 @ Y16))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y4)))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f867])).
% 130.39/20.04 thf(f867,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v5 @ Y21))))))))))))) | (~ (v9 @ Y17)))))) | (~ (v10 @ Y16))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y4))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f866,f358])).
% 130.39/20.04 thf(f866,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v5 @ Y21))))))))))))) | (~ (v9 @ Y17)))))) | (~ (v10 @ Y16))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y4))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f865])).
% 130.39/20.04 thf(f865,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v5 @ Y22))))))))))))) | (~ (v9 @ Y18)))))) | (~ (v10 @ Y17))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y5)))))))))))))))))))) @ X2))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f864])).
% 130.39/20.04 thf(f864,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v5 @ Y22))))))))))))) | (~ (v9 @ Y18)))))) | (~ (v10 @ Y17))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y5))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f863])).
% 130.39/20.04 thf(f863,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v5 @ Y22))))))))))))) | (~ (v9 @ Y18)))))) | (~ (v10 @ Y17))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y5)))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f862,f358])).
% 130.39/20.04 thf(f862,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v5 @ Y22))))))))))))) | (~ (v9 @ Y18)))))) | (~ (v10 @ Y17))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y5)))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f861])).
% 130.39/20.04 thf(f861,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v5 @ Y23))))))))))))) | (~ (v9 @ Y19)))))) | (~ (v10 @ Y18))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y6))))))))))))))))))))))) @ X1) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f338])).
% 130.39/20.04 thf(f338,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v5 @ Y23))))))))))))) | (~ (v9 @ Y19)))))) | (~ (v10 @ Y18))))))))))))))))))))))))))))))))))))))) | (~ (v22 @ Y6)))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f268])).
% 130.39/20.04 thf(f268,plain,(
% 130.39/20.04 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v22) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v10) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v9) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v5)))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f215,f207,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f192,f208,f201,f201,f201,f201])).
% 130.39/20.04 thf(f192,plain,(
% 130.39/20.04 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f144])).
% 130.39/20.04 thf(f144,plain,(
% 130.39/20.04 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f143])).
% 130.39/20.04 thf(f143,plain,(
% 130.39/20.04 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 130.39/20.04 inference(rectify,[status(thm)],[f4])).
% 130.39/20.04 thf(f4,axiom,(
% 130.39/20.04 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X3 @ X2))) = mor)),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mor_def)).
% 130.39/20.04 thf(f215,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v22) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mor @ (mnot @ v9) @ (mbox @ (mbox @ (mbox @ (mbox @ v5)))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f79])).
% 130.39/20.04 thf(f79,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v22) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mor @ (mnot @ v9) @ (mbox @ (mbox @ (mbox @ (mbox @ v5)))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f78])).
% 130.39/20.04 thf(f78,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v22) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mor @ (mnot @ v9) @ (mbox @ (mbox @ (mbox @ (mbox @ v5))))))))))))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f45])).
% 130.39/20.04 thf(f45,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v22) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v10) @ (mbox @ (mor @ (mnot @ v9) @ (mbox @ (mbox @ (mbox @ (mbox @ v5))))))))))))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod36)).
% 130.39/20.04 thf(f4740,plain,(
% 130.39/20.04 ~spl0_13 | ~spl0_19),
% 130.39/20.04 inference(avatar_contradiction_clause,[status(thm)],[f4739])).
% 130.39/20.04 thf(f4739,plain,(
% 130.39/20.04 $false | (~spl0_13 | ~spl0_19)),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f4738])).
% 130.39/20.04 thf(f4738,plain,(
% 130.39/20.04 ($true = $false) | (~spl0_13 | ~spl0_19)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4737,f3027])).
% 130.39/20.04 thf(f3027,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (((v9 @ X13) = $false)) ) | ~spl0_13),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f2121])).
% 130.39/20.04 thf(f2121,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (((~ (v9 @ X13)) = $true)) ) | ~spl0_13),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f2120])).
% 130.39/20.04 thf(f2120,definition,(
% 130.39/20.04 spl0_13 <=> ! [X13 : mworld] : ((~ (v9 @ X13)) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 130.39/20.04 thf(f4737,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (((v9 @ X5) = $true)) ) | ~spl0_19),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4736])).
% 130.39/20.04 thf(f4736,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (v9 @ X5)) = $true)) ) | ~spl0_19),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4735,f358])).
% 130.39/20.04 thf(f4735,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (v9 @ X5)) = $true)) ) | ~spl0_19),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4734])).
% 130.39/20.04 thf(f4734,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v9 @ Y0))) @ X5) = $true)) ) | ~spl0_19),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2807])).
% 130.39/20.04 thf(f2807,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v9 @ Y0)))) = $true)) ) | ~spl0_19),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f2806])).
% 130.39/20.04 thf(f2806,definition,(
% 130.39/20.04 spl0_19 <=> ! [X4 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v9 @ Y0)))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 130.39/20.04 thf(f4616,plain,(
% 130.39/20.04 ~spl0_39),
% 130.39/20.04 inference(avatar_contradiction_clause,[status(thm)],[f4615])).
% 130.39/20.04 thf(f4615,plain,(
% 130.39/20.04 $false | ~spl0_39),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f4611])).
% 130.39/20.04 thf(f4611,plain,(
% 130.39/20.04 ($true = $false) | ~spl0_39),
% 130.39/20.04 inference(superposition,[status(thm)],[f4607,f2274])).
% 130.39/20.04 thf(f2274,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (((v14 @ (sK17 @ X14)) = $false)) )),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f2273])).
% 130.39/20.04 thf(f2273,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = (~ (v14 @ (sK17 @ X14))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2272])).
% 130.39/20.04 thf(f2272,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = ((~ (v14 @ (sK17 @ X14))) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2271,f358])).
% 130.39/20.04 thf(f2271,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = ((~ (v14 @ (sK17 @ X14))) & (mrel @ X14 @ (sK17 @ X14))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2270])).
% 130.39/20.04 thf(f2270,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0))) @ (sK17 @ X14)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2260])).
% 130.39/20.04 thf(f2260,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0)))))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2259])).
% 130.39/20.04 thf(f2259,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2258])).
% 130.39/20.04 thf(f2258,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v14 @ Y0) & (mrel @ X14 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v14 @ Y0)) & (mrel @ X14 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2177,f2257])).
% 130.39/20.04 thf(f4607,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (($true = (v14 @ X7))) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4606])).
% 130.39/20.04 thf(f4606,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (v14 @ X7)) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4605,f358])).
% 130.39/20.04 thf(f4605,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (v14 @ X7)) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4604])).
% 130.39/20.04 thf(f4604,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (v14 @ Y0))) @ X7))) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4602])).
% 130.39/20.04 thf(f4602,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (v14 @ Y0)))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4601])).
% 130.39/20.04 thf(f4601,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (v14 @ Y0))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4600,f358])).
% 130.39/20.04 thf(f4600,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (v14 @ Y0))))))) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4599])).
% 130.39/20.04 thf(f4599,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v14 @ Y1)))))) @ X6))) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4591])).
% 130.39/20.04 thf(f4591,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v14 @ Y1))))))))) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4590])).
% 130.39/20.04 thf(f4590,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v14 @ Y1)))))))))) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4589,f358])).
% 130.39/20.04 thf(f4589,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v14 @ Y1)))))))))) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4588])).
% 130.39/20.04 thf(f4588,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v14 @ Y2))))))))) @ X5) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4586])).
% 130.39/20.04 thf(f4586,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v14 @ Y2)))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4585])).
% 130.39/20.04 thf(f4585,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v14 @ Y2))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4584,f358])).
% 130.39/20.04 thf(f4584,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v14 @ Y2))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4583])).
% 130.39/20.04 thf(f4583,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v14 @ Y3)))))))))))) @ X4) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4581])).
% 130.39/20.04 thf(f4581,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v14 @ Y3))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4580])).
% 130.39/20.04 thf(f4580,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v14 @ Y3)))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4579,f358])).
% 130.39/20.04 thf(f4579,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v14 @ Y3)))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4578])).
% 130.39/20.04 thf(f4578,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v14 @ Y4))))))))))))))) @ X3))) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4576])).
% 130.39/20.04 thf(f4576,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v14 @ Y4)))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4575])).
% 130.39/20.04 thf(f4575,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v14 @ Y4))))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4574,f358])).
% 130.39/20.04 thf(f4574,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v14 @ Y4))))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4573])).
% 130.39/20.04 thf(f4573,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v14 @ Y5)))))))))))))))))) @ X2))) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4571])).
% 130.39/20.04 thf(f4571,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v14 @ Y5))))))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4570])).
% 130.39/20.04 thf(f4570,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v14 @ Y5)))))))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4569,f358])).
% 130.39/20.04 thf(f4569,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK9 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v14 @ Y5)))))))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4566])).
% 130.39/20.04 thf(f4566,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK9 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6))))))))))))))))))))) @ X1))) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4547])).
% 130.39/20.04 thf(f4547,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK9 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6)))))))))))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4546])).
% 130.39/20.04 thf(f4546,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK9 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6)))))))))))))))))))))) | $false) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4542])).
% 130.39/20.04 thf(f4542,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK9 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6)))))))))))))))))))))) | (~ $true)) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(superposition,[status(thm)],[f4534,f1850])).
% 130.39/20.04 thf(f1850,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((v21 @ (sK9 @ X7)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1849])).
% 130.39/20.04 thf(f1849,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((((v21 @ (sK9 @ X7)) & $true) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1848,f358])).
% 130.39/20.04 thf(f1848,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (($true = ((v21 @ (sK9 @ X7)) & (mrel @ X7 @ (sK9 @ X7))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1847])).
% 130.39/20.04 thf(f1847,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((((^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0))) @ (sK9 @ X7)) = $true)) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f1844])).
% 130.39/20.04 thf(f1844,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f1819])).
% 130.39/20.04 thf(f1819,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1818])).
% 130.39/20.04 thf(f1818,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v21 @ Y0) & (mrel @ X7 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v21 @ Y0)) & (mrel @ X7 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f1811,f1817])).
% 130.39/20.04 thf(f4534,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6)))))))))))))))))))))) | (~ (v21 @ X8))))) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4533])).
% 130.39/20.04 thf(f4533,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6)))))))))))))))))))))) | (~ (v21 @ X8)))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4532,f358])).
% 130.39/20.04 thf(f4532,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((mrel @ X7 @ X8) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v14 @ Y6)))))))))))))))))))))) | (~ (v21 @ X8)))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4531])).
% 130.39/20.04 thf(f4531,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v14 @ Y7)))))))))))))))))))))) | (~ (v21 @ Y0))))) @ X8))) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4525])).
% 130.39/20.04 thf(f4525,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v14 @ Y7)))))))))))))))))))))) | (~ (v21 @ Y0)))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4524])).
% 130.39/20.04 thf(f4524,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v14 @ Y7)))))))))))))))))))))) | (~ (v21 @ Y0))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4523,f358])).
% 130.39/20.04 thf(f4523,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v14 @ Y7)))))))))))))))))))))) | (~ (v21 @ Y0))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4522])).
% 130.39/20.04 thf(f4522,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v14 @ Y8)))))))))))))))))))))) | (~ (v21 @ Y1)))))))) @ X7) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4517])).
% 130.39/20.04 thf(f4517,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v14 @ Y8)))))))))))))))))))))) | (~ (v21 @ Y1))))))))))) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4516])).
% 130.39/20.04 thf(f4516,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v14 @ Y8)))))))))))))))))))))) | (~ (v21 @ Y1)))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4515,f358])).
% 130.39/20.04 thf(f4515,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v14 @ Y8)))))))))))))))))))))) | (~ (v21 @ Y1)))))))))))) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4514])).
% 130.39/20.04 thf(f4514,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v14 @ Y9)))))))))))))))))))))) | (~ (v21 @ Y2))))))))))) @ X6) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4507])).
% 130.39/20.04 thf(f4507,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v14 @ Y9)))))))))))))))))))))) | (~ (v21 @ Y2)))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4506])).
% 130.39/20.04 thf(f4506,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v14 @ Y9)))))))))))))))))))))) | (~ (v21 @ Y2))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4505,f358])).
% 130.39/20.04 thf(f4505,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v14 @ Y9)))))))))))))))))))))) | (~ (v21 @ Y2))))))))))))) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4504])).
% 130.39/20.04 thf(f4504,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v14 @ Y10)))))))))))))))))))))) | (~ (v21 @ Y3)))))))))))))) @ X5) = $true)) ) | ~spl0_39),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4078])).
% 130.39/20.04 thf(f4078,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v14 @ Y10)))))))))))))))))))))) | (~ (v21 @ Y3))))))))))))))))) ) | ~spl0_39),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f4077])).
% 130.39/20.04 thf(f4077,definition,(
% 130.39/20.04 spl0_39 <=> ! [X4 : mworld] : ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v14 @ Y10)))))))))))))))))))))) | (~ (v21 @ Y3))))))))))))))))),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_39])],[avatar_definition])).
% 130.39/20.04 thf(f4484,plain,(
% 130.39/20.04 spl0_32 | spl0_31),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f4063,f3271,f3274])).
% 130.39/20.04 thf(f3274,definition,(
% 130.39/20.04 spl0_32 <=> ! [X1 : mworld] : ((~ (v28 @ X1)) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_32])],[avatar_definition])).
% 130.39/20.04 thf(f3271,definition,(
% 130.39/20.04 spl0_31 <=> ! [X2 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v18 @ Y8))))))))))))) | (v22 @ Y4)))))))) | (~ (v24 @ Y2)))))))))))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])).
% 130.39/20.04 thf(f4063,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v18 @ Y8))))))))))))) | (v22 @ Y4)))))))) | (~ (v24 @ Y2)))))))))))) = $true) | ((~ (v28 @ X1)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4062])).
% 130.39/20.04 thf(f4062,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v18 @ Y8))))))))))))) | (v22 @ Y4)))))))) | (~ (v24 @ Y2)))))))))))))) | ((~ (v28 @ X1)) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4061,f358])).
% 130.39/20.04 thf(f4061,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (((~ (v28 @ X1)) = $true) | (((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v18 @ Y8))))))))))))) | (v22 @ Y4)))))))) | (~ (v24 @ Y2))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4058])).
% 130.39/20.04 thf(f4058,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v18 @ Y9))))))))))))) | (v22 @ Y5)))))))) | (~ (v24 @ Y3)))))))))))))) @ X2)) | ((~ (v28 @ X1)) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f363])).
% 130.39/20.04 thf(f363,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v18 @ Y9))))))))))))) | (v22 @ Y5)))))))) | (~ (v24 @ Y3))))))))))))))) = $true) | ((~ (v28 @ X1)) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f362])).
% 130.39/20.04 thf(f362,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v18 @ Y9))))))))))))) | (v22 @ Y5)))))))) | (~ (v24 @ Y3))))))))))))))) | (~ (v28 @ X1))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f361])).
% 130.39/20.04 thf(f361,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v18 @ Y9))))))))))))) | (v22 @ Y5)))))))) | (~ (v24 @ Y3))))))))))))))) | (~ (v28 @ X1)))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f360,f358])).
% 130.39/20.04 thf(f360,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v18 @ Y9))))))))))))) | (v22 @ Y5)))))))) | (~ (v24 @ Y3))))))))))))))) | (~ (v28 @ X1)))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f359])).
% 130.39/20.04 thf(f359,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v18 @ Y10))))))))))))) | (v22 @ Y6)))))))) | (~ (v24 @ Y4))))))))))))))) | (~ (v28 @ Y0))))) @ X1) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f302])).
% 130.39/20.04 thf(f302,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v18 @ Y10))))))))))))) | (v22 @ Y6)))))))) | (~ (v24 @ Y4))))))))))))))) | (~ (v28 @ Y0)))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f259])).
% 130.39/20.04 thf(f259,plain,(
% 130.39/20.04 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v28) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v24) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v22 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v18))))))))))))))) = $true)),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f200,f207,f201,f192,f208,f201,f201,f201,f201,f192,f208,f201,f201,f192,f201,f201,f201,f201])).
% 130.39/20.04 thf(f200,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ v18))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f130])).
% 130.39/20.04 thf(f130,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ v18))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f129])).
% 130.39/20.04 thf(f129,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ v18)))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f17])).
% 130.39/20.04 thf(f17,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v24) @ (mbox @ (mbox @ (mor @ v22 @ (mbox @ (mbox @ (mbox @ (mbox @ v18)))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod8)).
% 130.39/20.04 thf(f4483,plain,(
% 130.39/20.04 spl0_19 | ~spl0_32),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f4482,f3274,f2806])).
% 130.39/20.04 thf(f4482,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v9 @ Y0)))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4481])).
% 130.39/20.04 thf(f4481,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v9 @ Y0))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4480,f358])).
% 130.39/20.04 thf(f4480,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (v9 @ Y0))))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4479])).
% 130.39/20.04 thf(f4479,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1)))))) @ X4))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4474])).
% 130.39/20.04 thf(f4474,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4473])).
% 130.39/20.04 thf(f4473,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1)))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4472,f358])).
% 130.39/20.04 thf(f4472,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v9 @ Y1)))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4471])).
% 130.39/20.04 thf(f4471,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2))))))))) @ X3))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4466])).
% 130.39/20.04 thf(f4466,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2)))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4465])).
% 130.39/20.04 thf(f4465,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4464,f358])).
% 130.39/20.04 thf(f4464,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v9 @ Y2))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4463])).
% 130.39/20.04 thf(f4463,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v9 @ Y3)))))))))))) @ X2))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4458])).
% 130.39/20.04 thf(f4458,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v9 @ Y3))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4457])).
% 130.39/20.04 thf(f4457,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v9 @ Y3)))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4456,f358])).
% 130.39/20.04 thf(f4456,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK17 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v9 @ Y3)))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4453])).
% 130.39/20.04 thf(f4453,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK17 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4))))))))))))))) @ X1) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4450])).
% 130.39/20.04 thf(f4450,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK17 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4)))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4449])).
% 130.39/20.04 thf(f4449,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK17 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4)))))))))))))))) | $false))) ) | ~spl0_32),
% 130.39/20.04 inference(superposition,[status(thm)],[f4442,f2274])).
% 130.39/20.04 thf(f4442,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4)))))))))))))))) | (v14 @ X1)) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4441])).
% 130.39/20.04 thf(f4441,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4)))))))))))))))) | (v14 @ X1))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4440,f358])).
% 130.39/20.04 thf(f4440,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK14 @ X0) @ X1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v9 @ Y4)))))))))))))))) | (v14 @ X1))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4437])).
% 130.39/20.04 thf(f4437,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK14 @ X0) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0)))) @ X1) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4436])).
% 130.39/20.04 thf(f4436,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK14 @ X0) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4435])).
% 130.39/20.04 thf(f4435,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK14 @ X0) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0))))) | $false) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4431])).
% 130.39/20.04 thf(f4431,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK14 @ X0) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0))))) | (~ $true)))) ) | ~spl0_32),
% 130.39/20.04 inference(superposition,[status(thm)],[f4429,f2222])).
% 130.39/20.04 thf(f2222,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = (v15 @ (sK14 @ X13)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2221])).
% 130.39/20.04 thf(f2221,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ((v15 @ (sK14 @ X13)) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2216,f358])).
% 130.39/20.04 thf(f2216,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ((v15 @ (sK14 @ X13)) & (mrel @ X13 @ (sK14 @ X13))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2215])).
% 130.39/20.04 thf(f2215,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ((^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0))) @ (sK14 @ X13)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2207])).
% 130.39/20.04 thf(f2207,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v15 @ Y0) & (mrel @ X13 @ Y0)))))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2166])).
% 130.39/20.04 thf(f4429,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0))))) | (~ (v15 @ X14))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4428])).
% 130.39/20.04 thf(f4428,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0))))) | (~ (v15 @ X14)))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4427,f358])).
% 130.39/20.04 thf(f4427,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : (($true = ((mrel @ X13 @ X14) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v9 @ Y5)))))))))))))))) | (v14 @ Y0))))) | (~ (v15 @ X14)))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4426])).
% 130.39/20.04 thf(f4426,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v9 @ Y6)))))))))))))))) | (v14 @ Y1))))) | (~ (v15 @ Y0))))) @ X14))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4425])).
% 130.39/20.04 thf(f4425,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v9 @ Y6)))))))))))))))) | (v14 @ Y1))))) | (~ (v15 @ Y0)))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4424])).
% 130.39/20.04 thf(f4424,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v9 @ Y6)))))))))))))))) | (v14 @ Y1))))) | (~ (v15 @ Y0))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4423,f358])).
% 130.39/20.04 thf(f4423,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((mrel @ X12 @ X13) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v9 @ Y6)))))))))))))))) | (v14 @ Y1))))) | (~ (v15 @ Y0))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4422])).
% 130.39/20.04 thf(f4422,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v9 @ Y7)))))))))))))))) | (v14 @ Y2))))) | (~ (v15 @ Y1)))))))) @ X13))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4421])).
% 130.39/20.04 thf(f4421,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v9 @ Y7)))))))))))))))) | (v14 @ Y2))))) | (~ (v15 @ Y1))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4420])).
% 130.39/20.04 thf(f4420,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v9 @ Y7)))))))))))))))) | (v14 @ Y2))))) | (~ (v15 @ Y1)))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4419,f358])).
% 130.39/20.04 thf(f4419,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v9 @ Y7)))))))))))))))) | (v14 @ Y2))))) | (~ (v15 @ Y1)))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4418])).
% 130.39/20.04 thf(f4418,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v9 @ Y8)))))))))))))))) | (v14 @ Y3))))) | (~ (v15 @ Y2))))))))))) @ X12))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4417])).
% 130.39/20.04 thf(f4417,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v9 @ Y8)))))))))))))))) | (v14 @ Y3))))) | (~ (v15 @ Y2)))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4416])).
% 130.39/20.04 thf(f4416,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v9 @ Y8)))))))))))))))) | (v14 @ Y3))))) | (~ (v15 @ Y2))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4415,f358])).
% 130.39/20.04 thf(f4415,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v9 @ Y8)))))))))))))))) | (v14 @ Y3))))) | (~ (v15 @ Y2))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4414])).
% 130.39/20.04 thf(f4414,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v9 @ Y9)))))))))))))))) | (v14 @ Y4))))) | (~ (v15 @ Y3)))))))))))))) @ X11))) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4413])).
% 130.39/20.04 thf(f4413,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v9 @ Y9)))))))))))))))) | (v14 @ Y4))))) | (~ (v15 @ Y3))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4412])).
% 130.39/20.04 thf(f4412,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v9 @ Y9)))))))))))))))) | (v14 @ Y4))))) | (~ (v15 @ Y3)))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4411,f358])).
% 130.39/20.04 thf(f4411,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v9 @ Y9)))))))))))))))) | (v14 @ Y4))))) | (~ (v15 @ Y3)))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4410])).
% 130.39/20.04 thf(f4410,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v9 @ Y10)))))))))))))))) | (v14 @ Y5))))) | (~ (v15 @ Y4))))))))))))))))) @ X10) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4409])).
% 130.39/20.04 thf(f4409,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v9 @ Y10)))))))))))))))) | (v14 @ Y5))))) | (~ (v15 @ Y4)))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4408])).
% 130.39/20.04 thf(f4408,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v9 @ Y10)))))))))))))))) | (v14 @ Y5))))) | (~ (v15 @ Y4))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4407,f358])).
% 130.39/20.04 thf(f4407,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : (($true = ((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v9 @ Y10)))))))))))))))) | (v14 @ Y5))))) | (~ (v15 @ Y4))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4406])).
% 130.39/20.04 thf(f4406,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v9 @ Y11)))))))))))))))) | (v14 @ Y6))))) | (~ (v15 @ Y5)))))))))))))))))))) @ X9) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4405])).
% 130.39/20.04 thf(f4405,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v9 @ Y11)))))))))))))))) | (v14 @ Y6))))) | (~ (v15 @ Y5))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4404])).
% 130.39/20.04 thf(f4404,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v9 @ Y11)))))))))))))))) | (v14 @ Y6))))) | (~ (v15 @ Y5)))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4403,f358])).
% 130.39/20.04 thf(f4403,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v9 @ Y11)))))))))))))))) | (v14 @ Y6))))) | (~ (v15 @ Y5)))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4402])).
% 130.39/20.04 thf(f4402,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v9 @ Y12)))))))))))))))) | (v14 @ Y7))))) | (~ (v15 @ Y6))))))))))))))))))))))) @ X8) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4401])).
% 130.39/20.04 thf(f4401,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v9 @ Y12)))))))))))))))) | (v14 @ Y7))))) | (~ (v15 @ Y6)))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4400])).
% 130.39/20.04 thf(f4400,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v9 @ Y12)))))))))))))))) | (v14 @ Y7))))) | (~ (v15 @ Y6))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4399,f358])).
% 130.39/20.04 thf(f4399,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v9 @ Y12)))))))))))))))) | (v14 @ Y7))))) | (~ (v15 @ Y6))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4398])).
% 130.39/20.04 thf(f4398,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v9 @ Y13)))))))))))))))) | (v14 @ Y8))))) | (~ (v15 @ Y7)))))))))))))))))))))))))) @ X7) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4391])).
% 130.39/20.04 thf(f4391,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v9 @ Y13)))))))))))))))) | (v14 @ Y8))))) | (~ (v15 @ Y7))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4390])).
% 130.39/20.04 thf(f4390,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v9 @ Y13)))))))))))))))) | (v14 @ Y8))))) | (~ (v15 @ Y7)))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4389,f358])).
% 130.39/20.04 thf(f4389,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v9 @ Y13)))))))))))))))) | (v14 @ Y8))))) | (~ (v15 @ Y7)))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4388])).
% 130.39/20.04 thf(f4388,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v9 @ Y14)))))))))))))))) | (v14 @ Y9))))) | (~ (v15 @ Y8))))))))))))))))))))))))))))) @ X6) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4382])).
% 130.39/20.04 thf(f4382,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v9 @ Y14)))))))))))))))) | (v14 @ Y9))))) | (~ (v15 @ Y8)))))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4381])).
% 130.39/20.04 thf(f4381,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v9 @ Y14)))))))))))))))) | (v14 @ Y9))))) | (~ (v15 @ Y8))))))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4380,f358])).
% 130.39/20.04 thf(f4380,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v9 @ Y14)))))))))))))))) | (v14 @ Y9))))) | (~ (v15 @ Y8))))))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4379])).
% 130.39/20.04 thf(f4379,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v9 @ Y15)))))))))))))))) | (v14 @ Y10))))) | (~ (v15 @ Y9)))))))))))))))))))))))))))))))) @ X5) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4374])).
% 130.39/20.04 thf(f4374,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v9 @ Y15)))))))))))))))) | (v14 @ Y10))))) | (~ (v15 @ Y9))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4373])).
% 130.39/20.04 thf(f4373,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v9 @ Y15)))))))))))))))) | (v14 @ Y10))))) | (~ (v15 @ Y9)))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4372,f358])).
% 130.39/20.04 thf(f4372,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v9 @ Y15)))))))))))))))) | (v14 @ Y10))))) | (~ (v15 @ Y9)))))))))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4371])).
% 130.39/20.04 thf(f4371,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v9 @ Y16)))))))))))))))) | (v14 @ Y11))))) | (~ (v15 @ Y10))))))))))))))))))))))))))))))))))) @ X4) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4366])).
% 130.39/20.04 thf(f4366,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v9 @ Y16)))))))))))))))) | (v14 @ Y11))))) | (~ (v15 @ Y10)))))))))))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4365])).
% 130.39/20.04 thf(f4365,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v9 @ Y16)))))))))))))))) | (v14 @ Y11))))) | (~ (v15 @ Y10))))))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4364,f358])).
% 130.39/20.04 thf(f4364,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v9 @ Y16)))))))))))))))) | (v14 @ Y11))))) | (~ (v15 @ Y10))))))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4363])).
% 130.39/20.04 thf(f4363,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v9 @ Y17)))))))))))))))) | (v14 @ Y12))))) | (~ (v15 @ Y11)))))))))))))))))))))))))))))))))))))) @ X3) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4358])).
% 130.39/20.04 thf(f4358,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v9 @ Y17)))))))))))))))) | (v14 @ Y12))))) | (~ (v15 @ Y11))))))))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4357])).
% 130.39/20.04 thf(f4357,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v9 @ Y17)))))))))))))))) | (v14 @ Y12))))) | (~ (v15 @ Y11)))))))))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4356,f358])).
% 130.39/20.04 thf(f4356,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v9 @ Y17)))))))))))))))) | (v14 @ Y12))))) | (~ (v15 @ Y11)))))))))))))))))))))))))))))))))))))))))) ) | ~spl0_32),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4355])).
% 130.39/20.04 thf(f4355,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))) | (v14 @ Y13))))) | (~ (v15 @ Y12))))))))))))))))))))))))))))))))))))))))) @ X2) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4254])).
% 130.39/20.04 thf(f4254,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))) | (v14 @ Y13))))) | (~ (v15 @ Y12)))))))))))))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4241])).
% 130.39/20.04 thf(f4241,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))) | (v14 @ Y13))))) | (~ (v15 @ Y12)))))))))))))))))))))))))))))))))))))))))) | $false) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f461,f4236])).
% 130.39/20.04 thf(f4236,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($false = (v28 @ X1))) ) | ~spl0_32),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f3275])).
% 130.39/20.04 thf(f3275,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((~ (v28 @ X1)) = $true)) ) | ~spl0_32),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3274])).
% 130.39/20.04 thf(f461,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))) | (v14 @ Y13))))) | (~ (v15 @ Y12)))))))))))))))))))))))))))))))))))))))))) | (v28 @ X1)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f460])).
% 130.39/20.04 thf(f460,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))) | (v14 @ Y13))))) | (~ (v15 @ Y12)))))))))))))))))))))))))))))))))))))))))) | (v28 @ X1))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f459,f358])).
% 130.39/20.04 thf(f459,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v9 @ Y18)))))))))))))))) | (v14 @ Y13))))) | (~ (v15 @ Y12)))))))))))))))))))))))))))))))))))))))))) | (v28 @ X1))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f458])).
% 130.39/20.04 thf(f458,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v9 @ Y19)))))))))))))))) | (v14 @ Y14))))) | (~ (v15 @ Y13)))))))))))))))))))))))))))))))))))))))))) | (v28 @ Y0)))) @ X1) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f316])).
% 130.39/20.04 thf(f316,plain,(
% 130.39/20.04 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v9 @ Y19)))))))))))))))) | (v14 @ Y14))))) | (~ (v15 @ Y13)))))))))))))))))))))))))))))))))))))))))) | (v28 @ Y0))))))),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f270])).
% 130.39/20.04 thf(f270,plain,(
% 130.39/20.04 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v28 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v15) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v14 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v9)))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f217,f207,f201,f192,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f192,f201,f201,f201,f201,f201])).
% 130.39/20.04 thf(f217,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9)))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f162])).
% 130.39/20.04 thf(f162,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9)))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f161])).
% 130.39/20.04 thf(f161,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9))))))))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f13])).
% 130.39/20.04 thf(f13,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v15) @ (mbox @ (mor @ v14 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v9))))))))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod4)).
% 130.39/20.04 thf(f4218,plain,(
% 130.39/20.04 ~spl0_31 | ~spl0_38),
% 130.39/20.04 inference(avatar_contradiction_clause,[status(thm)],[f4217])).
% 130.39/20.04 thf(f4217,plain,(
% 130.39/20.04 $false | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f4214])).
% 130.39/20.04 thf(f4214,plain,(
% 130.39/20.04 ($true = $false) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2555,f4204])).
% 130.39/20.04 thf(f4204,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((v6 @ X1) = $false)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f4199])).
% 130.39/20.04 thf(f4199,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((~ (v6 @ X1)) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4198])).
% 130.39/20.04 thf(f4198,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (~ (v6 @ X1))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4196,f358])).
% 130.39/20.04 thf(f4196,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK24 @ X0) @ X1) => (~ (v6 @ X1))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4194])).
% 130.39/20.04 thf(f4194,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK24 @ X0) @ Y0) => (~ (v6 @ Y0)))) @ X1) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4187])).
% 130.39/20.04 thf(f4187,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK24 @ X0) @ Y0) => (~ (v6 @ Y0))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4186])).
% 130.39/20.04 thf(f4186,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK24 @ X0) @ Y0) => (~ (v6 @ Y0))))) | $false))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4184])).
% 130.39/20.04 thf(f4184,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK24 @ X0) @ Y0) => (~ (v6 @ Y0))))) | (~ $true)) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(superposition,[status(thm)],[f4182,f2579])).
% 130.39/20.04 thf(f2579,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = (v7 @ (sK24 @ X21)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2578])).
% 130.39/20.04 thf(f2578,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = ((v7 @ (sK24 @ X21)) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2573,f358])).
% 130.39/20.04 thf(f2573,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : ((((v7 @ (sK24 @ X21)) & (mrel @ X21 @ (sK24 @ X21))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2572])).
% 130.39/20.04 thf(f2572,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = ((^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0))) @ (sK24 @ X21)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2571])).
% 130.39/20.04 thf(f2571,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2570])).
% 130.39/20.04 thf(f2570,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = ((?? @ mworld @ (^[Y0 : mworld]: ((v7 @ Y0) & (mrel @ X21 @ Y0)))) & $true))) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2515,f2568])).
% 130.39/20.04 thf(f2568,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v7 @ Y0)) & (mrel @ X21 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2515])).
% 130.39/20.04 thf(f4182,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => (~ (v6 @ Y0))))) | (~ (v7 @ X22))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4181])).
% 130.39/20.04 thf(f4181,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => (~ (v6 @ Y0))))) | (~ (v7 @ X22)))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4180,f358])).
% 130.39/20.04 thf(f4180,plain,(
% 130.39/20.04 ( ! [X21 : mworld,X22 : mworld] : (($true = ((mrel @ X21 @ X22) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => (~ (v6 @ Y0))))) | (~ (v7 @ X22)))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4179])).
% 130.39/20.04 thf(f4179,plain,(
% 130.39/20.04 ( ! [X21 : mworld,X22 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v6 @ Y1))))) | (~ (v7 @ Y0))))) @ X22) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4178])).
% 130.39/20.04 thf(f4178,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v6 @ Y1))))) | (~ (v7 @ Y0)))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4177])).
% 130.39/20.04 thf(f4177,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v6 @ Y1))))) | (~ (v7 @ Y0))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4176,f358])).
% 130.39/20.04 thf(f4176,plain,(
% 130.39/20.04 ( ! [X21 : mworld,X20 : mworld] : ((((mrel @ X20 @ X21) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v6 @ Y1))))) | (~ (v7 @ Y0))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4175])).
% 130.39/20.04 thf(f4175,plain,(
% 130.39/20.04 ( ! [X21 : mworld,X20 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X20 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v6 @ Y2))))) | (~ (v7 @ Y1)))))))) @ X21))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4174])).
% 130.39/20.04 thf(f4174,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v6 @ Y2))))) | (~ (v7 @ Y1))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4173])).
% 130.39/20.04 thf(f4173,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v6 @ Y2))))) | (~ (v7 @ Y1)))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4172,f358])).
% 130.39/20.04 thf(f4172,plain,(
% 130.39/20.04 ( ! [X19 : mworld,X20 : mworld] : ((((mrel @ X19 @ X20) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v6 @ Y2))))) | (~ (v7 @ Y1)))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4171])).
% 130.39/20.04 thf(f4171,plain,(
% 130.39/20.04 ( ! [X19 : mworld,X20 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v6 @ Y3))))) | (~ (v7 @ Y2))))))))))) @ X20) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4170])).
% 130.39/20.04 thf(f4170,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v6 @ Y3))))) | (~ (v7 @ Y2)))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4169])).
% 130.39/20.04 thf(f4169,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v6 @ Y3))))) | (~ (v7 @ Y2))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4168,f358])).
% 130.39/20.04 thf(f4168,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X19 : mworld] : ((((mrel @ X18 @ X19) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v6 @ Y3))))) | (~ (v7 @ Y2))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4167])).
% 130.39/20.04 thf(f4167,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X19 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v6 @ Y4))))) | (~ (v7 @ Y3)))))))))))))) @ X19) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4166])).
% 130.39/20.04 thf(f4166,plain,(
% 130.39/20.04 ( ! [X18 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v6 @ Y4))))) | (~ (v7 @ Y3))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4165])).
% 130.39/20.04 thf(f4165,plain,(
% 130.39/20.04 ( ! [X18 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v6 @ Y4))))) | (~ (v7 @ Y3)))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4164,f358])).
% 130.39/20.04 thf(f4164,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X17 : mworld] : ((((mrel @ X17 @ X18) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v6 @ Y4))))) | (~ (v7 @ Y3)))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4163])).
% 130.39/20.04 thf(f4163,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v6 @ Y5))))) | (~ (v7 @ Y4))))))))))))))))) @ X18) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4162])).
% 130.39/20.04 thf(f4162,plain,(
% 130.39/20.04 ( ! [X17 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v6 @ Y5))))) | (~ (v7 @ Y4)))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4161])).
% 130.39/20.04 thf(f4161,plain,(
% 130.39/20.04 ( ! [X17 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v6 @ Y5))))) | (~ (v7 @ Y4))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4160,f358])).
% 130.39/20.04 thf(f4160,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X17 : mworld] : (($true = ((mrel @ X16 @ X17) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v6 @ Y5))))) | (~ (v7 @ Y4))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4159])).
% 130.39/20.04 thf(f4159,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v6 @ Y6))))) | (~ (v7 @ Y5)))))))))))))))))))) @ X17) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4158])).
% 130.39/20.04 thf(f4158,plain,(
% 130.39/20.04 ( ! [X16 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v6 @ Y6))))) | (~ (v7 @ Y5))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4157])).
% 130.39/20.04 thf(f4157,plain,(
% 130.39/20.04 ( ! [X16 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v6 @ Y6))))) | (~ (v7 @ Y5)))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4156,f358])).
% 130.39/20.04 thf(f4156,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X15 : mworld] : ((((mrel @ X15 @ X16) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v6 @ Y6))))) | (~ (v7 @ Y5)))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4155])).
% 130.39/20.04 thf(f4155,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v6 @ Y7))))) | (~ (v7 @ Y6))))))))))))))))))))))) @ X16) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4154])).
% 130.39/20.04 thf(f4154,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v6 @ Y7))))) | (~ (v7 @ Y6)))))))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4153])).
% 130.39/20.04 thf(f4153,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v6 @ Y7))))) | (~ (v7 @ Y6))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4152,f358])).
% 130.39/20.04 thf(f4152,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : ((((mrel @ X14 @ X15) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v6 @ Y7))))) | (~ (v7 @ Y6))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4151])).
% 130.39/20.04 thf(f4151,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v6 @ Y8))))) | (~ (v7 @ Y7)))))))))))))))))))))))))) @ X15) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4150])).
% 130.39/20.04 thf(f4150,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v6 @ Y8))))) | (~ (v7 @ Y7))))))))))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4149])).
% 130.39/20.04 thf(f4149,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v6 @ Y8))))) | (~ (v7 @ Y7)))))))))))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4148,f358])).
% 130.39/20.04 thf(f4148,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((mrel @ X13 @ X14) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v6 @ Y8))))) | (~ (v7 @ Y7)))))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4147])).
% 130.39/20.04 thf(f4147,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v6 @ Y9))))) | (~ (v7 @ Y8))))))))))))))))))))))))))))) @ X14) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4146])).
% 130.39/20.04 thf(f4146,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v6 @ Y9))))) | (~ (v7 @ Y8)))))))))))))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4145])).
% 130.39/20.04 thf(f4145,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v6 @ Y9))))) | (~ (v7 @ Y8))))))))))))))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4144,f358])).
% 130.39/20.04 thf(f4144,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((mrel @ X12 @ X13) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v6 @ Y9))))) | (~ (v7 @ Y8))))))))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4143])).
% 130.39/20.04 thf(f4143,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v6 @ Y10))))) | (~ (v7 @ Y9)))))))))))))))))))))))))))))))) @ X13) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4142])).
% 130.39/20.04 thf(f4142,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v6 @ Y10))))) | (~ (v7 @ Y9))))))))))))))))))))))))))))))))))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4141])).
% 130.39/20.04 thf(f4141,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v6 @ Y10))))) | (~ (v7 @ Y9)))))))))))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4140,f358])).
% 130.39/20.04 thf(f4140,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v6 @ Y10))))) | (~ (v7 @ Y9)))))))))))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4139])).
% 130.39/20.04 thf(f4139,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10))))))))))))))))))))))))))))))))))) @ X12) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4138])).
% 130.39/20.04 thf(f4138,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10)))))))))))))))))))))))))))))))))))) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4137])).
% 130.39/20.04 thf(f4137,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10)))))))))))))))))))))))))))))))))))) | $false) = $true)) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4136])).
% 130.39/20.04 thf(f4136,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10)))))))))))))))))))))))))))))))))))) | (~ $true)))) ) | (~spl0_31 | ~spl0_38)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4135,f3328])).
% 130.39/20.04 thf(f3328,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((v18 @ X4) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3327])).
% 130.39/20.04 thf(f3327,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (v18 @ X4)) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3326,f358])).
% 130.39/20.04 thf(f3326,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (v18 @ X4)) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3325])).
% 130.39/20.04 thf(f3325,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v18 @ Y0))) @ X4) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3324])).
% 130.39/20.04 thf(f3324,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v18 @ Y0)))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3323])).
% 130.39/20.04 thf(f3323,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v18 @ Y0))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3322,f358])).
% 130.39/20.04 thf(f3322,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (v18 @ Y0))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3321])).
% 130.39/20.04 thf(f3321,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v18 @ Y1)))))) @ X3))) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3320])).
% 130.39/20.04 thf(f3320,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v18 @ Y1))))))))) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3319])).
% 130.39/20.04 thf(f3319,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v18 @ Y1)))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3318,f358])).
% 130.39/20.04 thf(f3318,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v18 @ Y1)))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3317])).
% 130.39/20.04 thf(f3317,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v18 @ Y2))))))))) @ X2))) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3316])).
% 130.39/20.04 thf(f3316,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v18 @ Y2)))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3315])).
% 130.39/20.04 thf(f3315,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v18 @ Y2))))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3314,f358])).
% 130.39/20.04 thf(f3314,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK11 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v18 @ Y2))))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3311])).
% 130.39/20.04 thf(f3311,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK11 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v18 @ Y3)))))))))))) @ X1))) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3310])).
% 130.39/20.04 thf(f3310,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK11 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v18 @ Y3))))))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3308])).
% 130.39/20.04 thf(f3308,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK11 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v18 @ Y3))))))))))))) | $false) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(superposition,[status(thm)],[f3305,f1884])).
% 130.39/20.04 thf(f1884,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((v22 @ (sK11 @ X6)) = $false)) )),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f1883])).
% 130.39/20.04 thf(f1883,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((~ (v22 @ (sK11 @ X6))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1882])).
% 130.39/20.04 thf(f1882,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ((~ (v22 @ (sK11 @ X6))) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1881,f358])).
% 130.39/20.04 thf(f1881,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((((~ (v22 @ (sK11 @ X6))) & (mrel @ X6 @ (sK11 @ X6))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1880])).
% 130.39/20.04 thf(f1880,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))) @ (sK11 @ X6)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f1807])).
% 130.39/20.04 thf(f1807,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0)))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1806])).
% 130.39/20.04 thf(f1806,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ($true & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v22 @ Y0)) & (mrel @ X6 @ Y0))))))) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f1800,f1805])).
% 130.39/20.04 thf(f3305,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v18 @ Y3))))))))))))) | (v22 @ X2)) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3304])).
% 130.39/20.04 thf(f3304,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v18 @ Y3))))))))))))) | (v22 @ X2))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3303,f358])).
% 130.39/20.04 thf(f3303,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v18 @ Y3))))))))))))) | (v22 @ X2))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3302])).
% 130.39/20.04 thf(f3302,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v18 @ Y4))))))))))))) | (v22 @ Y0)))) @ X2) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3301])).
% 130.39/20.04 thf(f3301,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v18 @ Y4))))))))))))) | (v22 @ Y0))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3300])).
% 130.39/20.04 thf(f3300,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v18 @ Y4))))))))))))) | (v22 @ Y0)))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3298,f358])).
% 130.39/20.04 thf(f3298,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK4 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v18 @ Y4))))))))))))) | (v22 @ Y0)))))))) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3296])).
% 130.39/20.04 thf(f3296,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK4 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1))))))) @ X1))) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3293])).
% 130.39/20.04 thf(f3293,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1)))))))))) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3292])).
% 130.39/20.04 thf(f3292,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1)))))))) | $false) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3290])).
% 130.39/20.04 thf(f3290,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1)))))))) | (~ $true)) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(superposition,[status(thm)],[f3288,f1637])).
% 130.39/20.04 thf(f1637,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = (v24 @ (sK4 @ X4)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1636])).
% 130.39/20.04 thf(f1636,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ((v24 @ (sK4 @ X4)) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1635,f358])).
% 130.39/20.04 thf(f1635,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ((v24 @ (sK4 @ X4)) & (mrel @ X4 @ (sK4 @ X4))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1634])).
% 130.39/20.04 thf(f1634,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ((^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0))) @ (sK4 @ X4)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f1631])).
% 130.39/20.04 thf(f1631,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f1629])).
% 130.39/20.04 thf(f1629,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1628])).
% 130.39/20.04 thf(f1628,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v24 @ Y0) & (mrel @ X4 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f1625,f1627])).
% 130.39/20.04 thf(f3288,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1)))))))) | (~ (v24 @ X5))))) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3287])).
% 130.39/20.04 thf(f3287,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1)))))))) | (~ (v24 @ X5)))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3286,f358])).
% 130.39/20.04 thf(f3286,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v18 @ Y5))))))))))))) | (v22 @ Y1)))))))) | (~ (v24 @ X5)))))) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3285])).
% 130.39/20.04 thf(f3285,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v18 @ Y6))))))))))))) | (v22 @ Y2)))))))) | (~ (v24 @ Y0))))) @ X5) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3284])).
% 130.39/20.04 thf(f3284,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v18 @ Y6))))))))))))) | (v22 @ Y2)))))))) | (~ (v24 @ Y0)))))))) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3283])).
% 130.39/20.04 thf(f3283,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v18 @ Y6))))))))))))) | (v22 @ Y2)))))))) | (~ (v24 @ Y0))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3282,f358])).
% 130.39/20.04 thf(f3282,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v18 @ Y6))))))))))))) | (v22 @ Y2)))))))) | (~ (v24 @ Y0))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3281])).
% 130.39/20.04 thf(f3281,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v18 @ Y7))))))))))))) | (v22 @ Y3)))))))) | (~ (v24 @ Y1)))))))) @ X4) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3280])).
% 130.39/20.04 thf(f3280,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v18 @ Y7))))))))))))) | (v22 @ Y3)))))))) | (~ (v24 @ Y1))))))))))) ) | ~spl0_31),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3279])).
% 130.39/20.04 thf(f3279,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v18 @ Y7))))))))))))) | (v22 @ Y3)))))))) | (~ (v24 @ Y1)))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3278,f358])).
% 130.39/20.04 thf(f3278,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v18 @ Y7))))))))))))) | (v22 @ Y3)))))))) | (~ (v24 @ Y1)))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3277])).
% 130.39/20.04 thf(f3277,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v18 @ Y8))))))))))))) | (v22 @ Y4)))))))) | (~ (v24 @ Y2))))))))))) @ X3))) ) | ~spl0_31),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3272])).
% 130.39/20.04 thf(f3272,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v18 @ Y8))))))))))))) | (v22 @ Y4)))))))) | (~ (v24 @ Y2)))))))))))) = $true)) ) | ~spl0_31),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3271])).
% 130.39/20.04 thf(f4135,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10)))))))))))))))))))))))))))))))))))) | (~ (v18 @ X11))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4134])).
% 130.39/20.04 thf(f4134,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10)))))))))))))))))))))))))))))))))))) | (~ (v18 @ X11)))))) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4133,f358])).
% 130.39/20.04 thf(f4133,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((mrel @ X10 @ X11) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v6 @ Y11))))) | (~ (v7 @ Y10)))))))))))))))))))))))))))))))))))) | (~ (v18 @ X11)))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4132])).
% 130.39/20.04 thf(f4132,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v6 @ Y12))))) | (~ (v7 @ Y11)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y0))))) @ X11) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4131])).
% 130.39/20.04 thf(f4131,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v6 @ Y12))))) | (~ (v7 @ Y11)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y0)))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4130])).
% 130.39/20.04 thf(f4130,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v6 @ Y12))))) | (~ (v7 @ Y11)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y0))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4129,f358])).
% 130.39/20.04 thf(f4129,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : (($true = ((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v6 @ Y12))))) | (~ (v7 @ Y11)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y0))))))))) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4128])).
% 130.39/20.04 thf(f4128,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v6 @ Y13))))) | (~ (v7 @ Y12)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y1)))))))) @ X10))) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4127])).
% 130.39/20.04 thf(f4127,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v6 @ Y13))))) | (~ (v7 @ Y12)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y1))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4126])).
% 130.39/20.04 thf(f4126,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v6 @ Y13))))) | (~ (v7 @ Y12)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y1)))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4125,f358])).
% 130.39/20.04 thf(f4125,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v6 @ Y13))))) | (~ (v7 @ Y12)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y1)))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4124])).
% 130.39/20.04 thf(f4124,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v6 @ Y14))))) | (~ (v7 @ Y13)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y2))))))))))) @ X9))) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4123])).
% 130.39/20.04 thf(f4123,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v6 @ Y14))))) | (~ (v7 @ Y13)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y2)))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4122])).
% 130.39/20.04 thf(f4122,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v6 @ Y14))))) | (~ (v7 @ Y13)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y2))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4121,f358])).
% 130.39/20.04 thf(f4121,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : (($true = ((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v6 @ Y14))))) | (~ (v7 @ Y13)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y2))))))))))))))) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4120])).
% 130.39/20.04 thf(f4120,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v6 @ Y15))))) | (~ (v7 @ Y14)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y3)))))))))))))) @ X8) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4119])).
% 130.39/20.04 thf(f4119,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v6 @ Y15))))) | (~ (v7 @ Y14)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y3))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4118])).
% 130.39/20.04 thf(f4118,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v6 @ Y15))))) | (~ (v7 @ Y14)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y3)))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4117,f358])).
% 130.39/20.04 thf(f4117,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v6 @ Y15))))) | (~ (v7 @ Y14)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y3)))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4116])).
% 130.39/20.04 thf(f4116,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v6 @ Y16))))) | (~ (v7 @ Y15)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y4))))))))))))))))) @ X7) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4115])).
% 130.39/20.04 thf(f4115,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v6 @ Y16))))) | (~ (v7 @ Y15)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y4)))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4114])).
% 130.39/20.04 thf(f4114,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v6 @ Y16))))) | (~ (v7 @ Y15)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y4))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4113,f358])).
% 130.39/20.04 thf(f4113,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v6 @ Y16))))) | (~ (v7 @ Y15)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y4))))))))))))))))))))) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4112])).
% 130.39/20.04 thf(f4112,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v6 @ Y17))))) | (~ (v7 @ Y16)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y5)))))))))))))))))))) @ X6))) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4111])).
% 130.39/20.04 thf(f4111,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v6 @ Y17))))) | (~ (v7 @ Y16)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y5))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4110])).
% 130.39/20.04 thf(f4110,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v6 @ Y17))))) | (~ (v7 @ Y16)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y5)))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4109,f358])).
% 130.39/20.04 thf(f4109,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v6 @ Y17))))) | (~ (v7 @ Y16)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y5)))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4108])).
% 130.39/20.04 thf(f4108,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v6 @ Y18))))) | (~ (v7 @ Y17)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y6))))))))))))))))))))))) @ X5) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4107])).
% 130.39/20.04 thf(f4107,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v6 @ Y18))))) | (~ (v7 @ Y17)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y6)))))))))))))))))))))))))) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4106])).
% 130.39/20.04 thf(f4106,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v6 @ Y18))))) | (~ (v7 @ Y17)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y6))))))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4105,f358])).
% 130.39/20.04 thf(f4105,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v6 @ Y18))))) | (~ (v7 @ Y17)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y6))))))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4104])).
% 130.39/20.04 thf(f4104,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7)))))))))))))))))))))))))) @ X4) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4093])).
% 130.39/20.04 thf(f4093,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f4092])).
% 130.39/20.04 thf(f4092,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = $false) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4085])).
% 130.39/20.04 thf(f4085,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((~ $true) = $true) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) = $true)) ) | ~spl0_38),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f832,f3929])).
% 130.39/20.04 thf(f3929,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (v26 @ X3))) ) | ~spl0_38),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3928])).
% 130.39/20.04 thf(f3928,definition,(
% 130.39/20.04 spl0_38 <=> ! [X3 : mworld] : ($true = (v26 @ X3))),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_38])],[avatar_definition])).
% 130.39/20.04 thf(f832,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) = $true) | ($true = (~ (v26 @ X3)))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f831])).
% 130.39/20.04 thf(f831,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) | (~ (v26 @ X3))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f830])).
% 130.39/20.04 thf(f830,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) | (~ (v26 @ X3)))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f829,f358])).
% 130.39/20.04 thf(f829,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v6 @ Y19))))) | (~ (v7 @ Y18)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y7))))))))))))))))))))))))))) | (~ (v26 @ X3)))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f828])).
% 130.39/20.04 thf(f828,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v6 @ Y20))))) | (~ (v7 @ Y19)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y8))))))))))))))))))))))))))) | (~ (v26 @ Y0))))) @ X3) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f827])).
% 130.39/20.04 thf(f827,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v6 @ Y20))))) | (~ (v7 @ Y19)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y8))))))))))))))))))))))))))) | (~ (v26 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f826])).
% 130.39/20.04 thf(f826,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v6 @ Y20))))) | (~ (v7 @ Y19)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y8))))))))))))))))))))))))))) | (~ (v26 @ Y0))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f825,f358])).
% 130.39/20.04 thf(f825,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v6 @ Y20))))) | (~ (v7 @ Y19)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y8))))))))))))))))))))))))))) | (~ (v26 @ Y0))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f824])).
% 130.39/20.04 thf(f824,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v6 @ Y21))))) | (~ (v7 @ Y20)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y9))))))))))))))))))))))))))) | (~ (v26 @ Y1)))))))) @ X2) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f805])).
% 130.39/20.04 thf(f805,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v6 @ Y21))))) | (~ (v7 @ Y20)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y9))))))))))))))))))))))))))) | (~ (v26 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f804])).
% 130.39/20.04 thf(f804,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v6 @ Y21))))) | (~ (v7 @ Y20)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y9))))))))))))))))))))))))))) | (~ (v26 @ Y1)))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f803,f358])).
% 130.39/20.04 thf(f803,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v6 @ Y21))))) | (~ (v7 @ Y20)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y9))))))))))))))))))))))))))) | (~ (v26 @ Y1)))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f802])).
% 130.39/20.04 thf(f802,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (~ (v6 @ Y22))))) | (~ (v7 @ Y21)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y10))))))))))))))))))))))))))) | (~ (v26 @ Y2))))))))))) @ X1))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f320])).
% 130.39/20.04 thf(f320,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (~ (v6 @ Y22))))) | (~ (v7 @ Y21)))))))))))))))))))))))))))))))))))) | (~ (v18 @ Y10))))))))))))))))))))))))))) | (~ (v26 @ Y2)))))))))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f283])).
% 130.39/20.04 thf(f283,plain,(
% 130.39/20.04 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v26) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v18) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v7) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v6)))))))))))))))))))))))))))))),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f231,f207,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f208])).
% 130.39/20.04 thf(f231,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v26) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v18) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v7) @ (mbox @ (mnot @ v6)))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f73])).
% 130.39/20.04 thf(f73,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v26) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v18) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v7) @ (mbox @ (mnot @ v6)))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f72])).
% 130.39/20.04 thf(f72,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v26) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v18) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v7) @ (mbox @ (mnot @ v6))))))))))))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f33])).
% 130.39/20.04 thf(f33,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v26) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v18) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v7) @ (mbox @ (mnot @ v6))))))))))))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod24)).
% 130.39/20.04 thf(f2555,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = (v6 @ (sK22 @ X22)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2554])).
% 130.39/20.04 thf(f2554,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = ((v6 @ (sK22 @ X22)) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2542,f358])).
% 130.39/20.04 thf(f2542,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((((v6 @ (sK22 @ X22)) & (mrel @ X22 @ (sK22 @ X22))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2541])).
% 130.39/20.04 thf(f2541,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = ((^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0))) @ (sK22 @ X22)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2540])).
% 130.39/20.04 thf(f2540,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2539])).
% 130.39/20.04 thf(f2539,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & $true) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2536,f2537])).
% 130.39/20.04 thf(f2537,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2536])).
% 130.39/20.04 thf(f2536,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2535])).
% 130.39/20.04 thf(f2535,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v6 @ Y0) & (mrel @ X22 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2527,f2534])).
% 130.39/20.04 thf(f4079,plain,(
% 130.39/20.04 spl0_38 | spl0_39 | ~spl0_36),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f4075,f3399,f4077,f3928])).
% 130.39/20.04 thf(f3399,definition,(
% 130.39/20.04 spl0_36 <=> ! [X2 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v14 @ Y12)))))))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))) | (v26 @ Y0))))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_36])],[avatar_definition])).
% 130.39/20.04 thf(f4075,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = (v26 @ X3)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v14 @ Y10)))))))))))))))))))))) | (~ (v21 @ Y3))))))))))))))))) ) | ~spl0_36),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4074])).
% 130.39/20.04 thf(f4074,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v14 @ Y10)))))))))))))))))))))) | (~ (v21 @ Y3))))))))))))))))) | ($true = (v26 @ X3))) ) | ~spl0_36),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4073,f358])).
% 130.39/20.04 thf(f4073,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = (v26 @ X3)) | (((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v14 @ Y10)))))))))))))))))))))) | (~ (v21 @ Y3)))))))))))))))) = $true)) ) | ~spl0_36),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4070])).
% 130.39/20.04 thf(f4070,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = (v26 @ X3)) | (((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v14 @ Y11)))))))))))))))))))))) | (~ (v21 @ Y4))))))))))))))))) @ X4) = $true)) ) | ~spl0_36),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f4046])).
% 130.39/20.04 thf(f4046,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v14 @ Y11)))))))))))))))))))))) | (~ (v21 @ Y4))))))))))))))))))) | ($true = (v26 @ X3))) ) | ~spl0_36),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f4045])).
% 130.39/20.04 thf(f4045,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v14 @ Y11)))))))))))))))))))))) | (~ (v21 @ Y4)))))))))))))))))) | (v26 @ X3)))) ) | ~spl0_36),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f4044])).
% 130.39/20.04 thf(f4044,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v14 @ Y11)))))))))))))))))))))) | (~ (v21 @ Y4)))))))))))))))))) | (v26 @ X3))) = $true)) ) | ~spl0_36),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f4043,f358])).
% 130.39/20.04 thf(f4043,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((mrel @ X2 @ X3) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v14 @ Y11)))))))))))))))))))))) | (~ (v21 @ Y4)))))))))))))))))) | (v26 @ X3))))) ) | ~spl0_36),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f4042])).
% 130.39/20.04 thf(f4042,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v14 @ Y12)))))))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))) | (v26 @ Y0)))) @ X3) = $true)) ) | ~spl0_36),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3400])).
% 130.39/20.04 thf(f3400,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v14 @ Y12)))))))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))) | (v26 @ Y0))))) = $true)) ) | ~spl0_36),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3399])).
% 130.39/20.04 thf(f4004,plain,(
% 130.39/20.04 ~spl0_37),
% 130.39/20.04 inference(avatar_contradiction_clause,[status(thm)],[f4003])).
% 130.39/20.04 thf(f4003,plain,(
% 130.39/20.04 $false | ~spl0_37),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f4002])).
% 130.39/20.04 thf(f4002,plain,(
% 130.39/20.04 ($true = $false) | ~spl0_37),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2304,f3992])).
% 130.39/20.04 thf(f3992,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((v13 @ X3) = $false)) ) | ~spl0_37),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f3987])).
% 130.39/20.04 thf(f3987,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (((~ (v13 @ X3)) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3986])).
% 130.39/20.04 thf(f3986,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (~ (v13 @ X3))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3985,f358])).
% 130.39/20.04 thf(f3985,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (~ (v13 @ X3))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3984])).
% 130.39/20.04 thf(f3984,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v13 @ Y0)))) @ X3) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3983])).
% 130.39/20.04 thf(f3983,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v13 @ Y0))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3982])).
% 130.39/20.04 thf(f3982,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v13 @ Y0)))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3981,f358])).
% 130.39/20.04 thf(f3981,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (~ (v13 @ Y0)))))))) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3980])).
% 130.39/20.04 thf(f3980,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v13 @ Y1))))))) @ X2) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3979])).
% 130.39/20.04 thf(f3979,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v13 @ Y1)))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3978])).
% 130.39/20.04 thf(f3978,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v13 @ Y1))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3976,f358])).
% 130.39/20.04 thf(f3976,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((mrel @ (sK12 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v13 @ Y1))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3974])).
% 130.39/20.04 thf(f3974,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ (sK12 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2)))))))))) @ X1) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3973])).
% 130.39/20.04 thf(f3973,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3972])).
% 130.39/20.04 thf(f3972,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2))))))))))) | $false))) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3968])).
% 130.39/20.04 thf(f3968,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2))))))))))) | (~ $true)) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(superposition,[status(thm)],[f3966,f2186])).
% 130.39/20.04 thf(f2186,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = (v16 @ (sK12 @ X12)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2185])).
% 130.39/20.04 thf(f2185,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = ((v16 @ (sK12 @ X12)) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2171,f358])).
% 130.39/20.04 thf(f2171,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : ((((v16 @ (sK12 @ X12)) & (mrel @ X12 @ (sK12 @ X12))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2170])).
% 130.39/20.04 thf(f2170,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : ((((^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0))) @ (sK12 @ X12)) = $true)) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2163])).
% 130.39/20.04 thf(f2163,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((v16 @ Y0) & (mrel @ X12 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2154])).
% 130.39/20.04 thf(f3966,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2))))))))))) | (~ (v16 @ X13))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3965])).
% 130.39/20.04 thf(f3965,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2))))))))))) | (~ (v16 @ X13)))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3964,f358])).
% 130.39/20.04 thf(f3964,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : (($true = ((mrel @ X12 @ X13) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v13 @ Y2))))))))))) | (~ (v16 @ X13)))))) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3963])).
% 130.39/20.04 thf(f3963,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v13 @ Y3))))))))))) | (~ (v16 @ Y0))))) @ X13) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3962])).
% 130.39/20.04 thf(f3962,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v13 @ Y3))))))))))) | (~ (v16 @ Y0)))))))) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3961])).
% 130.39/20.04 thf(f3961,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v13 @ Y3))))))))))) | (~ (v16 @ Y0))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3960,f358])).
% 130.39/20.04 thf(f3960,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v13 @ Y3))))))))))) | (~ (v16 @ Y0))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3959])).
% 130.39/20.04 thf(f3959,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v13 @ Y4))))))))))) | (~ (v16 @ Y1)))))))) @ X12))) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3958])).
% 130.39/20.04 thf(f3958,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v13 @ Y4))))))))))) | (~ (v16 @ Y1))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3957])).
% 130.39/20.04 thf(f3957,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v13 @ Y4))))))))))) | (~ (v16 @ Y1)))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3956,f358])).
% 130.39/20.04 thf(f3956,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v13 @ Y4))))))))))) | (~ (v16 @ Y1)))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3955])).
% 130.39/20.04 thf(f3955,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v13 @ Y5))))))))))) | (~ (v16 @ Y2))))))))))) @ X11) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3954])).
% 130.39/20.04 thf(f3954,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v13 @ Y5))))))))))) | (~ (v16 @ Y2)))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3953])).
% 130.39/20.04 thf(f3953,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v13 @ Y5))))))))))) | (~ (v16 @ Y2))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3952,f358])).
% 130.39/20.04 thf(f3952,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v13 @ Y5))))))))))) | (~ (v16 @ Y2))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3951])).
% 130.39/20.04 thf(f3951,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v13 @ Y6))))))))))) | (~ (v16 @ Y3)))))))))))))) @ X10) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3950])).
% 130.39/20.04 thf(f3950,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v13 @ Y6))))))))))) | (~ (v16 @ Y3))))))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3949])).
% 130.39/20.04 thf(f3949,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v13 @ Y6))))))))))) | (~ (v16 @ Y3)))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3948,f358])).
% 130.39/20.04 thf(f3948,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v13 @ Y6))))))))))) | (~ (v16 @ Y3)))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3947])).
% 130.39/20.04 thf(f3947,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v13 @ Y7))))))))))) | (~ (v16 @ Y4))))))))))))))))) @ X9))) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3946])).
% 130.39/20.04 thf(f3946,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v13 @ Y7))))))))))) | (~ (v16 @ Y4)))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3945])).
% 130.39/20.04 thf(f3945,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v13 @ Y7))))))))))) | (~ (v16 @ Y4))))))))))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3944,f358])).
% 130.39/20.04 thf(f3944,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : (($true = ((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v13 @ Y7))))))))))) | (~ (v16 @ Y4))))))))))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3943])).
% 130.39/20.04 thf(f3943,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v13 @ Y8))))))))))) | (~ (v16 @ Y5)))))))))))))))))))) @ X8) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3942])).
% 130.39/20.04 thf(f3942,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v13 @ Y8))))))))))) | (~ (v16 @ Y5))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3941])).
% 130.39/20.04 thf(f3941,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v13 @ Y8))))))))))) | (~ (v16 @ Y5)))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3940,f358])).
% 130.39/20.04 thf(f3940,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v13 @ Y8))))))))))) | (~ (v16 @ Y5)))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3939])).
% 130.39/20.04 thf(f3939,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v13 @ Y9))))))))))) | (~ (v16 @ Y6))))))))))))))))))))))) @ X7))) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3938])).
% 130.39/20.04 thf(f3938,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v13 @ Y9))))))))))) | (~ (v16 @ Y6)))))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3937])).
% 130.39/20.04 thf(f3937,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v13 @ Y9))))))))))) | (~ (v16 @ Y6))))))))))))))))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3936,f358])).
% 130.39/20.04 thf(f3936,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v13 @ Y9))))))))))) | (~ (v16 @ Y6))))))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3935])).
% 130.39/20.04 thf(f3935,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v13 @ Y10))))))))))) | (~ (v16 @ Y7)))))))))))))))))))))))))) @ X6) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3934])).
% 130.39/20.04 thf(f3934,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v13 @ Y10))))))))))) | (~ (v16 @ Y7))))))))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3933])).
% 130.39/20.04 thf(f3933,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v13 @ Y10))))))))))) | (~ (v16 @ Y7)))))))))))))))))))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3932,f358])).
% 130.39/20.04 thf(f3932,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v13 @ Y10))))))))))) | (~ (v16 @ Y7)))))))))))))))))))))))))))))) ) | ~spl0_37),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3931])).
% 130.39/20.04 thf(f3931,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v13 @ Y11))))))))))) | (~ (v16 @ Y8))))))))))))))))))))))))))))) @ X5))) ) | ~spl0_37),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3926])).
% 130.39/20.04 thf(f3926,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v13 @ Y11))))))))))) | (~ (v16 @ Y8)))))))))))))))))))))))))))))) = $true)) ) | ~spl0_37),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3925])).
% 130.39/20.04 thf(f3925,definition,(
% 130.39/20.04 spl0_37 <=> ! [X4 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v13 @ Y11))))))))))) | (~ (v16 @ Y8)))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_37])],[avatar_definition])).
% 130.39/20.04 thf(f2304,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (((v13 @ (sK18 @ X15)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2303])).
% 130.39/20.04 thf(f2303,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (($true = ((v13 @ (sK18 @ X15)) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2302,f358])).
% 130.39/20.04 thf(f2302,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : ((((v13 @ (sK18 @ X15)) & (mrel @ X15 @ (sK18 @ X15))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2301])).
% 130.39/20.04 thf(f2301,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (($true = ((^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0))) @ (sK18 @ X15)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2300])).
% 130.39/20.04 thf(f2300,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (($true = (?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2299])).
% 130.39/20.04 thf(f2299,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & $true) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2296,f2297])).
% 130.39/20.04 thf(f2297,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2296])).
% 130.39/20.04 thf(f2296,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : ((((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2295])).
% 130.39/20.04 thf(f2295,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : ((($true & ((?? @ mworld @ (^[Y0 : mworld]: ((v13 @ Y0) & (mrel @ X15 @ Y0)))) & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v13 @ Y0)) & (mrel @ X15 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f2288,f2294])).
% 130.39/20.04 thf(f3930,plain,(
% 130.39/20.04 spl0_37 | spl0_38 | ~spl0_35),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f3923,f3396,f3928,f3925])).
% 130.39/20.04 thf(f3396,definition,(
% 130.39/20.04 spl0_35 <=> ! [X1 : mworld] : ($true = (v28 @ X1))),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_35])],[avatar_definition])).
% 130.39/20.04 thf(f3923,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v13 @ Y11))))))))))) | (~ (v16 @ Y8)))))))))))))))))))))))))))))) = $true) | ($true = (v26 @ X3))) ) | ~spl0_35),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3922])).
% 130.39/20.04 thf(f3922,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v13 @ Y11))))))))))) | (~ (v16 @ Y8)))))))))))))))))))))))))))))))) | ($true = (v26 @ X3))) ) | ~spl0_35),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3920,f358])).
% 130.39/20.04 thf(f3920,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = (v26 @ X3)) | (((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v13 @ Y11))))))))))) | (~ (v16 @ Y8))))))))))))))))))))))))))))))) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3918])).
% 130.39/20.04 thf(f3918,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = (v26 @ X3)) | (((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v13 @ Y12))))))))))) | (~ (v16 @ Y9)))))))))))))))))))))))))))))))) @ X4) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3470])).
% 130.39/20.04 thf(f3470,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v13 @ Y12))))))))))) | (~ (v16 @ Y9)))))))))))))))))))))))))))))))))) | ($true = (v26 @ X3))) ) | ~spl0_35),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f3469])).
% 130.39/20.04 thf(f3469,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v13 @ Y12))))))))))) | (~ (v16 @ Y9))))))))))))))))))))))))))))))))) | (v26 @ X3)) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3468])).
% 130.39/20.04 thf(f3468,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v13 @ Y12))))))))))) | (~ (v16 @ Y9))))))))))))))))))))))))))))))))) | (v26 @ X3))) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3467,f358])).
% 130.39/20.04 thf(f3467,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v13 @ Y12))))))))))) | (~ (v16 @ Y9))))))))))))))))))))))))))))))))) | (v26 @ X3))) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3466])).
% 130.39/20.04 thf(f3466,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v13 @ Y13))))))))))) | (~ (v16 @ Y10))))))))))))))))))))))))))))))))) | (v26 @ Y0)))) @ X3) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3465])).
% 130.39/20.04 thf(f3465,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v13 @ Y13))))))))))) | (~ (v16 @ Y10))))))))))))))))))))))))))))))))) | (v26 @ Y0))))))) ) | ~spl0_35),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3464])).
% 130.39/20.04 thf(f3464,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v13 @ Y13))))))))))) | (~ (v16 @ Y10))))))))))))))))))))))))))))))))) | (v26 @ Y0)))))) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3463,f358])).
% 130.39/20.04 thf(f3463,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v13 @ Y13))))))))))) | (~ (v16 @ Y10))))))))))))))))))))))))))))))))) | (v26 @ Y0)))))) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3462])).
% 130.39/20.04 thf(f3462,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1))))))) @ X2) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3450])).
% 130.39/20.04 thf(f3450,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1)))))))))) ) | ~spl0_35),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3449])).
% 130.39/20.04 thf(f3449,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1)))))))) | $false) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3405])).
% 130.39/20.04 thf(f3405,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1)))))))) | (~ $true)) = $true)) ) | ~spl0_35),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f398,f3397])).
% 130.39/20.04 thf(f3397,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = (v28 @ X1))) ) | ~spl0_35),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3396])).
% 130.39/20.04 thf(f398,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1)))))))) | (~ (v28 @ X1))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f397])).
% 130.39/20.04 thf(f397,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1)))))))) | (~ (v28 @ X1)))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f396,f358])).
% 130.39/20.04 thf(f396,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v13 @ Y14))))))))))) | (~ (v16 @ Y11))))))))))))))))))))))))))))))))) | (v26 @ Y1)))))))) | (~ (v28 @ X1)))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f395])).
% 130.39/20.04 thf(f395,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v13 @ Y15))))))))))) | (~ (v16 @ Y12))))))))))))))))))))))))))))))))) | (v26 @ Y2)))))))) | (~ (v28 @ Y0))))) @ X1) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f311])).
% 130.39/20.04 thf(f311,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v13 @ Y15))))))))))) | (~ (v16 @ Y12))))))))))))))))))))))))))))))))) | (v26 @ Y2)))))))) | (~ (v28 @ Y0)))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f277])).
% 130.39/20.04 thf(f277,plain,(
% 130.39/20.04 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v28) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v26 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v16) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v13))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f224,f207,f201,f192,f208,f201,f201,f192,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f208])).
% 130.39/20.04 thf(f224,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v16) @ (mbox @ (mbox @ (mbox @ (mnot @ v13))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f114])).
% 130.39/20.04 thf(f114,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v16) @ (mbox @ (mbox @ (mbox @ (mnot @ v13))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f113])).
% 130.39/20.04 thf(f113,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v16) @ (mbox @ (mbox @ (mbox @ (mnot @ v13)))))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f15])).
% 130.39/20.04 thf(f15,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ (mnot @ v28) @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v16) @ (mbox @ (mbox @ (mbox @ (mnot @ v13)))))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod6)).
% 130.39/20.04 thf(f3401,plain,(
% 130.39/20.04 spl0_35 | spl0_36),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f3394,f3399,f3396])).
% 130.39/20.04 thf(f3394,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = (v28 @ X1)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v14 @ Y12)))))))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))) | (v26 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3393])).
% 130.39/20.04 thf(f3393,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v14 @ Y12)))))))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))) | (v26 @ Y0)))))) = $true) | ($true = (v28 @ X1))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3391,f358])).
% 130.39/20.04 thf(f3391,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = (v28 @ X1)) | ($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v14 @ Y12)))))))))))))))))))))) | (~ (v21 @ Y5)))))))))))))))))) | (v26 @ Y0)))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3389])).
% 130.39/20.04 thf(f3389,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v14 @ Y13)))))))))))))))))))))) | (~ (v21 @ Y6)))))))))))))))))) | (v26 @ Y1))))))) @ X2) = $true) | ($true = (v28 @ X1))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f385])).
% 130.39/20.04 thf(f385,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v14 @ Y13)))))))))))))))))))))) | (~ (v21 @ Y6)))))))))))))))))) | (v26 @ Y1)))))))) = $true) | ($true = (v28 @ X1))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f384])).
% 130.39/20.04 thf(f384,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v14 @ Y13)))))))))))))))))))))) | (~ (v21 @ Y6)))))))))))))))))) | (v26 @ Y1)))))))) | (v28 @ X1)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f383])).
% 130.39/20.04 thf(f383,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v14 @ Y13)))))))))))))))))))))) | (~ (v21 @ Y6)))))))))))))))))) | (v26 @ Y1)))))))) | (v28 @ X1))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f382,f358])).
% 130.39/20.04 thf(f382,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v14 @ Y13)))))))))))))))))))))) | (~ (v21 @ Y6)))))))))))))))))) | (v26 @ Y1)))))))) | (v28 @ X1))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f381])).
% 130.39/20.04 thf(f381,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v14 @ Y14)))))))))))))))))))))) | (~ (v21 @ Y7)))))))))))))))))) | (v26 @ Y2)))))))) | (v28 @ Y0)))) @ X1))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f345])).
% 130.39/20.04 thf(f345,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v14 @ Y14)))))))))))))))))))))) | (~ (v21 @ Y7)))))))))))))))))) | (v26 @ Y2)))))))) | (v28 @ Y0))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f252])).
% 130.39/20.04 thf(f252,plain,(
% 130.39/20.04 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v28 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v26 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v21) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v14))))))))))))))))))))),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f191,f207,f201,f192,f201,f201,f192,f201,f201,f201,f201,f201,f192,f208,f201,f201,f201,f201,f201,f201,f201])).
% 130.39/20.04 thf(f191,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v14))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f180])).
% 130.39/20.04 thf(f180,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v14))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f179])).
% 130.39/20.04 thf(f179,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v14)))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f11])).
% 130.39/20.04 thf(f11,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mor @ v28 @ (mbox @ (mbox @ (mor @ v26 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ (mnot @ v21) @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ v14)))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod2)).
% 130.39/20.04 thf(f3142,plain,(
% 130.39/20.04 ~spl0_16 | ~spl0_25),
% 130.39/20.04 inference(avatar_contradiction_clause,[status(thm)],[f3141])).
% 130.39/20.04 thf(f3141,plain,(
% 130.39/20.04 $false | (~spl0_16 | ~spl0_25)),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f3140])).
% 130.39/20.04 thf(f3140,plain,(
% 130.39/20.04 ($true = $false) | (~spl0_16 | ~spl0_25)),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3139])).
% 130.39/20.04 thf(f3139,plain,(
% 130.39/20.04 ((~ $true) = $true) | (~spl0_16 | ~spl0_25)),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3138,f3019])).
% 130.39/20.04 thf(f3019,plain,(
% 130.39/20.04 ( ! [X25 : mworld] : (((v4 @ X25) = $true)) ) | ~spl0_16),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3018])).
% 130.39/20.04 thf(f3018,plain,(
% 130.39/20.04 ( ! [X25 : mworld] : ((($true => (v4 @ X25)) = $true)) ) | ~spl0_16),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3017,f358])).
% 130.39/20.04 thf(f3017,plain,(
% 130.39/20.04 ( ! [X24 : mworld,X25 : mworld] : (($true = ((mrel @ X24 @ X25) => (v4 @ X25)))) ) | ~spl0_16),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3016])).
% 130.39/20.04 thf(f3016,plain,(
% 130.39/20.04 ( ! [X24 : mworld,X25 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (v4 @ Y0))) @ X25) = $true)) ) | ~spl0_16),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2395])).
% 130.39/20.04 thf(f2395,plain,(
% 130.39/20.04 ( ! [X24 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (v4 @ Y0)))) = $true)) ) | ~spl0_16),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f2394])).
% 130.39/20.04 thf(f2394,definition,(
% 130.39/20.04 spl0_16 <=> ! [X24 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (v4 @ Y0)))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 130.39/20.04 thf(f3138,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((~ (v4 @ X1)) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3137])).
% 130.39/20.04 thf(f3137,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => (~ (v4 @ X1))))) ) | ~spl0_25),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3135,f358])).
% 130.39/20.04 thf(f3135,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK27 @ X0) @ X1) => (~ (v4 @ X1))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3133])).
% 130.39/20.04 thf(f3133,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK27 @ X0) @ Y0) => (~ (v4 @ Y0)))) @ X1))) ) | ~spl0_25),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3132])).
% 130.39/20.04 thf(f3132,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK27 @ X0) @ Y0) => (~ (v4 @ Y0))))))) ) | ~spl0_25),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3130])).
% 130.39/20.04 thf(f3130,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK27 @ X0) @ Y0) => (~ (v4 @ Y0))))) | $false))) ) | ~spl0_25),
% 130.39/20.04 inference(superposition,[status(thm)],[f3127,f2702])).
% 130.39/20.04 thf(f3127,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v4 @ Y0))))) | (v5 @ X19)))) ) | ~spl0_25),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3126])).
% 130.39/20.04 thf(f3126,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v4 @ Y0))))) | (v5 @ X19))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3125,f358])).
% 130.39/20.04 thf(f3125,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X19 : mworld] : ((((mrel @ X18 @ X19) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (~ (v4 @ Y0))))) | (v5 @ X19))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3124])).
% 130.39/20.04 thf(f3124,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X19 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))) | (v5 @ Y0)))) @ X19) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3123])).
% 130.39/20.04 thf(f3123,plain,(
% 130.39/20.04 ( ! [X18 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))) | (v5 @ Y0))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3122])).
% 130.39/20.04 thf(f3122,plain,(
% 130.39/20.04 ( ! [X18 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))) | (v5 @ Y0)))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3121,f358])).
% 130.39/20.04 thf(f3121,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X17 : mworld] : (($true = ((mrel @ X17 @ X18) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (v4 @ Y1))))) | (v5 @ Y0)))))))) ) | ~spl0_25),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3120])).
% 130.39/20.04 thf(f3120,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v4 @ Y2))))) | (v5 @ Y1))))))) @ X18) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3119])).
% 130.39/20.04 thf(f3119,plain,(
% 130.39/20.04 ( ! [X17 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v4 @ Y2))))) | (v5 @ Y1)))))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3118])).
% 130.39/20.04 thf(f3118,plain,(
% 130.39/20.04 ( ! [X17 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v4 @ Y2))))) | (v5 @ Y1))))))))))) ) | ~spl0_25),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3117,f358])).
% 130.39/20.04 thf(f3117,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X17 : mworld] : ((((mrel @ X16 @ X17) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (~ (v4 @ Y2))))) | (v5 @ Y1))))))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3116])).
% 130.39/20.04 thf(f3116,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v4 @ Y3))))) | (v5 @ Y2)))))))))) @ X17) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3115])).
% 130.39/20.04 thf(f3115,plain,(
% 130.39/20.04 ( ! [X16 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v4 @ Y3))))) | (v5 @ Y2))))))))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3114])).
% 130.39/20.04 thf(f3114,plain,(
% 130.39/20.04 ( ! [X16 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v4 @ Y3))))) | (v5 @ Y2)))))))))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3113,f358])).
% 130.39/20.04 thf(f3113,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X15 : mworld] : ((((mrel @ X15 @ X16) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (~ (v4 @ Y3))))) | (v5 @ Y2)))))))))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3112])).
% 130.39/20.04 thf(f3112,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v4 @ Y4))))) | (v5 @ Y3))))))))))))) @ X16) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f3110])).
% 130.39/20.04 thf(f3110,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v4 @ Y4))))) | (v5 @ Y3)))))))))))))) = $true)) ) | ~spl0_25),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f3109])).
% 130.39/20.04 thf(f3109,definition,(
% 130.39/20.04 spl0_25 <=> ! [X15 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v4 @ Y4))))) | (v5 @ Y3)))))))))))))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 130.39/20.04 thf(f3111,plain,(
% 130.39/20.04 spl0_6 | spl0_25),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f3107,f3109,f1046])).
% 130.39/20.04 thf(f3107,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : (($true = (v10 @ X14)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v4 @ Y4))))) | (v5 @ Y3)))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f3106])).
% 130.39/20.04 thf(f3106,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v4 @ Y4))))) | (v5 @ Y3))))))))))))))) = $true) | ($true = (v10 @ X14))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f3105,f358])).
% 130.39/20.04 thf(f3105,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : (($true = (v10 @ X14)) | (((mrel @ X14 @ X15) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (~ (v4 @ Y4))))) | (v5 @ Y3))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f3102])).
% 130.39/20.04 thf(f3102,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : (($true = (v10 @ X14)) | (((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v4 @ Y5))))) | (v5 @ Y4)))))))))))))))) @ X15) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2143])).
% 130.39/20.04 thf(f2143,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v4 @ Y5))))) | (v5 @ Y4))))))))))))))))) = $true) | ($true = (v10 @ X14))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f1752])).
% 130.39/20.04 thf(f1752,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v4 @ Y5))))) | (v5 @ Y4))))))))))))))))) | (v10 @ X14)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1751])).
% 130.39/20.04 thf(f1751,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v4 @ Y5))))) | (v5 @ Y4))))))))))))))))) | (v10 @ X14))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1750,f358])).
% 130.39/20.04 thf(f1750,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((mrel @ X13 @ X14) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (~ (v4 @ Y5))))) | (v5 @ Y4))))))))))))))))) | (v10 @ X14))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1749])).
% 130.39/20.04 thf(f1749,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v4 @ Y6))))) | (v5 @ Y5))))))))))))))))) | (v10 @ Y0)))) @ X14))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1748])).
% 130.39/20.04 thf(f1748,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v4 @ Y6))))) | (v5 @ Y5))))))))))))))))) | (v10 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1747])).
% 130.39/20.04 thf(f1747,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v4 @ Y6))))) | (v5 @ Y5))))))))))))))))) | (v10 @ Y0)))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1746,f358])).
% 130.39/20.04 thf(f1746,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((mrel @ X12 @ X13) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (~ (v4 @ Y6))))) | (v5 @ Y5))))))))))))))))) | (v10 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1745])).
% 130.39/20.04 thf(f1745,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v4 @ Y7))))) | (v5 @ Y6))))))))))))))))) | (v10 @ Y1))))))) @ X13) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1744])).
% 130.39/20.04 thf(f1744,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v4 @ Y7))))) | (v5 @ Y6))))))))))))))))) | (v10 @ Y1)))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1743])).
% 130.39/20.04 thf(f1743,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v4 @ Y7))))) | (v5 @ Y6))))))))))))))))) | (v10 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1742,f358])).
% 130.39/20.04 thf(f1742,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((mrel @ X11 @ X12) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (~ (v4 @ Y7))))) | (v5 @ Y6))))))))))))))))) | (v10 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1741])).
% 130.39/20.04 thf(f1741,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v4 @ Y8))))) | (v5 @ Y7))))))))))))))))) | (v10 @ Y2)))))))))) @ X12))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1740])).
% 130.39/20.04 thf(f1740,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v4 @ Y8))))) | (v5 @ Y7))))))))))))))))) | (v10 @ Y2))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1739])).
% 130.39/20.04 thf(f1739,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v4 @ Y8))))) | (v5 @ Y7))))))))))))))))) | (v10 @ Y2)))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1738,f358])).
% 130.39/20.04 thf(f1738,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : (($true = ((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (~ (v4 @ Y8))))) | (v5 @ Y7))))))))))))))))) | (v10 @ Y2)))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1737])).
% 130.39/20.04 thf(f1737,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v4 @ Y9))))) | (v5 @ Y8))))))))))))))))) | (v10 @ Y3))))))))))))) @ X11))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1736])).
% 130.39/20.04 thf(f1736,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v4 @ Y9))))) | (v5 @ Y8))))))))))))))))) | (v10 @ Y3)))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1735])).
% 130.39/20.04 thf(f1735,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v4 @ Y9))))) | (v5 @ Y8))))))))))))))))) | (v10 @ Y3))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1734,f358])).
% 130.39/20.04 thf(f1734,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (~ (v4 @ Y9))))) | (v5 @ Y8))))))))))))))))) | (v10 @ Y3))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1733])).
% 130.39/20.04 thf(f1733,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v4 @ Y10))))) | (v5 @ Y9))))))))))))))))) | (v10 @ Y4)))))))))))))))) @ X10) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1732])).
% 130.39/20.04 thf(f1732,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v4 @ Y10))))) | (v5 @ Y9))))))))))))))))) | (v10 @ Y4))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1731])).
% 130.39/20.04 thf(f1731,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v4 @ Y10))))) | (v5 @ Y9))))))))))))))))) | (v10 @ Y4)))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1730,f358])).
% 130.39/20.04 thf(f1730,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : (($true = ((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (~ (v4 @ Y10))))) | (v5 @ Y9))))))))))))))))) | (v10 @ Y4)))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1729])).
% 130.39/20.04 thf(f1729,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v4 @ Y11))))) | (v5 @ Y10))))))))))))))))) | (v10 @ Y5))))))))))))))))))) @ X9) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1727])).
% 130.39/20.04 thf(f1727,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v4 @ Y11))))) | (v5 @ Y10))))))))))))))))) | (v10 @ Y5)))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1726])).
% 130.39/20.04 thf(f1726,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v4 @ Y11))))) | (v5 @ Y10))))))))))))))))) | (v10 @ Y5))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1725,f358])).
% 130.39/20.04 thf(f1725,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (~ (v4 @ Y11))))) | (v5 @ Y10))))))))))))))))) | (v10 @ Y5))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1724])).
% 130.39/20.04 thf(f1724,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v4 @ Y12))))) | (v5 @ Y11))))))))))))))))) | (v10 @ Y6)))))))))))))))))))))) @ X8) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1719])).
% 130.39/20.04 thf(f1719,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v4 @ Y12))))) | (v5 @ Y11))))))))))))))))) | (v10 @ Y6))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1718])).
% 130.39/20.04 thf(f1718,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v4 @ Y12))))) | (v5 @ Y11))))))))))))))))) | (v10 @ Y6)))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1717,f358])).
% 130.39/20.04 thf(f1717,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : (($true = ((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (~ (v4 @ Y12))))) | (v5 @ Y11))))))))))))))))) | (v10 @ Y6)))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1716])).
% 130.39/20.04 thf(f1716,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v4 @ Y13))))) | (v5 @ Y12))))))))))))))))) | (v10 @ Y7))))))))))))))))))))))))) @ X7) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1711])).
% 130.39/20.04 thf(f1711,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v4 @ Y13))))) | (v5 @ Y12))))))))))))))))) | (v10 @ Y7)))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1710])).
% 130.39/20.04 thf(f1710,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v4 @ Y13))))) | (v5 @ Y12))))))))))))))))) | (v10 @ Y7))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1709,f358])).
% 130.39/20.04 thf(f1709,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (~ (v4 @ Y13))))) | (v5 @ Y12))))))))))))))))) | (v10 @ Y7))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1708])).
% 130.39/20.04 thf(f1708,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v4 @ Y14))))) | (v5 @ Y13))))))))))))))))) | (v10 @ Y8)))))))))))))))))))))))))))) @ X6) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1703])).
% 130.39/20.04 thf(f1703,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v4 @ Y14))))) | (v5 @ Y13))))))))))))))))) | (v10 @ Y8))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1702])).
% 130.39/20.04 thf(f1702,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v4 @ Y14))))) | (v5 @ Y13))))))))))))))))) | (v10 @ Y8)))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1701,f358])).
% 130.39/20.04 thf(f1701,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : ((((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (~ (v4 @ Y14))))) | (v5 @ Y13))))))))))))))))) | (v10 @ Y8)))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1700])).
% 130.39/20.04 thf(f1700,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v4 @ Y15))))) | (v5 @ Y14))))))))))))))))) | (v10 @ Y9))))))))))))))))))))))))))))))) @ X5))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1695])).
% 130.39/20.04 thf(f1695,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v4 @ Y15))))) | (v5 @ Y14))))))))))))))))) | (v10 @ Y9)))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1694])).
% 130.39/20.04 thf(f1694,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v4 @ Y15))))) | (v5 @ Y14))))))))))))))))) | (v10 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1693,f358])).
% 130.39/20.04 thf(f1693,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (~ (v4 @ Y15))))) | (v5 @ Y14))))))))))))))))) | (v10 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1692])).
% 130.39/20.04 thf(f1692,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v4 @ Y16))))) | (v5 @ Y15))))))))))))))))) | (v10 @ Y10)))))))))))))))))))))))))))))))))) @ X4))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1685])).
% 130.39/20.04 thf(f1685,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v4 @ Y16))))) | (v5 @ Y15))))))))))))))))) | (v10 @ Y10))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1684])).
% 130.39/20.04 thf(f1684,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v4 @ Y16))))) | (v5 @ Y15))))))))))))))))) | (v10 @ Y10)))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1683,f358])).
% 130.39/20.04 thf(f1683,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (~ (v4 @ Y16))))) | (v5 @ Y15))))))))))))))))) | (v10 @ Y10)))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1682])).
% 130.39/20.04 thf(f1682,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v4 @ Y17))))) | (v5 @ Y16))))))))))))))))) | (v10 @ Y11))))))))))))))))))))))))))))))))))))) @ X3))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1680])).
% 130.39/20.04 thf(f1680,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v4 @ Y17))))) | (v5 @ Y16))))))))))))))))) | (v10 @ Y11)))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1679])).
% 130.39/20.04 thf(f1679,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v4 @ Y17))))) | (v5 @ Y16))))))))))))))))) | (v10 @ Y11))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1678,f358])).
% 130.39/20.04 thf(f1678,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (~ (v4 @ Y17))))) | (v5 @ Y16))))))))))))))))) | (v10 @ Y11))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1677])).
% 130.39/20.04 thf(f1677,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v4 @ Y18))))) | (v5 @ Y17))))))))))))))))) | (v10 @ Y12)))))))))))))))))))))))))))))))))))))))) @ X2) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1670])).
% 130.39/20.04 thf(f1670,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v4 @ Y18))))) | (v5 @ Y17))))))))))))))))) | (v10 @ Y12))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1669])).
% 130.39/20.04 thf(f1669,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v4 @ Y18))))) | (v5 @ Y17))))))))))))))))) | (v10 @ Y12)))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1667,f358])).
% 130.39/20.04 thf(f1667,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK5 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (~ (v4 @ Y18))))) | (v5 @ Y17))))))))))))))))) | (v10 @ Y12)))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1665])).
% 130.39/20.04 thf(f1665,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK5 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v4 @ Y19))))) | (v5 @ Y18))))))))))))))))) | (v10 @ Y13))))))))))))))))))))))))))))))))))))))))))) @ X1))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1662])).
% 130.39/20.04 thf(f1662,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v4 @ Y19))))) | (v5 @ Y18))))))))))))))))) | (v10 @ Y13)))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1657])).
% 130.39/20.04 thf(f1657,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v4 @ Y19))))) | (v5 @ Y18))))))))))))))))) | (v10 @ Y13)))))))))))))))))))))))))))))))))))))))))))) | $false) = $true)) )),
% 130.39/20.04 inference(superposition,[status(thm)],[f991,f1650])).
% 130.39/20.04 thf(f1650,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($false = (v24 @ (sK5 @ X4)))) )),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f1641])).
% 130.39/20.04 thf(f1641,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((~ (v24 @ (sK5 @ X4))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1640])).
% 130.39/20.04 thf(f1640,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ((~ (v24 @ (sK5 @ X4))) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1639,f358])).
% 130.39/20.04 thf(f1639,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((((~ (v24 @ (sK5 @ X4))) & (mrel @ X4 @ (sK5 @ X4))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1638])).
% 130.39/20.04 thf(f1638,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((((^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0))) @ (sK5 @ X4)) = $true)) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f1633])).
% 130.39/20.04 thf(f1633,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1632])).
% 130.39/20.04 thf(f1632,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : ((($true & (?? @ mworld @ (^[Y0 : mworld]: ((~ (v24 @ Y0)) & (mrel @ X4 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(backward_demodulation,[status(thm)],[f1629,f1631])).
% 130.39/20.04 thf(f991,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v4 @ Y19))))) | (v5 @ Y18))))))))))))))))) | (v10 @ Y13)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ X5)))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f990])).
% 130.39/20.04 thf(f990,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v4 @ Y19))))) | (v5 @ Y18))))))))))))))))) | (v10 @ Y13)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ X5))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f989,f358])).
% 130.39/20.04 thf(f989,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (~ (v4 @ Y19))))) | (v5 @ Y18))))))))))))))))) | (v10 @ Y13)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ X5))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f988])).
% 130.39/20.04 thf(f988,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v4 @ Y20))))) | (v5 @ Y19))))))))))))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y0)))) @ X5))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f987])).
% 130.39/20.04 thf(f987,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v4 @ Y20))))) | (v5 @ Y19))))))))))))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y0))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f986])).
% 130.39/20.04 thf(f986,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v4 @ Y20))))) | (v5 @ Y19))))))))))))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y0)))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f985,f358])).
% 130.39/20.04 thf(f985,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (~ (v4 @ Y20))))) | (v5 @ Y19))))))))))))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f984])).
% 130.39/20.04 thf(f984,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v4 @ Y21))))) | (v5 @ Y20))))))))))))))))) | (v10 @ Y15)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y1))))))) @ X4) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f983])).
% 130.39/20.04 thf(f983,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v4 @ Y21))))) | (v5 @ Y20))))))))))))))))) | (v10 @ Y15)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y1)))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f982])).
% 130.39/20.04 thf(f982,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v4 @ Y21))))) | (v5 @ Y20))))))))))))))))) | (v10 @ Y15)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y1))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f981,f358])).
% 130.39/20.04 thf(f981,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (~ (v4 @ Y21))))) | (v5 @ Y20))))))))))))))))) | (v10 @ Y15)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f980])).
% 130.39/20.04 thf(f980,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (~ (v4 @ Y22))))) | (v5 @ Y21))))))))))))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y2)))))))))) @ X3) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f979])).
% 130.39/20.04 thf(f979,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (~ (v4 @ Y22))))) | (v5 @ Y21))))))))))))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y2))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f978])).
% 130.39/20.04 thf(f978,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (~ (v4 @ Y22))))) | (v5 @ Y21))))))))))))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y2)))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f977,f358])).
% 130.39/20.04 thf(f977,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (~ (v4 @ Y22))))) | (v5 @ Y21))))))))))))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y2)))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f976])).
% 130.39/20.04 thf(f976,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (~ (v4 @ Y23))))) | (v5 @ Y22))))))))))))))))) | (v10 @ Y17)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y3))))))))))))) @ X2) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f975])).
% 130.39/20.04 thf(f975,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (~ (v4 @ Y23))))) | (v5 @ Y22))))))))))))))))) | (v10 @ Y17)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y3)))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f974])).
% 130.39/20.04 thf(f974,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (~ (v4 @ Y23))))) | (v5 @ Y22))))))))))))))))) | (v10 @ Y17)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y3))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f973,f358])).
% 130.39/20.04 thf(f973,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (~ (v4 @ Y23))))) | (v5 @ Y22))))))))))))))))) | (v10 @ Y17)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y3))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f972])).
% 130.39/20.04 thf(f972,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (~ (v4 @ Y24))))) | (v5 @ Y23))))))))))))))))) | (v10 @ Y18)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y4)))))))))))))))) @ X1))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f354])).
% 130.39/20.04 thf(f354,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => ((!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (~ (v4 @ Y24))))) | (v5 @ Y23))))))))))))))))) | (v10 @ Y18)))))))))))))))))))))))))))))))))))))))))))) | (v24 @ Y4))))))))))))))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f271])).
% 130.39/20.04 thf(f271,plain,(
% 130.39/20.04 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v24 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v10 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v5 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ v4)))))))))))))))))))))))))))))))),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f218,f207,f201,f201,f201,f201,f201,f192,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f201,f201,f201,f201,f201,f192,f201,f208])).
% 130.39/20.04 thf(f218,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v24 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v5 @ (mbox @ (mnot @ v4)))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f112])).
% 130.39/20.04 thf(f112,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v24 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v5 @ (mbox @ (mnot @ v4)))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f111])).
% 130.39/20.04 thf(f111,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v24 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v5 @ (mbox @ (mnot @ v4))))))))))))))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f40])).
% 130.39/20.04 thf(f40,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v24 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v5 @ (mbox @ (mnot @ v4))))))))))))))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod31)).
% 130.39/20.04 thf(f2990,plain,(
% 130.39/20.04 spl0_7 | ~spl0_5),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f2628,f1043,f1300])).
% 130.39/20.04 thf(f1300,definition,(
% 130.39/20.04 spl0_7 <=> ! [X22 : mworld] : ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v4 @ Y2))))))) | (v6 @ Y0))))) = $true)),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 130.39/20.04 thf(f1043,definition,(
% 130.39/20.04 spl0_5 <=> ! [X20 : mworld] : ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v4 @ Y4))))))) | (v6 @ Y2)))))))) | (v8 @ Y0))))))),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 130.39/20.04 thf(f2628,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v4 @ Y2))))))) | (v6 @ Y0))))) = $true)) ) | ~spl0_5),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2627])).
% 130.39/20.04 thf(f2627,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v4 @ Y2))))))) | (v6 @ Y0)))))) = $true)) ) | ~spl0_5),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2626,f358])).
% 130.39/20.04 thf(f2626,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ (sK21 @ X0) @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v4 @ Y2))))))) | (v6 @ Y0)))))) = $true)) ) | ~spl0_5),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2623])).
% 130.39/20.04 thf(f2623,plain,(
% 130.39/20.04 ( ! [X0 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ (sK21 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v4 @ Y3))))))) | (v6 @ Y1))))))) @ X1))) ) | ~spl0_5),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2532])).
% 130.39/20.04 thf(f2532,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK21 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v4 @ Y3))))))) | (v6 @ Y1)))))))))) ) | ~spl0_5),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2529])).
% 130.39/20.04 thf(f2529,plain,(
% 130.39/20.04 ( ! [X0 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK21 @ X0) @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v4 @ Y3))))))) | (v6 @ Y1)))))))) | $false))) ) | ~spl0_5),
% 130.39/20.04 inference(superposition,[status(thm)],[f2134,f2519])).
% 130.39/20.04 thf(f2519,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : (($false = (v8 @ (sK21 @ X20)))) )),
% 130.39/20.04 inference(not_proxy_clausification,[status(thm)],[f2514])).
% 130.39/20.04 thf(f2514,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : (($true = (~ (v8 @ (sK21 @ X20))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2513])).
% 130.39/20.04 thf(f2513,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : (($true = ((~ (v8 @ (sK21 @ X20))) & $true))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2512,f358])).
% 130.39/20.04 thf(f2512,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : ((((~ (v8 @ (sK21 @ X20))) & (mrel @ X20 @ (sK21 @ X20))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2511])).
% 130.39/20.04 thf(f2511,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : ((((^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0))) @ (sK21 @ X20)) = $true)) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2483])).
% 130.39/20.04 thf(f2483,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((~ (v8 @ Y0)) & (mrel @ X20 @ Y0)))) = $true)) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2479])).
% 130.39/20.04 thf(f2134,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v4 @ Y3))))))) | (v6 @ Y1)))))))) | (v8 @ X21)) = $true)) ) | ~spl0_5),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2133])).
% 130.39/20.04 thf(f2133,plain,(
% 130.39/20.04 ( ! [X21 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v4 @ Y3))))))) | (v6 @ Y1)))))))) | (v8 @ X21))))) ) | ~spl0_5),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2132,f358])).
% 130.39/20.04 thf(f2132,plain,(
% 130.39/20.04 ( ! [X21 : mworld,X20 : mworld] : ((((mrel @ X20 @ X21) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X21 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v4 @ Y3))))))) | (v6 @ Y1)))))))) | (v8 @ X21))) = $true)) ) | ~spl0_5),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2131])).
% 130.39/20.04 thf(f2131,plain,(
% 130.39/20.04 ( ! [X21 : mworld,X20 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v4 @ Y4))))))) | (v6 @ Y2)))))))) | (v8 @ Y0)))) @ X21) = $true)) ) | ~spl0_5),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1044])).
% 130.39/20.04 thf(f1044,plain,(
% 130.39/20.04 ( ! [X20 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v4 @ Y4))))))) | (v6 @ Y2)))))))) | (v8 @ Y0))))))) ) | ~spl0_5),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f1043])).
% 130.39/20.04 thf(f2927,plain,(
% 130.39/20.04 spl0_13 | spl0_14 | ~spl0_21),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f2926,f2908,f2123,f2120])).
% 130.39/20.04 thf(f2926,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v5 @ Y2)))))))))) = $true) | ((~ (v9 @ X13)) = $true)) ) | ~spl0_21),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2925])).
% 130.39/20.04 thf(f2925,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : (((~ (v9 @ X13)) = $true) | ($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v5 @ Y2))))))))))))) ) | ~spl0_21),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2923,f358])).
% 130.39/20.04 thf(f2923,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((mrel @ X13 @ X14) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v5 @ Y2))))))))))) = $true) | ((~ (v9 @ X13)) = $true)) ) | ~spl0_21),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2921])).
% 130.39/20.04 thf(f2921,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3)))))))))))) @ X14) = $true) | ((~ (v9 @ X13)) = $true)) ) | ~spl0_21),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2914])).
% 130.39/20.04 thf(f2914,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) = $true) | ((~ (v9 @ X13)) = $true)) ) | ~spl0_21),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2909])).
% 130.39/20.04 thf(f2909,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (v5 @ Y3))))))))))))) | (~ (v9 @ X13))) = $true)) ) | ~spl0_21),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f2908])).
% 130.39/20.04 thf(f2551,plain,(
% 130.39/20.04 ~spl0_15),
% 130.39/20.04 inference(avatar_contradiction_clause,[status(thm)],[f2550])).
% 130.39/20.04 thf(f2550,plain,(
% 130.39/20.04 $false | ~spl0_15),
% 130.39/20.04 inference(trivial_inequality_removal,[status(thm)],[f2549])).
% 130.39/20.04 thf(f2549,plain,(
% 130.39/20.04 ($true = $false) | ~spl0_15),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2548])).
% 130.39/20.04 thf(f2548,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = ($false & (mrel @ X22 @ (sK23 @ X22))))) ) | ~spl0_15),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2547])).
% 130.39/20.04 thf(f2547,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((((~ $true) & (mrel @ X22 @ (sK23 @ X22))) = $true)) ) | ~spl0_15),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2546,f2392])).
% 130.39/20.04 thf(f2392,plain,(
% 130.39/20.04 ( ! [X23 : mworld] : (($true = (v6 @ X23))) ) | ~spl0_15),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f2391])).
% 130.39/20.04 thf(f2391,definition,(
% 130.39/20.04 spl0_15 <=> ! [X23 : mworld] : ($true = (v6 @ X23))),
% 130.39/20.04 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 130.39/20.04 thf(f2546,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : ((((~ (v6 @ (sK23 @ X22))) & (mrel @ X22 @ (sK23 @ X22))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2545])).
% 130.39/20.04 thf(f2545,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (($true = ((^[Y0 : mworld]: ((~ (v6 @ Y0)) & (mrel @ X22 @ Y0))) @ (sK23 @ X22)))) )),
% 130.39/20.04 inference(sigma_clausification,[status(thm)],[f2537])).
% 130.39/20.04 thf(f2396,plain,(
% 130.39/20.04 spl0_15 | spl0_16 | ~spl0_7),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f2389,f1300,f2394,f2391])).
% 130.39/20.04 thf(f2389,plain,(
% 130.39/20.04 ( ! [X24 : mworld,X23 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (v4 @ Y0)))) = $true) | ($true = (v6 @ X23))) ) | ~spl0_7),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2388])).
% 130.39/20.04 thf(f2388,plain,(
% 130.39/20.04 ( ! [X24 : mworld,X23 : mworld] : (($true = (v6 @ X23)) | ($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (v4 @ Y0))))))) ) | ~spl0_7),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2387,f358])).
% 130.39/20.04 thf(f2387,plain,(
% 130.39/20.04 ( ! [X24 : mworld,X23 : mworld] : (($true = (v6 @ X23)) | (((mrel @ X23 @ X24) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X24 @ Y0) => (v4 @ Y0))))) = $true)) ) | ~spl0_7),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2384])).
% 130.39/20.04 thf(f2384,plain,(
% 130.39/20.04 ( ! [X24 : mworld,X23 : mworld] : (($true = (v6 @ X23)) | (((^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1)))))) @ X24) = $true)) ) | ~spl0_7),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f2130])).
% 130.39/20.04 thf(f2130,plain,(
% 130.39/20.04 ( ! [X23 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) = $true) | ($true = (v6 @ X23))) ) | ~spl0_7),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f2129])).
% 130.39/20.04 thf(f2129,plain,(
% 130.39/20.04 ( ! [X23 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (v6 @ X23)) = $true)) ) | ~spl0_7),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f2128])).
% 130.39/20.04 thf(f2128,plain,(
% 130.39/20.04 ( ! [X23 : mworld] : ((($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (v6 @ X23))) = $true)) ) | ~spl0_7),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f2127,f358])).
% 130.39/20.04 thf(f2127,plain,(
% 130.39/20.04 ( ! [X22 : mworld,X23 : mworld] : ((((mrel @ X22 @ X23) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X23 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (v4 @ Y1))))))) | (v6 @ X23))) = $true)) ) | ~spl0_7),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f2126])).
% 130.39/20.04 thf(f2126,plain,(
% 130.39/20.04 ( ! [X22 : mworld,X23 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v4 @ Y2))))))) | (v6 @ Y0)))) @ X23))) ) | ~spl0_7),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f1301])).
% 130.39/20.04 thf(f1301,plain,(
% 130.39/20.04 ( ! [X22 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X22 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (v4 @ Y2))))))) | (v6 @ Y0))))) = $true)) ) | ~spl0_7),
% 130.39/20.04 inference(avatar_component_clause,[status(thm)],[f1300])).
% 130.39/20.04 thf(f1048,plain,(
% 130.39/20.04 spl0_5 | spl0_6),
% 130.39/20.04 inference(avatar_split_clause,[status(thm)],[f1041,f1046,f1043])).
% 130.39/20.04 thf(f1041,plain,(
% 130.39/20.04 ( ! [X19 : mworld,X20 : mworld] : (($true = (v10 @ X19)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v4 @ Y4))))))) | (v6 @ Y2)))))))) | (v8 @ Y0))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f1040])).
% 130.39/20.04 thf(f1040,plain,(
% 130.39/20.04 ( ! [X19 : mworld,X20 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v4 @ Y4))))))) | (v6 @ Y2)))))))) | (v8 @ Y0))))))) | ($true = (v10 @ X19))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f1038,f358])).
% 130.39/20.04 thf(f1038,plain,(
% 130.39/20.04 ( ! [X19 : mworld,X20 : mworld] : ((((mrel @ X19 @ X20) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X20 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (v4 @ Y4))))))) | (v6 @ Y2)))))))) | (v8 @ Y0)))))) = $true) | ($true = (v10 @ X19))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f1036])).
% 130.39/20.04 thf(f1036,plain,(
% 130.39/20.04 ( ! [X19 : mworld,X20 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v4 @ Y5))))))) | (v6 @ Y3)))))))) | (v8 @ Y1))))))) @ X20) = $true) | ($true = (v10 @ X19))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f971])).
% 130.39/20.04 thf(f971,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v4 @ Y5))))))) | (v6 @ Y3)))))))) | (v8 @ Y1)))))))) = $true) | ($true = (v10 @ X19))) )),
% 130.39/20.04 inference(binary_proxy_clausification,[status(thm)],[f970])).
% 130.39/20.04 thf(f970,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v4 @ Y5))))))) | (v6 @ Y3)))))))) | (v8 @ Y1)))))))) | (v10 @ X19)) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f969])).
% 130.39/20.04 thf(f969,plain,(
% 130.39/20.04 ( ! [X19 : mworld] : (($true = ($true => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v4 @ Y5))))))) | (v6 @ Y3)))))))) | (v8 @ Y1)))))))) | (v10 @ X19))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f968,f358])).
% 130.39/20.04 thf(f968,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X19 : mworld] : ((((mrel @ X18 @ X19) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X19 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (v4 @ Y5))))))) | (v6 @ Y3)))))))) | (v8 @ Y1)))))))) | (v10 @ X19))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f967])).
% 130.39/20.04 thf(f967,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X19 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v4 @ Y6))))))) | (v6 @ Y4)))))))) | (v8 @ Y2)))))))) | (v10 @ Y0)))) @ X19) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f966])).
% 130.39/20.04 thf(f966,plain,(
% 130.39/20.04 ( ! [X18 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v4 @ Y6))))))) | (v6 @ Y4)))))))) | (v8 @ Y2)))))))) | (v10 @ Y0))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f965])).
% 130.39/20.04 thf(f965,plain,(
% 130.39/20.04 ( ! [X18 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v4 @ Y6))))))) | (v6 @ Y4)))))))) | (v8 @ Y2)))))))) | (v10 @ Y0)))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f964,f358])).
% 130.39/20.04 thf(f964,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X17 : mworld] : (($true = ((mrel @ X17 @ X18) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X18 @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (v4 @ Y6))))))) | (v6 @ Y4)))))))) | (v8 @ Y2)))))))) | (v10 @ Y0)))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f963])).
% 130.39/20.04 thf(f963,plain,(
% 130.39/20.04 ( ! [X18 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v4 @ Y7))))))) | (v6 @ Y5)))))))) | (v8 @ Y3)))))))) | (v10 @ Y1))))))) @ X18) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f962])).
% 130.39/20.04 thf(f962,plain,(
% 130.39/20.04 ( ! [X17 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v4 @ Y7))))))) | (v6 @ Y5)))))))) | (v8 @ Y3)))))))) | (v10 @ Y1)))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f961])).
% 130.39/20.04 thf(f961,plain,(
% 130.39/20.04 ( ! [X17 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v4 @ Y7))))))) | (v6 @ Y5)))))))) | (v8 @ Y3)))))))) | (v10 @ Y1))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f960,f358])).
% 130.39/20.04 thf(f960,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X17 : mworld] : (($true = ((mrel @ X16 @ X17) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X17 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (v4 @ Y7))))))) | (v6 @ Y5)))))))) | (v8 @ Y3)))))))) | (v10 @ Y1))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f959])).
% 130.39/20.04 thf(f959,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X17 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v4 @ Y8))))))) | (v6 @ Y6)))))))) | (v8 @ Y4)))))))) | (v10 @ Y2)))))))))) @ X17) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f958])).
% 130.39/20.04 thf(f958,plain,(
% 130.39/20.04 ( ! [X16 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v4 @ Y8))))))) | (v6 @ Y6)))))))) | (v8 @ Y4)))))))) | (v10 @ Y2))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f957])).
% 130.39/20.04 thf(f957,plain,(
% 130.39/20.04 ( ! [X16 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v4 @ Y8))))))) | (v6 @ Y6)))))))) | (v8 @ Y4)))))))) | (v10 @ Y2)))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f956,f358])).
% 130.39/20.04 thf(f956,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X15 : mworld] : ((((mrel @ X15 @ X16) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X16 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (v4 @ Y8))))))) | (v6 @ Y6)))))))) | (v8 @ Y4)))))))) | (v10 @ Y2)))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f955])).
% 130.39/20.04 thf(f955,plain,(
% 130.39/20.04 ( ! [X16 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v4 @ Y9))))))) | (v6 @ Y7)))))))) | (v8 @ Y5)))))))) | (v10 @ Y3))))))))))))) @ X16) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f954])).
% 130.39/20.04 thf(f954,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v4 @ Y9))))))) | (v6 @ Y7)))))))) | (v8 @ Y5)))))))) | (v10 @ Y3)))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f953])).
% 130.39/20.04 thf(f953,plain,(
% 130.39/20.04 ( ! [X15 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v4 @ Y9))))))) | (v6 @ Y7)))))))) | (v8 @ Y5)))))))) | (v10 @ Y3))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f952,f358])).
% 130.39/20.04 thf(f952,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : (($true = ((mrel @ X14 @ X15) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X15 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (v4 @ Y9))))))) | (v6 @ Y7)))))))) | (v8 @ Y5)))))))) | (v10 @ Y3))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f951])).
% 130.39/20.04 thf(f951,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X15 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v4 @ Y10))))))) | (v6 @ Y8)))))))) | (v8 @ Y6)))))))) | (v10 @ Y4)))))))))))))))) @ X15) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f950])).
% 130.39/20.04 thf(f950,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v4 @ Y10))))))) | (v6 @ Y8)))))))) | (v8 @ Y6)))))))) | (v10 @ Y4))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f949])).
% 130.39/20.04 thf(f949,plain,(
% 130.39/20.04 ( ! [X14 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v4 @ Y10))))))) | (v6 @ Y8)))))))) | (v8 @ Y6)))))))) | (v10 @ Y4)))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f948,f358])).
% 130.39/20.04 thf(f948,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((mrel @ X13 @ X14) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X14 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (v4 @ Y10))))))) | (v6 @ Y8)))))))) | (v8 @ Y6)))))))) | (v10 @ Y4)))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f947])).
% 130.39/20.04 thf(f947,plain,(
% 130.39/20.04 ( ! [X14 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v4 @ Y11))))))) | (v6 @ Y9)))))))) | (v8 @ Y7)))))))) | (v10 @ Y5))))))))))))))))))) @ X14) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f946])).
% 130.39/20.04 thf(f946,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v4 @ Y11))))))) | (v6 @ Y9)))))))) | (v8 @ Y7)))))))) | (v10 @ Y5)))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f945])).
% 130.39/20.04 thf(f945,plain,(
% 130.39/20.04 ( ! [X13 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v4 @ Y11))))))) | (v6 @ Y9)))))))) | (v8 @ Y7)))))))) | (v10 @ Y5))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f944,f358])).
% 130.39/20.04 thf(f944,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((mrel @ X12 @ X13) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X13 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => ((!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (v4 @ Y11))))))) | (v6 @ Y9)))))))) | (v8 @ Y7)))))))) | (v10 @ Y5))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f943])).
% 130.39/20.04 thf(f943,plain,(
% 130.39/20.04 ( ! [X12 : mworld,X13 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v4 @ Y12))))))) | (v6 @ Y10)))))))) | (v8 @ Y8)))))))) | (v10 @ Y6)))))))))))))))))))))) @ X13) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f942])).
% 130.39/20.04 thf(f942,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v4 @ Y12))))))) | (v6 @ Y10)))))))) | (v8 @ Y8)))))))) | (v10 @ Y6))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f941])).
% 130.39/20.04 thf(f941,plain,(
% 130.39/20.04 ( ! [X12 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v4 @ Y12))))))) | (v6 @ Y10)))))))) | (v8 @ Y8)))))))) | (v10 @ Y6)))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f940,f358])).
% 130.39/20.04 thf(f940,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : (($true = ((mrel @ X11 @ X12) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X12 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => ((!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (v4 @ Y12))))))) | (v6 @ Y10)))))))) | (v8 @ Y8)))))))) | (v10 @ Y6)))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f939])).
% 130.39/20.04 thf(f939,plain,(
% 130.39/20.04 ( ! [X11 : mworld,X12 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v4 @ Y13))))))) | (v6 @ Y11)))))))) | (v8 @ Y9)))))))) | (v10 @ Y7))))))))))))))))))))))))) @ X12) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f938])).
% 130.39/20.04 thf(f938,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v4 @ Y13))))))) | (v6 @ Y11)))))))) | (v8 @ Y9)))))))) | (v10 @ Y7)))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f937])).
% 130.39/20.04 thf(f937,plain,(
% 130.39/20.04 ( ! [X11 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v4 @ Y13))))))) | (v6 @ Y11)))))))) | (v8 @ Y9)))))))) | (v10 @ Y7))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f936,f358])).
% 130.39/20.04 thf(f936,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : ((((mrel @ X10 @ X11) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X11 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => ((!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (v4 @ Y13))))))) | (v6 @ Y11)))))))) | (v8 @ Y9)))))))) | (v10 @ Y7))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f935])).
% 130.39/20.04 thf(f935,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X11 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v4 @ Y14))))))) | (v6 @ Y12)))))))) | (v8 @ Y10)))))))) | (v10 @ Y8)))))))))))))))))))))))))))) @ X11))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f934])).
% 130.39/20.04 thf(f934,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v4 @ Y14))))))) | (v6 @ Y12)))))))) | (v8 @ Y10)))))))) | (v10 @ Y8))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f933])).
% 130.39/20.04 thf(f933,plain,(
% 130.39/20.04 ( ! [X10 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v4 @ Y14))))))) | (v6 @ Y12)))))))) | (v8 @ Y10)))))))) | (v10 @ Y8)))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f932,f358])).
% 130.39/20.04 thf(f932,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((mrel @ X9 @ X10) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X10 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => ((!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (v4 @ Y14))))))) | (v6 @ Y12)))))))) | (v8 @ Y10)))))))) | (v10 @ Y8)))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f931])).
% 130.39/20.04 thf(f931,plain,(
% 130.39/20.04 ( ! [X10 : mworld,X9 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v4 @ Y15))))))) | (v6 @ Y13)))))))) | (v8 @ Y11)))))))) | (v10 @ Y9))))))))))))))))))))))))))))))) @ X10) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f930])).
% 130.39/20.04 thf(f930,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v4 @ Y15))))))) | (v6 @ Y13)))))))) | (v8 @ Y11)))))))) | (v10 @ Y9)))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f929])).
% 130.39/20.04 thf(f929,plain,(
% 130.39/20.04 ( ! [X9 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v4 @ Y15))))))) | (v6 @ Y13)))))))) | (v8 @ Y11)))))))) | (v10 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f928,f358])).
% 130.39/20.04 thf(f928,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : ((((mrel @ X8 @ X9) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X9 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => ((!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (v4 @ Y15))))))) | (v6 @ Y13)))))))) | (v8 @ Y11)))))))) | (v10 @ Y9))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f927])).
% 130.39/20.04 thf(f927,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X9 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v4 @ Y16))))))) | (v6 @ Y14)))))))) | (v8 @ Y12)))))))) | (v10 @ Y10)))))))))))))))))))))))))))))))))) @ X9))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f926])).
% 130.39/20.04 thf(f926,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v4 @ Y16))))))) | (v6 @ Y14)))))))) | (v8 @ Y12)))))))) | (v10 @ Y10))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f925])).
% 130.39/20.04 thf(f925,plain,(
% 130.39/20.04 ( ! [X8 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v4 @ Y16))))))) | (v6 @ Y14)))))))) | (v8 @ Y12)))))))) | (v10 @ Y10)))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f924,f358])).
% 130.39/20.04 thf(f924,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : ((((mrel @ X7 @ X8) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X8 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => ((!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (v4 @ Y16))))))) | (v6 @ Y14)))))))) | (v8 @ Y12)))))))) | (v10 @ Y10)))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f923])).
% 130.39/20.04 thf(f923,plain,(
% 130.39/20.04 ( ! [X8 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v4 @ Y17))))))) | (v6 @ Y15)))))))) | (v8 @ Y13)))))))) | (v10 @ Y11))))))))))))))))))))))))))))))))))))) @ X8))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f922])).
% 130.39/20.04 thf(f922,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v4 @ Y17))))))) | (v6 @ Y15)))))))) | (v8 @ Y13)))))))) | (v10 @ Y11)))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f921])).
% 130.39/20.04 thf(f921,plain,(
% 130.39/20.04 ( ! [X7 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v4 @ Y17))))))) | (v6 @ Y15)))))))) | (v8 @ Y13)))))))) | (v10 @ Y11))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f920,f358])).
% 130.39/20.04 thf(f920,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : ((((mrel @ X6 @ X7) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X7 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => ((!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (v4 @ Y17))))))) | (v6 @ Y15)))))))) | (v8 @ Y13)))))))) | (v10 @ Y11))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f919])).
% 130.39/20.04 thf(f919,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X7 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v4 @ Y18))))))) | (v6 @ Y16)))))))) | (v8 @ Y14)))))))) | (v10 @ Y12)))))))))))))))))))))))))))))))))))))))) @ X7))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f918])).
% 130.39/20.04 thf(f918,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v4 @ Y18))))))) | (v6 @ Y16)))))))) | (v8 @ Y14)))))))) | (v10 @ Y12))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f917])).
% 130.39/20.04 thf(f917,plain,(
% 130.39/20.04 ( ! [X6 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v4 @ Y18))))))) | (v6 @ Y16)))))))) | (v8 @ Y14)))))))) | (v10 @ Y12)))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f916,f358])).
% 130.39/20.04 thf(f916,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : (($true = ((mrel @ X5 @ X6) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X6 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => ((!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (v4 @ Y18))))))) | (v6 @ Y16)))))))) | (v8 @ Y14)))))))) | (v10 @ Y12)))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f915])).
% 130.39/20.04 thf(f915,plain,(
% 130.39/20.04 ( ! [X6 : mworld,X5 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v4 @ Y19))))))) | (v6 @ Y17)))))))) | (v8 @ Y15)))))))) | (v10 @ Y13))))))))))))))))))))))))))))))))))))))))))) @ X6) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f914])).
% 130.39/20.04 thf(f914,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v4 @ Y19))))))) | (v6 @ Y17)))))))) | (v8 @ Y15)))))))) | (v10 @ Y13)))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f913])).
% 130.39/20.04 thf(f913,plain,(
% 130.39/20.04 ( ! [X5 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v4 @ Y19))))))) | (v6 @ Y17)))))))) | (v8 @ Y15)))))))) | (v10 @ Y13))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f912,f358])).
% 130.39/20.04 thf(f912,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((mrel @ X4 @ X5) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X5 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => ((!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (v4 @ Y19))))))) | (v6 @ Y17)))))))) | (v8 @ Y15)))))))) | (v10 @ Y13))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f911])).
% 130.39/20.04 thf(f911,plain,(
% 130.39/20.04 ( ! [X4 : mworld,X5 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v4 @ Y20))))))) | (v6 @ Y18)))))))) | (v8 @ Y16)))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))))) @ X5))) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f910])).
% 130.39/20.04 thf(f910,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v4 @ Y20))))))) | (v6 @ Y18)))))))) | (v8 @ Y16)))))))) | (v10 @ Y14))))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f909])).
% 130.39/20.04 thf(f909,plain,(
% 130.39/20.04 ( ! [X4 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v4 @ Y20))))))) | (v6 @ Y18)))))))) | (v8 @ Y16)))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f908,f358])).
% 130.39/20.04 thf(f908,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((mrel @ X3 @ X4) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X4 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => ((!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (v4 @ Y20))))))) | (v6 @ Y18)))))))) | (v8 @ Y16)))))))) | (v10 @ Y14)))))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f907])).
% 130.39/20.04 thf(f907,plain,(
% 130.39/20.04 ( ! [X3 : mworld,X4 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v4 @ Y21))))))) | (v6 @ Y19)))))))) | (v8 @ Y17)))))))) | (v10 @ Y15))))))))))))))))))))))))))))))))))))))))))))))))) @ X4) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f906])).
% 130.39/20.04 thf(f906,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v4 @ Y21))))))) | (v6 @ Y19)))))))) | (v8 @ Y17)))))))) | (v10 @ Y15)))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f905])).
% 130.39/20.04 thf(f905,plain,(
% 130.39/20.04 ( ! [X3 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v4 @ Y21))))))) | (v6 @ Y19)))))))) | (v8 @ Y17)))))))) | (v10 @ Y15))))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f904,f358])).
% 130.39/20.04 thf(f904,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : (($true = ((mrel @ X2 @ X3) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X3 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => ((!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (v4 @ Y21))))))) | (v6 @ Y19)))))))) | (v8 @ Y17)))))))) | (v10 @ Y15))))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f903])).
% 130.39/20.04 thf(f903,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X3 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v4 @ Y22))))))) | (v6 @ Y20)))))))) | (v8 @ Y18)))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))))))))))) @ X3) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f902])).
% 130.39/20.04 thf(f902,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v4 @ Y22))))))) | (v6 @ Y20)))))))) | (v8 @ Y18)))))))) | (v10 @ Y16))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f901])).
% 130.39/20.04 thf(f901,plain,(
% 130.39/20.04 ( ! [X2 : mworld] : ((($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v4 @ Y22))))))) | (v6 @ Y20)))))))) | (v8 @ Y18)))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f900,f358])).
% 130.39/20.04 thf(f900,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : (($true = ((mrel @ X1 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => ((!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (v4 @ Y22))))))) | (v6 @ Y20)))))))) | (v8 @ Y18)))))))) | (v10 @ Y16)))))))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f899])).
% 130.39/20.04 thf(f899,plain,(
% 130.39/20.04 ( ! [X2 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v4 @ Y23))))))) | (v6 @ Y21)))))))) | (v8 @ Y19)))))))) | (v10 @ Y17))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ X2) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f898])).
% 130.39/20.04 thf(f898,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v4 @ Y23))))))) | (v6 @ Y21)))))))) | (v8 @ Y19)))))))) | (v10 @ Y17)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(boolean_simplification,[status(thm)],[f897])).
% 130.39/20.04 thf(f897,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ($true => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v4 @ Y23))))))) | (v6 @ Y21)))))))) | (v8 @ Y19)))))))) | (v10 @ Y17))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(forward_demodulation,[status(thm)],[f896,f358])).
% 130.39/20.04 thf(f896,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => ((!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => (!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => ((!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => (!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => ((!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => (!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (v4 @ Y23))))))) | (v6 @ Y21)))))))) | (v8 @ Y19)))))))) | (v10 @ Y17))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) )),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f895])).
% 130.39/20.04 thf(f895,plain,(
% 130.39/20.04 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (v4 @ Y24))))))) | (v6 @ Y22)))))))) | (v8 @ Y20)))))))) | (v10 @ Y18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ X1) = $true)) )),
% 130.39/20.04 inference(pi_clausification,[status(thm)],[f334])).
% 130.39/20.04 thf(f334,plain,(
% 130.39/20.04 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (!! @ mworld @ (^[Y7 : mworld]: ((mrel @ Y6 @ Y7) => (!! @ mworld @ (^[Y8 : mworld]: ((mrel @ Y7 @ Y8) => (!! @ mworld @ (^[Y9 : mworld]: ((mrel @ Y8 @ Y9) => (!! @ mworld @ (^[Y10 : mworld]: ((mrel @ Y9 @ Y10) => (!! @ mworld @ (^[Y11 : mworld]: ((mrel @ Y10 @ Y11) => (!! @ mworld @ (^[Y12 : mworld]: ((mrel @ Y11 @ Y12) => (!! @ mworld @ (^[Y13 : mworld]: ((mrel @ Y12 @ Y13) => (!! @ mworld @ (^[Y14 : mworld]: ((mrel @ Y13 @ Y14) => (!! @ mworld @ (^[Y15 : mworld]: ((mrel @ Y14 @ Y15) => (!! @ mworld @ (^[Y16 : mworld]: ((mrel @ Y15 @ Y16) => (!! @ mworld @ (^[Y17 : mworld]: ((mrel @ Y16 @ Y17) => (!! @ mworld @ (^[Y18 : mworld]: ((mrel @ Y17 @ Y18) => ((!! @ mworld @ (^[Y19 : mworld]: ((mrel @ Y18 @ Y19) => (!! @ mworld @ (^[Y20 : mworld]: ((mrel @ Y19 @ Y20) => ((!! @ mworld @ (^[Y21 : mworld]: ((mrel @ Y20 @ Y21) => (!! @ mworld @ (^[Y22 : mworld]: ((mrel @ Y21 @ Y22) => ((!! @ mworld @ (^[Y23 : mworld]: ((mrel @ Y22 @ Y23) => (!! @ mworld @ (^[Y24 : mworld]: ((mrel @ Y23 @ Y24) => (v4 @ Y24))))))) | (v6 @ Y22)))))))) | (v8 @ Y20)))))))) | (v10 @ Y18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(beta_eta_normalization,[status(thm)],[f263])).
% 130.39/20.04 thf(f263,plain,(
% 130.39/20.04 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v10 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v8 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ v6 @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ v4))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(definition_unfolding,[status(thm)],[f206,f207,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f201,f192,f201,f201,f192,f201,f201,f192,f201,f201])).
% 130.39/20.04 thf(f206,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mor @ v8 @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ v4))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(cnf_transformation,[status(thm)],[f83])).
% 130.39/20.04 thf(f83,plain,(
% 130.39/20.04 ((mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mor @ v8 @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ v4))))))))))))))))))))))))))))) = $true)),
% 130.39/20.04 inference(fool_elimination,[status(thm)],[f82])).
% 130.39/20.04 thf(f82,plain,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mor @ v8 @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ v4)))))))))))))))))))))))))))))),
% 130.39/20.04 inference(rectify,[status(thm)],[f57])).
% 130.39/20.04 thf(f57,axiom,(
% 130.39/20.04 (mlocal @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mbox @ (mor @ v10 @ (mbox @ (mbox @ (mor @ v8 @ (mbox @ (mbox @ (mor @ v6 @ (mbox @ (mbox @ v4)))))))))))))))))))))))))))))),
% 130.39/20.04 file('/export/starexec/sandbox/tmp/tmp.TVDuk5m6KE/DTF2THF_23992.p',mod48)).
% 130.39/20.04 % SZS output end Proof for DTF2THF_23992
% 130.39/20.04 % (24359)------------------------------
% 130.39/20.04 % (24359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 130.39/20.05 % (24359)Termination reason: Refutation
% 130.39/20.05
% 130.39/20.05 % (24359)Memory used [KB]: 16375
% 130.39/20.05 % (24359)Time elapsed: 5.632 s
% 130.39/20.05 % (24359)Instructions burned: 13422 (million)
% 130.39/20.05 % (24359)------------------------------
% 130.39/20.05 % (24359)------------------------------
% 130.39/20.05 % (24089)Success in time 18.363 s
%------------------------------------------------------------------------------